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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 15 Nov 2011 09:28:47 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/15/t1321367351ger5zjf4125ay1o.htm/, Retrieved Sat, 20 Apr 2024 09:16:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=142927, Retrieved Sat, 20 Apr 2024 09:16:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
- RM D    [Central Tendency] [] [2011-11-15 14:28:47] [885a9dbaf162325773a0a0afdf9f947e] [Current]
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Dataseries X:
31.82
32.23
30.51
30.68
31.32
30.77
30.88
31.92
29.68
28.56
32.85
36.35
35.13
30.05
30.80
32.00
31.78
29.92
31.77
29.93
31.05
32.25
33.34
35.35
33.45
32.48
31.55
32.02
29.49
27.18
28.66
30.05
31.14
29.66
30.05
26.32
25.32
23.06
24.45
24.91
26.65
28.20
30.50
26.90
28.00
26.12
29.80
32.23
31.64
29.66
31.30
33.42
35.65
35.87
34.73
34.40
33.56
34.36
33.45
32.98
32.72
32.75
34.21
36.69
37.50
37.52
37.23
35.72
35.61
39.34
39.31
40.62
40.62
41.80
42.60
43.67
45.47
46.40
45.84
46.59
46.70
48.81
48.92
46.95
44.90
43.63
45.28
46.05
46.51
46.95
46.45
49.82
51.82
52.50
53.25
53.95
54.54
53.23
52.00
51.13
50.16
50.19
51.28
53.34
53.08
51.75
52.20
51.11
51.30
52.61
51.41
51.61
52.35
52.21
52.64
52.50
53.55
52.41
53.80
54.22
53.21
53.50
52.30
52.47
51.32
51.37
52.32
52.24
53.40
52.83
53.08
53.62
54.14
54.62
54.13
52.94
54.43
53.98
54.05
53.45
53.39
53.43
53.03
52.16
51.72
51.42
50.54
50.13
50.63
52.10
52.64
53.47
53.39
54.11
54.70
54.34
53.39
52.47
52.74
53.44
51.61
53.30
53.10
53.26
53.09
53.39
52.56
52.57
53.18
52.00
51.75
50.34
51.96
53.07
53.14
52.60
52.70
53.20
52.23
53.21
54.17
54.33
55.12
56.58
55.91
54.65
55.03
55.56
57.15
58.24
58.77
58.97
57.29
56.04
56.72
56.46
57.10
56.81
56.32
55.81
56.03
56.90
56.59
54.60
55.08
55.48
54.42
54.55
55.17
55.10
53.89
53.02
53.24
52.32
52.57
51.69
50.26
47.94
47.32
48.72
49.84
50.15
50.00
49.34




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=142927&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=142927&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=142927&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean45.66794642857140.678138046026267.3431415567665
Geometric Mean44.3795342591813
Harmonic Mean42.9442709125863
Quadratic Mean46.7772659602321
Winsorized Mean ( 1 / 74 )45.67325892857140.67716012465345867.448240476276
Winsorized Mean ( 2 / 74 )45.67263392857140.67618632768742467.5444504841929
Winsorized Mean ( 3 / 74 )45.66540178571430.67441489701219267.7111404092973
Winsorized Mean ( 4 / 74 )45.67718750.67232454517500967.9391936941853
Winsorized Mean ( 5 / 74 )45.68053571428570.67165960148705168.0114385518337
Winsorized Mean ( 6 / 74 )45.68401785714290.67012011028045268.1728799901612
Winsorized Mean ( 7 / 74 )45.68901785714290.66892015045111668.302648419741
Winsorized Mean ( 8 / 74 )45.69580357142860.66742947847059168.4653660730421
Winsorized Mean ( 9 / 74 )45.72352678571430.66301984116176368.9625316575688
Winsorized Mean ( 10 / 74 )45.73200892857140.66192164383083369.0897621414826
Winsorized Mean ( 11 / 74 )45.74379464285710.65940752728994269.3710531799003
Winsorized Mean ( 12 / 74 )45.74165178571430.65823927379083469.4909185869232
Winsorized Mean ( 13 / 74 )45.77357142857140.65157720155999370.2504190124843
Winsorized Mean ( 14 / 74 )45.78357142857140.65034705819385470.3986753714574
Winsorized Mean ( 15 / 74 )45.77553571428570.64978217805511370.4475088117962
Winsorized Mean ( 16 / 74 )45.76982142857140.6491258411436770.5099358668749
Winsorized Mean ( 17 / 74 )45.75995535714290.64681328892081970.7467767607116
Winsorized Mean ( 18 / 74 )45.76316964285710.64531355897493170.9161755651796
Winsorized Mean ( 19 / 74 )45.73772321428570.6434681561616471.0800103724113
Winsorized Mean ( 20 / 74 )45.74397321428570.64199782401078271.2525362290285
Winsorized Mean ( 21 / 74 )45.74209821428570.64187513569152471.2632343438658
Winsorized Mean ( 22 / 74 )45.74013392857140.64174682808046771.2744215119614
Winsorized Mean ( 23 / 74 )45.78120535714290.63639124251680471.9387733496883
Winsorized Mean ( 24 / 74 )45.74691964285720.63400413112204672.1555545101817
Winsorized Mean ( 25 / 74 )45.76031250.63161325148382772.4498930199721
Winsorized Mean ( 26 / 74 )45.76727678571430.63027713592842472.6145280810436
Winsorized Mean ( 27 / 74 )45.76848214285710.62973977401322472.6784046864031
Winsorized Mean ( 28 / 74 )45.77223214285710.62828306017122772.8528827920058
Winsorized Mean ( 29 / 74 )45.79294642857140.62586981522656173.1668876090384
Winsorized Mean ( 30 / 74 )45.79026785714290.62367911323805773.4195949250345
Winsorized Mean ( 31 / 74 )45.81102678571430.62126726243034873.7380344274141
Winsorized Mean ( 32 / 74 )45.80245535714290.620260262206373.8439299564685
Winsorized Mean ( 33 / 74 )45.83486607142860.61663538136036874.3305808536507
Winsorized Mean ( 34 / 74 )45.83183035714290.61419106182447874.62145447216
Winsorized Mean ( 35 / 74 )45.84433035714290.61161296715799274.9564394786618
Winsorized Mean ( 36 / 74 )45.84111607142860.6111531856313175.0075711772255
Winsorized Mean ( 37 / 74 )45.84607142857140.61037136723050975.1117661966891
Winsorized Mean ( 38 / 74 )45.85964285714290.6084194331766375.3750461547624
Winsorized Mean ( 39 / 74 )45.8631250.60635603830536975.6372858563053
Winsorized Mean ( 40 / 74 )45.85419642857140.60523522236776875.7626039165123
Winsorized Mean ( 41 / 74 )45.88714285714290.60097628324408376.3543323364494
Winsorized Mean ( 42 / 74 )45.87589285714290.60030112061078376.421467963388
Winsorized Mean ( 43 / 74 )45.86245535714290.59887920070430476.5804778379461
Winsorized Mean ( 44 / 74 )45.87227678571430.59219790036427377.4610594828136
Winsorized Mean ( 45 / 74 )45.90642857142860.58649914992256278.2719439192534
Winsorized Mean ( 46 / 74 )45.90232142857140.58527927830858378.4280652498513
Winsorized Mean ( 47 / 74 )45.91700892857140.58280115718906378.78674975533
Winsorized Mean ( 48 / 74 )45.94058035714290.57975542100555679.241312271753
Winsorized Mean ( 49 / 74 )46.01714285714290.57176585327553880.4824957515727
Winsorized Mean ( 50 / 74 )46.03276785714290.56986201021021380.778797379671
Winsorized Mean ( 51 / 74 )46.03276785714290.56878709521917980.9314561530345
Winsorized Mean ( 52 / 74 )46.03044642857140.56865231375852980.9465561202618
Winsorized Mean ( 53 / 74 )46.05647321428570.56607303009874581.3613628726521
Winsorized Mean ( 54 / 74 )46.21316964285710.55065724316905983.9236570773103
Winsorized Mean ( 55 / 74 )46.250.54706237135140584.54246247233
Winsorized Mean ( 56 / 74 )46.24750.54535767198305384.802144309867
Winsorized Mean ( 57 / 74 )46.32129464285710.53660654040657286.322642671781
Winsorized Mean ( 58 / 74 )46.41450892857140.52600375252407288.2398817610095
Winsorized Mean ( 59 / 74 )46.46982142857140.520285745743789.3159611016196
Winsorized Mean ( 60 / 74 )46.53678571428570.51346874282486790.6321686852093
Winsorized Mean ( 61 / 74 )46.54495535714290.51227017470636590.8601703853296
Winsorized Mean ( 62 / 74 )46.55879464285710.51009937542499391.2739691242836
Winsorized Mean ( 63 / 74 )46.60098214285710.50608375553408492.0815608745984
Winsorized Mean ( 64 / 74 )46.73526785714290.49291680025300894.8137045301645
Winsorized Mean ( 65 / 74 )46.8281250.48327359071124596.897752950005
Winsorized Mean ( 66 / 74 )46.97544642857140.467659312031727100.448008240205
Winsorized Mean ( 67 / 74 )47.04424107142860.459416889919424102.399894526471
Winsorized Mean ( 68 / 74 )47.04727678571430.458671927979904102.572828018757
Winsorized Mean ( 69 / 74 )47.59558035714290.40764826568409116.756489267214
Winsorized Mean ( 70 / 74 )47.60495535714290.406793950368495117.024737742584
Winsorized Mean ( 71 / 74 )48.00750.369938238261636129.771661955224
Winsorized Mean ( 72 / 74 )47.99464285714290.369150517606348130.013749319249
Winsorized Mean ( 73 / 74 )48.37593750.334773796192792144.503357342045
Winsorized Mean ( 74 / 74 )48.61379464285710.309983592671754156.826992757436
Trimmed Mean ( 1 / 74 )45.70986486486490.67392958919284567.8258761714423
Trimmed Mean ( 2 / 74 )45.74713636363640.67049819609400868.2285748569297
Trimmed Mean ( 3 / 74 )45.78541284403670.66737516312419968.6052094442658
Trimmed Mean ( 4 / 74 )45.82689814814810.66469411702105268.9443414265945
Trimmed Mean ( 5 / 74 )45.86607476635510.66241576436362569.240614782799
Trimmed Mean ( 6 / 74 )45.90528301886790.66012365900008869.5404298770359
Trimmed Mean ( 7 / 74 )45.9446190476190.65796185537869569.8286970164483
Trimmed Mean ( 8 / 74 )45.98394230769230.65584002770384870.1145711838998
Trimmed Mean ( 9 / 74 )46.02310679611650.65378085827565870.3953109265116
Trimmed Mean ( 10 / 74 )46.05965686274510.65216984484057270.625247743561
Trimmed Mean ( 11 / 74 )46.09599009900990.65055531049156270.8563735559696
Trimmed Mean ( 12 / 74 )46.131850.64909073270531371.0714969041838
Trimmed Mean ( 13 / 74 )46.16863636363640.6476117689060471.2906073983575
Trimmed Mean ( 14 / 74 )46.20336734693880.64667766591937371.4472909486554
Trimmed Mean ( 15 / 74 )46.23798969072160.64574515821485271.60408266714
Trimmed Mean ( 16 / 74 )46.27395833333330.64474048006940471.7714487670328
Trimmed Mean ( 17 / 74 )46.31110526315790.6436640725249471.9491847377631
Trimmed Mean ( 18 / 74 )46.34973404255320.64264565465095172.1233135354004
Trimmed Mean ( 19 / 74 )46.38897849462370.64161624116559172.300193664598
Trimmed Mean ( 20 / 74 )46.43070652173910.64058527564375872.4816949235657
Trimmed Mean ( 21 / 74 )46.4729670329670.63952760834067972.6676478495525
Trimmed Mean ( 22 / 74 )46.51627777777780.6383330684955372.871483671386
Trimmed Mean ( 23 / 74 )46.56067415730340.63699177857058673.0946233902514
Trimmed Mean ( 24 / 74 )46.60380681818180.63588127693632973.2901069877676
Trimmed Mean ( 25 / 74 )46.64977011494250.63476507118392273.4913942695909
Trimmed Mean ( 26 / 74 )46.69610465116280.63365569997245773.6931817281727
Trimmed Mean ( 27 / 74 )46.74317647058820.63247444390782773.9052414225298
Trimmed Mean ( 28 / 74 )46.79130952380950.63115753526987474.1357060782015
Trimmed Mean ( 29 / 74 )46.8404216867470.62975438313449374.3788736389685
Trimmed Mean ( 30 / 74 )46.8897560975610.62832524041707174.6265677094817
Trimmed Mean ( 31 / 74 )46.94043209876540.62683730006864374.8845547219751
Trimmed Mean ( 32 / 74 )46.99143750.62530767802131975.1493051367872
Trimmed Mean ( 33 / 74 )47.04411392405060.62362491886061175.4365524873544
Trimmed Mean ( 34 / 74 )47.09673076923080.62196057420056575.7230164142902
Trimmed Mean ( 35 / 74 )47.15084415584420.62021675426192676.0231706606424
Trimmed Mean ( 36 / 74 )47.20585526315790.61839989782995776.3354836066584
Trimmed Mean ( 37 / 74 )47.26246666666670.6163596594994876.6800129408965
Trimmed Mean ( 38 / 74 )47.32040540540540.61410079882961477.0564140212668
Trimmed Mean ( 39 / 74 )47.37938356164380.6116812534409477.4576354843585
Trimmed Mean ( 40 / 74 )47.43986111111110.6090840594478777.8872150325442
Trimmed Mean ( 41 / 74 )47.50239436619720.60622207446763778.3580743210516
Trimmed Mean ( 42 / 74 )47.56542857142860.60329751941428978.8424070060945
Trimmed Mean ( 43 / 74 )47.63072463768120.60003928639745479.3793435154036
Trimmed Mean ( 44 / 74 )47.69845588235290.59645835519715379.9694655406189
Trimmed Mean ( 45 / 74 )47.76783582089550.59287703608066880.5695496939371
Trimmed Mean ( 46 / 74 )47.83803030303030.58924592616428281.1851693475995
Trimmed Mean ( 47 / 74 )47.91053846153850.58522753003818281.8665151627652
Trimmed Mean ( 48 / 74 )47.9847656250.58088109498957482.6068640189801
Trimmed Mean ( 49 / 74 )48.06047619047620.57621709816499583.4068901175065
Trimmed Mean ( 50 / 74 )48.13580645161290.57159099138422884.2137248087866
Trimmed Mean ( 51 / 74 )48.21303278688520.56651860160387285.1040595143553
Trimmed Mean ( 52 / 74 )48.29283333333330.56087101109176686.1032793250068
Trimmed Mean ( 53 / 74 )48.37542372881360.55450780207773987.240294090635
Trimmed Mean ( 54 / 74 )48.45991379310340.54755712764179288.502023527316
Trimmed Mean ( 55 / 74 )48.54166666666670.54108167806929789.7122719805897
Trimmed Mean ( 56 / 74 )48.6250.53407470893433591.0453147969201
Trimmed Mean ( 57 / 74 )48.71145454545450.5262617283998392.5612711636249
Trimmed Mean ( 58 / 74 )48.79842592592590.51821232576344494.1668569037505
Trimmed Mean ( 59 / 74 )48.88528301886790.51007490610607695.839419727701
Trimmed Mean ( 60 / 74 )48.97346153846150.50137042904206797.6791982567294
Trimmed Mean ( 61 / 74 )48.97346153846150.49213414712126699.5124232385241
Trimmed Mean ( 62 / 74 )49.15510.481682939748175102.048663018247
Trimmed Mean ( 63 / 74 )49.25081632653060.469917775383171104.807306525852
Trimmed Mean ( 64 / 74 )49.34895833333330.456855035723517108.018856036423
Trimmed Mean ( 65 / 74 )49.44627659574470.443411954229955111.513178939018
Trimmed Mean ( 66 / 74 )49.5443478260870.42906425769063115.470694512639
Trimmed Mean ( 67 / 74 )49.64122222222220.414445219112114119.777524104563
Trimmed Mean ( 68 / 74 )49.73988636363640.398470052600166124.82716339425
Trimmed Mean ( 69 / 74 )49.8430232558140.379744246491366131.254189408627
Trimmed Mean ( 70 / 74 )49.9298809523810.365636552817666136.556043337603
Trimmed Mean ( 71 / 74 )50.02060975609760.349073594262602143.295312444825
Trimmed Mean ( 72 / 74 )50.10.335450056649763149.351592008549
Trimmed Mean ( 73 / 74 )50.18397435897440.319257502086974157.189647951649
Trimmed Mean ( 74 / 74 )50.25697368421050.30591381768468164.284745503104
Median51.39
Midrange41.015
Midmean - Weighted Average at Xnp48.4987610619469
Midmean - Weighted Average at X(n+1)p48.625
Midmean - Empirical Distribution Function48.4987610619469
Midmean - Empirical Distribution Function - Averaging48.625
Midmean - Empirical Distribution Function - Interpolation48.625
Midmean - Closest Observation48.4987610619469
Midmean - True Basic - Statistics Graphics Toolkit48.625
Midmean - MS Excel (old versions)48.6659829059829
Number of observations224

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 45.6679464285714 & 0.6781380460262 & 67.3431415567665 \tabularnewline
Geometric Mean & 44.3795342591813 &  &  \tabularnewline
Harmonic Mean & 42.9442709125863 &  &  \tabularnewline
Quadratic Mean & 46.7772659602321 &  &  \tabularnewline
Winsorized Mean ( 1 / 74 ) & 45.6732589285714 & 0.677160124653458 & 67.448240476276 \tabularnewline
Winsorized Mean ( 2 / 74 ) & 45.6726339285714 & 0.676186327687424 & 67.5444504841929 \tabularnewline
Winsorized Mean ( 3 / 74 ) & 45.6654017857143 & 0.674414897012192 & 67.7111404092973 \tabularnewline
Winsorized Mean ( 4 / 74 ) & 45.6771875 & 0.672324545175009 & 67.9391936941853 \tabularnewline
Winsorized Mean ( 5 / 74 ) & 45.6805357142857 & 0.671659601487051 & 68.0114385518337 \tabularnewline
Winsorized Mean ( 6 / 74 ) & 45.6840178571429 & 0.670120110280452 & 68.1728799901612 \tabularnewline
Winsorized Mean ( 7 / 74 ) & 45.6890178571429 & 0.668920150451116 & 68.302648419741 \tabularnewline
Winsorized Mean ( 8 / 74 ) & 45.6958035714286 & 0.667429478470591 & 68.4653660730421 \tabularnewline
Winsorized Mean ( 9 / 74 ) & 45.7235267857143 & 0.663019841161763 & 68.9625316575688 \tabularnewline
Winsorized Mean ( 10 / 74 ) & 45.7320089285714 & 0.661921643830833 & 69.0897621414826 \tabularnewline
Winsorized Mean ( 11 / 74 ) & 45.7437946428571 & 0.659407527289942 & 69.3710531799003 \tabularnewline
Winsorized Mean ( 12 / 74 ) & 45.7416517857143 & 0.658239273790834 & 69.4909185869232 \tabularnewline
Winsorized Mean ( 13 / 74 ) & 45.7735714285714 & 0.651577201559993 & 70.2504190124843 \tabularnewline
Winsorized Mean ( 14 / 74 ) & 45.7835714285714 & 0.650347058193854 & 70.3986753714574 \tabularnewline
Winsorized Mean ( 15 / 74 ) & 45.7755357142857 & 0.649782178055113 & 70.4475088117962 \tabularnewline
Winsorized Mean ( 16 / 74 ) & 45.7698214285714 & 0.64912584114367 & 70.5099358668749 \tabularnewline
Winsorized Mean ( 17 / 74 ) & 45.7599553571429 & 0.646813288920819 & 70.7467767607116 \tabularnewline
Winsorized Mean ( 18 / 74 ) & 45.7631696428571 & 0.645313558974931 & 70.9161755651796 \tabularnewline
Winsorized Mean ( 19 / 74 ) & 45.7377232142857 & 0.64346815616164 & 71.0800103724113 \tabularnewline
Winsorized Mean ( 20 / 74 ) & 45.7439732142857 & 0.641997824010782 & 71.2525362290285 \tabularnewline
Winsorized Mean ( 21 / 74 ) & 45.7420982142857 & 0.641875135691524 & 71.2632343438658 \tabularnewline
Winsorized Mean ( 22 / 74 ) & 45.7401339285714 & 0.641746828080467 & 71.2744215119614 \tabularnewline
Winsorized Mean ( 23 / 74 ) & 45.7812053571429 & 0.636391242516804 & 71.9387733496883 \tabularnewline
Winsorized Mean ( 24 / 74 ) & 45.7469196428572 & 0.634004131122046 & 72.1555545101817 \tabularnewline
Winsorized Mean ( 25 / 74 ) & 45.7603125 & 0.631613251483827 & 72.4498930199721 \tabularnewline
Winsorized Mean ( 26 / 74 ) & 45.7672767857143 & 0.630277135928424 & 72.6145280810436 \tabularnewline
Winsorized Mean ( 27 / 74 ) & 45.7684821428571 & 0.629739774013224 & 72.6784046864031 \tabularnewline
Winsorized Mean ( 28 / 74 ) & 45.7722321428571 & 0.628283060171227 & 72.8528827920058 \tabularnewline
Winsorized Mean ( 29 / 74 ) & 45.7929464285714 & 0.625869815226561 & 73.1668876090384 \tabularnewline
Winsorized Mean ( 30 / 74 ) & 45.7902678571429 & 0.623679113238057 & 73.4195949250345 \tabularnewline
Winsorized Mean ( 31 / 74 ) & 45.8110267857143 & 0.621267262430348 & 73.7380344274141 \tabularnewline
Winsorized Mean ( 32 / 74 ) & 45.8024553571429 & 0.6202602622063 & 73.8439299564685 \tabularnewline
Winsorized Mean ( 33 / 74 ) & 45.8348660714286 & 0.616635381360368 & 74.3305808536507 \tabularnewline
Winsorized Mean ( 34 / 74 ) & 45.8318303571429 & 0.614191061824478 & 74.62145447216 \tabularnewline
Winsorized Mean ( 35 / 74 ) & 45.8443303571429 & 0.611612967157992 & 74.9564394786618 \tabularnewline
Winsorized Mean ( 36 / 74 ) & 45.8411160714286 & 0.61115318563131 & 75.0075711772255 \tabularnewline
Winsorized Mean ( 37 / 74 ) & 45.8460714285714 & 0.610371367230509 & 75.1117661966891 \tabularnewline
Winsorized Mean ( 38 / 74 ) & 45.8596428571429 & 0.60841943317663 & 75.3750461547624 \tabularnewline
Winsorized Mean ( 39 / 74 ) & 45.863125 & 0.606356038305369 & 75.6372858563053 \tabularnewline
Winsorized Mean ( 40 / 74 ) & 45.8541964285714 & 0.605235222367768 & 75.7626039165123 \tabularnewline
Winsorized Mean ( 41 / 74 ) & 45.8871428571429 & 0.600976283244083 & 76.3543323364494 \tabularnewline
Winsorized Mean ( 42 / 74 ) & 45.8758928571429 & 0.600301120610783 & 76.421467963388 \tabularnewline
Winsorized Mean ( 43 / 74 ) & 45.8624553571429 & 0.598879200704304 & 76.5804778379461 \tabularnewline
Winsorized Mean ( 44 / 74 ) & 45.8722767857143 & 0.592197900364273 & 77.4610594828136 \tabularnewline
Winsorized Mean ( 45 / 74 ) & 45.9064285714286 & 0.586499149922562 & 78.2719439192534 \tabularnewline
Winsorized Mean ( 46 / 74 ) & 45.9023214285714 & 0.585279278308583 & 78.4280652498513 \tabularnewline
Winsorized Mean ( 47 / 74 ) & 45.9170089285714 & 0.582801157189063 & 78.78674975533 \tabularnewline
Winsorized Mean ( 48 / 74 ) & 45.9405803571429 & 0.579755421005556 & 79.241312271753 \tabularnewline
Winsorized Mean ( 49 / 74 ) & 46.0171428571429 & 0.571765853275538 & 80.4824957515727 \tabularnewline
Winsorized Mean ( 50 / 74 ) & 46.0327678571429 & 0.569862010210213 & 80.778797379671 \tabularnewline
Winsorized Mean ( 51 / 74 ) & 46.0327678571429 & 0.568787095219179 & 80.9314561530345 \tabularnewline
Winsorized Mean ( 52 / 74 ) & 46.0304464285714 & 0.568652313758529 & 80.9465561202618 \tabularnewline
Winsorized Mean ( 53 / 74 ) & 46.0564732142857 & 0.566073030098745 & 81.3613628726521 \tabularnewline
Winsorized Mean ( 54 / 74 ) & 46.2131696428571 & 0.550657243169059 & 83.9236570773103 \tabularnewline
Winsorized Mean ( 55 / 74 ) & 46.25 & 0.547062371351405 & 84.54246247233 \tabularnewline
Winsorized Mean ( 56 / 74 ) & 46.2475 & 0.545357671983053 & 84.802144309867 \tabularnewline
Winsorized Mean ( 57 / 74 ) & 46.3212946428571 & 0.536606540406572 & 86.322642671781 \tabularnewline
Winsorized Mean ( 58 / 74 ) & 46.4145089285714 & 0.526003752524072 & 88.2398817610095 \tabularnewline
Winsorized Mean ( 59 / 74 ) & 46.4698214285714 & 0.5202857457437 & 89.3159611016196 \tabularnewline
Winsorized Mean ( 60 / 74 ) & 46.5367857142857 & 0.513468742824867 & 90.6321686852093 \tabularnewline
Winsorized Mean ( 61 / 74 ) & 46.5449553571429 & 0.512270174706365 & 90.8601703853296 \tabularnewline
Winsorized Mean ( 62 / 74 ) & 46.5587946428571 & 0.510099375424993 & 91.2739691242836 \tabularnewline
Winsorized Mean ( 63 / 74 ) & 46.6009821428571 & 0.506083755534084 & 92.0815608745984 \tabularnewline
Winsorized Mean ( 64 / 74 ) & 46.7352678571429 & 0.492916800253008 & 94.8137045301645 \tabularnewline
Winsorized Mean ( 65 / 74 ) & 46.828125 & 0.483273590711245 & 96.897752950005 \tabularnewline
Winsorized Mean ( 66 / 74 ) & 46.9754464285714 & 0.467659312031727 & 100.448008240205 \tabularnewline
Winsorized Mean ( 67 / 74 ) & 47.0442410714286 & 0.459416889919424 & 102.399894526471 \tabularnewline
Winsorized Mean ( 68 / 74 ) & 47.0472767857143 & 0.458671927979904 & 102.572828018757 \tabularnewline
Winsorized Mean ( 69 / 74 ) & 47.5955803571429 & 0.40764826568409 & 116.756489267214 \tabularnewline
Winsorized Mean ( 70 / 74 ) & 47.6049553571429 & 0.406793950368495 & 117.024737742584 \tabularnewline
Winsorized Mean ( 71 / 74 ) & 48.0075 & 0.369938238261636 & 129.771661955224 \tabularnewline
Winsorized Mean ( 72 / 74 ) & 47.9946428571429 & 0.369150517606348 & 130.013749319249 \tabularnewline
Winsorized Mean ( 73 / 74 ) & 48.3759375 & 0.334773796192792 & 144.503357342045 \tabularnewline
Winsorized Mean ( 74 / 74 ) & 48.6137946428571 & 0.309983592671754 & 156.826992757436 \tabularnewline
Trimmed Mean ( 1 / 74 ) & 45.7098648648649 & 0.673929589192845 & 67.8258761714423 \tabularnewline
Trimmed Mean ( 2 / 74 ) & 45.7471363636364 & 0.670498196094008 & 68.2285748569297 \tabularnewline
Trimmed Mean ( 3 / 74 ) & 45.7854128440367 & 0.667375163124199 & 68.6052094442658 \tabularnewline
Trimmed Mean ( 4 / 74 ) & 45.8268981481481 & 0.664694117021052 & 68.9443414265945 \tabularnewline
Trimmed Mean ( 5 / 74 ) & 45.8660747663551 & 0.662415764363625 & 69.240614782799 \tabularnewline
Trimmed Mean ( 6 / 74 ) & 45.9052830188679 & 0.660123659000088 & 69.5404298770359 \tabularnewline
Trimmed Mean ( 7 / 74 ) & 45.944619047619 & 0.657961855378695 & 69.8286970164483 \tabularnewline
Trimmed Mean ( 8 / 74 ) & 45.9839423076923 & 0.655840027703848 & 70.1145711838998 \tabularnewline
Trimmed Mean ( 9 / 74 ) & 46.0231067961165 & 0.653780858275658 & 70.3953109265116 \tabularnewline
Trimmed Mean ( 10 / 74 ) & 46.0596568627451 & 0.652169844840572 & 70.625247743561 \tabularnewline
Trimmed Mean ( 11 / 74 ) & 46.0959900990099 & 0.650555310491562 & 70.8563735559696 \tabularnewline
Trimmed Mean ( 12 / 74 ) & 46.13185 & 0.649090732705313 & 71.0714969041838 \tabularnewline
Trimmed Mean ( 13 / 74 ) & 46.1686363636364 & 0.64761176890604 & 71.2906073983575 \tabularnewline
Trimmed Mean ( 14 / 74 ) & 46.2033673469388 & 0.646677665919373 & 71.4472909486554 \tabularnewline
Trimmed Mean ( 15 / 74 ) & 46.2379896907216 & 0.645745158214852 & 71.60408266714 \tabularnewline
Trimmed Mean ( 16 / 74 ) & 46.2739583333333 & 0.644740480069404 & 71.7714487670328 \tabularnewline
Trimmed Mean ( 17 / 74 ) & 46.3111052631579 & 0.64366407252494 & 71.9491847377631 \tabularnewline
Trimmed Mean ( 18 / 74 ) & 46.3497340425532 & 0.642645654650951 & 72.1233135354004 \tabularnewline
Trimmed Mean ( 19 / 74 ) & 46.3889784946237 & 0.641616241165591 & 72.300193664598 \tabularnewline
Trimmed Mean ( 20 / 74 ) & 46.4307065217391 & 0.640585275643758 & 72.4816949235657 \tabularnewline
Trimmed Mean ( 21 / 74 ) & 46.472967032967 & 0.639527608340679 & 72.6676478495525 \tabularnewline
Trimmed Mean ( 22 / 74 ) & 46.5162777777778 & 0.63833306849553 & 72.871483671386 \tabularnewline
Trimmed Mean ( 23 / 74 ) & 46.5606741573034 & 0.636991778570586 & 73.0946233902514 \tabularnewline
Trimmed Mean ( 24 / 74 ) & 46.6038068181818 & 0.635881276936329 & 73.2901069877676 \tabularnewline
Trimmed Mean ( 25 / 74 ) & 46.6497701149425 & 0.634765071183922 & 73.4913942695909 \tabularnewline
Trimmed Mean ( 26 / 74 ) & 46.6961046511628 & 0.633655699972457 & 73.6931817281727 \tabularnewline
Trimmed Mean ( 27 / 74 ) & 46.7431764705882 & 0.632474443907827 & 73.9052414225298 \tabularnewline
Trimmed Mean ( 28 / 74 ) & 46.7913095238095 & 0.631157535269874 & 74.1357060782015 \tabularnewline
Trimmed Mean ( 29 / 74 ) & 46.840421686747 & 0.629754383134493 & 74.3788736389685 \tabularnewline
Trimmed Mean ( 30 / 74 ) & 46.889756097561 & 0.628325240417071 & 74.6265677094817 \tabularnewline
Trimmed Mean ( 31 / 74 ) & 46.9404320987654 & 0.626837300068643 & 74.8845547219751 \tabularnewline
Trimmed Mean ( 32 / 74 ) & 46.9914375 & 0.625307678021319 & 75.1493051367872 \tabularnewline
Trimmed Mean ( 33 / 74 ) & 47.0441139240506 & 0.623624918860611 & 75.4365524873544 \tabularnewline
Trimmed Mean ( 34 / 74 ) & 47.0967307692308 & 0.621960574200565 & 75.7230164142902 \tabularnewline
Trimmed Mean ( 35 / 74 ) & 47.1508441558442 & 0.620216754261926 & 76.0231706606424 \tabularnewline
Trimmed Mean ( 36 / 74 ) & 47.2058552631579 & 0.618399897829957 & 76.3354836066584 \tabularnewline
Trimmed Mean ( 37 / 74 ) & 47.2624666666667 & 0.61635965949948 & 76.6800129408965 \tabularnewline
Trimmed Mean ( 38 / 74 ) & 47.3204054054054 & 0.614100798829614 & 77.0564140212668 \tabularnewline
Trimmed Mean ( 39 / 74 ) & 47.3793835616438 & 0.61168125344094 & 77.4576354843585 \tabularnewline
Trimmed Mean ( 40 / 74 ) & 47.4398611111111 & 0.60908405944787 & 77.8872150325442 \tabularnewline
Trimmed Mean ( 41 / 74 ) & 47.5023943661972 & 0.606222074467637 & 78.3580743210516 \tabularnewline
Trimmed Mean ( 42 / 74 ) & 47.5654285714286 & 0.603297519414289 & 78.8424070060945 \tabularnewline
Trimmed Mean ( 43 / 74 ) & 47.6307246376812 & 0.600039286397454 & 79.3793435154036 \tabularnewline
Trimmed Mean ( 44 / 74 ) & 47.6984558823529 & 0.596458355197153 & 79.9694655406189 \tabularnewline
Trimmed Mean ( 45 / 74 ) & 47.7678358208955 & 0.592877036080668 & 80.5695496939371 \tabularnewline
Trimmed Mean ( 46 / 74 ) & 47.8380303030303 & 0.589245926164282 & 81.1851693475995 \tabularnewline
Trimmed Mean ( 47 / 74 ) & 47.9105384615385 & 0.585227530038182 & 81.8665151627652 \tabularnewline
Trimmed Mean ( 48 / 74 ) & 47.984765625 & 0.580881094989574 & 82.6068640189801 \tabularnewline
Trimmed Mean ( 49 / 74 ) & 48.0604761904762 & 0.576217098164995 & 83.4068901175065 \tabularnewline
Trimmed Mean ( 50 / 74 ) & 48.1358064516129 & 0.571590991384228 & 84.2137248087866 \tabularnewline
Trimmed Mean ( 51 / 74 ) & 48.2130327868852 & 0.566518601603872 & 85.1040595143553 \tabularnewline
Trimmed Mean ( 52 / 74 ) & 48.2928333333333 & 0.560871011091766 & 86.1032793250068 \tabularnewline
Trimmed Mean ( 53 / 74 ) & 48.3754237288136 & 0.554507802077739 & 87.240294090635 \tabularnewline
Trimmed Mean ( 54 / 74 ) & 48.4599137931034 & 0.547557127641792 & 88.502023527316 \tabularnewline
Trimmed Mean ( 55 / 74 ) & 48.5416666666667 & 0.541081678069297 & 89.7122719805897 \tabularnewline
Trimmed Mean ( 56 / 74 ) & 48.625 & 0.534074708934335 & 91.0453147969201 \tabularnewline
Trimmed Mean ( 57 / 74 ) & 48.7114545454545 & 0.52626172839983 & 92.5612711636249 \tabularnewline
Trimmed Mean ( 58 / 74 ) & 48.7984259259259 & 0.518212325763444 & 94.1668569037505 \tabularnewline
Trimmed Mean ( 59 / 74 ) & 48.8852830188679 & 0.510074906106076 & 95.839419727701 \tabularnewline
Trimmed Mean ( 60 / 74 ) & 48.9734615384615 & 0.501370429042067 & 97.6791982567294 \tabularnewline
Trimmed Mean ( 61 / 74 ) & 48.9734615384615 & 0.492134147121266 & 99.5124232385241 \tabularnewline
Trimmed Mean ( 62 / 74 ) & 49.1551 & 0.481682939748175 & 102.048663018247 \tabularnewline
Trimmed Mean ( 63 / 74 ) & 49.2508163265306 & 0.469917775383171 & 104.807306525852 \tabularnewline
Trimmed Mean ( 64 / 74 ) & 49.3489583333333 & 0.456855035723517 & 108.018856036423 \tabularnewline
Trimmed Mean ( 65 / 74 ) & 49.4462765957447 & 0.443411954229955 & 111.513178939018 \tabularnewline
Trimmed Mean ( 66 / 74 ) & 49.544347826087 & 0.42906425769063 & 115.470694512639 \tabularnewline
Trimmed Mean ( 67 / 74 ) & 49.6412222222222 & 0.414445219112114 & 119.777524104563 \tabularnewline
Trimmed Mean ( 68 / 74 ) & 49.7398863636364 & 0.398470052600166 & 124.82716339425 \tabularnewline
Trimmed Mean ( 69 / 74 ) & 49.843023255814 & 0.379744246491366 & 131.254189408627 \tabularnewline
Trimmed Mean ( 70 / 74 ) & 49.929880952381 & 0.365636552817666 & 136.556043337603 \tabularnewline
Trimmed Mean ( 71 / 74 ) & 50.0206097560976 & 0.349073594262602 & 143.295312444825 \tabularnewline
Trimmed Mean ( 72 / 74 ) & 50.1 & 0.335450056649763 & 149.351592008549 \tabularnewline
Trimmed Mean ( 73 / 74 ) & 50.1839743589744 & 0.319257502086974 & 157.189647951649 \tabularnewline
Trimmed Mean ( 74 / 74 ) & 50.2569736842105 & 0.30591381768468 & 164.284745503104 \tabularnewline
Median & 51.39 &  &  \tabularnewline
Midrange & 41.015 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 48.4987610619469 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 48.625 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 48.4987610619469 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 48.625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 48.625 &  &  \tabularnewline
Midmean - Closest Observation & 48.4987610619469 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 48.625 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 48.6659829059829 &  &  \tabularnewline
Number of observations & 224 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=142927&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]45.6679464285714[/C][C]0.6781380460262[/C][C]67.3431415567665[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]44.3795342591813[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]42.9442709125863[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]46.7772659602321[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 74 )[/C][C]45.6732589285714[/C][C]0.677160124653458[/C][C]67.448240476276[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 74 )[/C][C]45.6726339285714[/C][C]0.676186327687424[/C][C]67.5444504841929[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 74 )[/C][C]45.6654017857143[/C][C]0.674414897012192[/C][C]67.7111404092973[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 74 )[/C][C]45.6771875[/C][C]0.672324545175009[/C][C]67.9391936941853[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 74 )[/C][C]45.6805357142857[/C][C]0.671659601487051[/C][C]68.0114385518337[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 74 )[/C][C]45.6840178571429[/C][C]0.670120110280452[/C][C]68.1728799901612[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 74 )[/C][C]45.6890178571429[/C][C]0.668920150451116[/C][C]68.302648419741[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 74 )[/C][C]45.6958035714286[/C][C]0.667429478470591[/C][C]68.4653660730421[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 74 )[/C][C]45.7235267857143[/C][C]0.663019841161763[/C][C]68.9625316575688[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 74 )[/C][C]45.7320089285714[/C][C]0.661921643830833[/C][C]69.0897621414826[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 74 )[/C][C]45.7437946428571[/C][C]0.659407527289942[/C][C]69.3710531799003[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 74 )[/C][C]45.7416517857143[/C][C]0.658239273790834[/C][C]69.4909185869232[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 74 )[/C][C]45.7735714285714[/C][C]0.651577201559993[/C][C]70.2504190124843[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 74 )[/C][C]45.7835714285714[/C][C]0.650347058193854[/C][C]70.3986753714574[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 74 )[/C][C]45.7755357142857[/C][C]0.649782178055113[/C][C]70.4475088117962[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 74 )[/C][C]45.7698214285714[/C][C]0.64912584114367[/C][C]70.5099358668749[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 74 )[/C][C]45.7599553571429[/C][C]0.646813288920819[/C][C]70.7467767607116[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 74 )[/C][C]45.7631696428571[/C][C]0.645313558974931[/C][C]70.9161755651796[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 74 )[/C][C]45.7377232142857[/C][C]0.64346815616164[/C][C]71.0800103724113[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 74 )[/C][C]45.7439732142857[/C][C]0.641997824010782[/C][C]71.2525362290285[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 74 )[/C][C]45.7420982142857[/C][C]0.641875135691524[/C][C]71.2632343438658[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 74 )[/C][C]45.7401339285714[/C][C]0.641746828080467[/C][C]71.2744215119614[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 74 )[/C][C]45.7812053571429[/C][C]0.636391242516804[/C][C]71.9387733496883[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 74 )[/C][C]45.7469196428572[/C][C]0.634004131122046[/C][C]72.1555545101817[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 74 )[/C][C]45.7603125[/C][C]0.631613251483827[/C][C]72.4498930199721[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 74 )[/C][C]45.7672767857143[/C][C]0.630277135928424[/C][C]72.6145280810436[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 74 )[/C][C]45.7684821428571[/C][C]0.629739774013224[/C][C]72.6784046864031[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 74 )[/C][C]45.7722321428571[/C][C]0.628283060171227[/C][C]72.8528827920058[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 74 )[/C][C]45.7929464285714[/C][C]0.625869815226561[/C][C]73.1668876090384[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 74 )[/C][C]45.7902678571429[/C][C]0.623679113238057[/C][C]73.4195949250345[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 74 )[/C][C]45.8110267857143[/C][C]0.621267262430348[/C][C]73.7380344274141[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 74 )[/C][C]45.8024553571429[/C][C]0.6202602622063[/C][C]73.8439299564685[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 74 )[/C][C]45.8348660714286[/C][C]0.616635381360368[/C][C]74.3305808536507[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 74 )[/C][C]45.8318303571429[/C][C]0.614191061824478[/C][C]74.62145447216[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 74 )[/C][C]45.8443303571429[/C][C]0.611612967157992[/C][C]74.9564394786618[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 74 )[/C][C]45.8411160714286[/C][C]0.61115318563131[/C][C]75.0075711772255[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 74 )[/C][C]45.8460714285714[/C][C]0.610371367230509[/C][C]75.1117661966891[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 74 )[/C][C]45.8596428571429[/C][C]0.60841943317663[/C][C]75.3750461547624[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 74 )[/C][C]45.863125[/C][C]0.606356038305369[/C][C]75.6372858563053[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 74 )[/C][C]45.8541964285714[/C][C]0.605235222367768[/C][C]75.7626039165123[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 74 )[/C][C]45.8871428571429[/C][C]0.600976283244083[/C][C]76.3543323364494[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 74 )[/C][C]45.8758928571429[/C][C]0.600301120610783[/C][C]76.421467963388[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 74 )[/C][C]45.8624553571429[/C][C]0.598879200704304[/C][C]76.5804778379461[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 74 )[/C][C]45.8722767857143[/C][C]0.592197900364273[/C][C]77.4610594828136[/C][/ROW]
[ROW][C]Winsorized Mean ( 45 / 74 )[/C][C]45.9064285714286[/C][C]0.586499149922562[/C][C]78.2719439192534[/C][/ROW]
[ROW][C]Winsorized Mean ( 46 / 74 )[/C][C]45.9023214285714[/C][C]0.585279278308583[/C][C]78.4280652498513[/C][/ROW]
[ROW][C]Winsorized Mean ( 47 / 74 )[/C][C]45.9170089285714[/C][C]0.582801157189063[/C][C]78.78674975533[/C][/ROW]
[ROW][C]Winsorized Mean ( 48 / 74 )[/C][C]45.9405803571429[/C][C]0.579755421005556[/C][C]79.241312271753[/C][/ROW]
[ROW][C]Winsorized Mean ( 49 / 74 )[/C][C]46.0171428571429[/C][C]0.571765853275538[/C][C]80.4824957515727[/C][/ROW]
[ROW][C]Winsorized Mean ( 50 / 74 )[/C][C]46.0327678571429[/C][C]0.569862010210213[/C][C]80.778797379671[/C][/ROW]
[ROW][C]Winsorized Mean ( 51 / 74 )[/C][C]46.0327678571429[/C][C]0.568787095219179[/C][C]80.9314561530345[/C][/ROW]
[ROW][C]Winsorized Mean ( 52 / 74 )[/C][C]46.0304464285714[/C][C]0.568652313758529[/C][C]80.9465561202618[/C][/ROW]
[ROW][C]Winsorized Mean ( 53 / 74 )[/C][C]46.0564732142857[/C][C]0.566073030098745[/C][C]81.3613628726521[/C][/ROW]
[ROW][C]Winsorized Mean ( 54 / 74 )[/C][C]46.2131696428571[/C][C]0.550657243169059[/C][C]83.9236570773103[/C][/ROW]
[ROW][C]Winsorized Mean ( 55 / 74 )[/C][C]46.25[/C][C]0.547062371351405[/C][C]84.54246247233[/C][/ROW]
[ROW][C]Winsorized Mean ( 56 / 74 )[/C][C]46.2475[/C][C]0.545357671983053[/C][C]84.802144309867[/C][/ROW]
[ROW][C]Winsorized Mean ( 57 / 74 )[/C][C]46.3212946428571[/C][C]0.536606540406572[/C][C]86.322642671781[/C][/ROW]
[ROW][C]Winsorized Mean ( 58 / 74 )[/C][C]46.4145089285714[/C][C]0.526003752524072[/C][C]88.2398817610095[/C][/ROW]
[ROW][C]Winsorized Mean ( 59 / 74 )[/C][C]46.4698214285714[/C][C]0.5202857457437[/C][C]89.3159611016196[/C][/ROW]
[ROW][C]Winsorized Mean ( 60 / 74 )[/C][C]46.5367857142857[/C][C]0.513468742824867[/C][C]90.6321686852093[/C][/ROW]
[ROW][C]Winsorized Mean ( 61 / 74 )[/C][C]46.5449553571429[/C][C]0.512270174706365[/C][C]90.8601703853296[/C][/ROW]
[ROW][C]Winsorized Mean ( 62 / 74 )[/C][C]46.5587946428571[/C][C]0.510099375424993[/C][C]91.2739691242836[/C][/ROW]
[ROW][C]Winsorized Mean ( 63 / 74 )[/C][C]46.6009821428571[/C][C]0.506083755534084[/C][C]92.0815608745984[/C][/ROW]
[ROW][C]Winsorized Mean ( 64 / 74 )[/C][C]46.7352678571429[/C][C]0.492916800253008[/C][C]94.8137045301645[/C][/ROW]
[ROW][C]Winsorized Mean ( 65 / 74 )[/C][C]46.828125[/C][C]0.483273590711245[/C][C]96.897752950005[/C][/ROW]
[ROW][C]Winsorized Mean ( 66 / 74 )[/C][C]46.9754464285714[/C][C]0.467659312031727[/C][C]100.448008240205[/C][/ROW]
[ROW][C]Winsorized Mean ( 67 / 74 )[/C][C]47.0442410714286[/C][C]0.459416889919424[/C][C]102.399894526471[/C][/ROW]
[ROW][C]Winsorized Mean ( 68 / 74 )[/C][C]47.0472767857143[/C][C]0.458671927979904[/C][C]102.572828018757[/C][/ROW]
[ROW][C]Winsorized Mean ( 69 / 74 )[/C][C]47.5955803571429[/C][C]0.40764826568409[/C][C]116.756489267214[/C][/ROW]
[ROW][C]Winsorized Mean ( 70 / 74 )[/C][C]47.6049553571429[/C][C]0.406793950368495[/C][C]117.024737742584[/C][/ROW]
[ROW][C]Winsorized Mean ( 71 / 74 )[/C][C]48.0075[/C][C]0.369938238261636[/C][C]129.771661955224[/C][/ROW]
[ROW][C]Winsorized Mean ( 72 / 74 )[/C][C]47.9946428571429[/C][C]0.369150517606348[/C][C]130.013749319249[/C][/ROW]
[ROW][C]Winsorized Mean ( 73 / 74 )[/C][C]48.3759375[/C][C]0.334773796192792[/C][C]144.503357342045[/C][/ROW]
[ROW][C]Winsorized Mean ( 74 / 74 )[/C][C]48.6137946428571[/C][C]0.309983592671754[/C][C]156.826992757436[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 74 )[/C][C]45.7098648648649[/C][C]0.673929589192845[/C][C]67.8258761714423[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 74 )[/C][C]45.7471363636364[/C][C]0.670498196094008[/C][C]68.2285748569297[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 74 )[/C][C]45.7854128440367[/C][C]0.667375163124199[/C][C]68.6052094442658[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 74 )[/C][C]45.8268981481481[/C][C]0.664694117021052[/C][C]68.9443414265945[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 74 )[/C][C]45.8660747663551[/C][C]0.662415764363625[/C][C]69.240614782799[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 74 )[/C][C]45.9052830188679[/C][C]0.660123659000088[/C][C]69.5404298770359[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 74 )[/C][C]45.944619047619[/C][C]0.657961855378695[/C][C]69.8286970164483[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 74 )[/C][C]45.9839423076923[/C][C]0.655840027703848[/C][C]70.1145711838998[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 74 )[/C][C]46.0231067961165[/C][C]0.653780858275658[/C][C]70.3953109265116[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 74 )[/C][C]46.0596568627451[/C][C]0.652169844840572[/C][C]70.625247743561[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 74 )[/C][C]46.0959900990099[/C][C]0.650555310491562[/C][C]70.8563735559696[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 74 )[/C][C]46.13185[/C][C]0.649090732705313[/C][C]71.0714969041838[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 74 )[/C][C]46.1686363636364[/C][C]0.64761176890604[/C][C]71.2906073983575[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 74 )[/C][C]46.2033673469388[/C][C]0.646677665919373[/C][C]71.4472909486554[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 74 )[/C][C]46.2379896907216[/C][C]0.645745158214852[/C][C]71.60408266714[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 74 )[/C][C]46.2739583333333[/C][C]0.644740480069404[/C][C]71.7714487670328[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 74 )[/C][C]46.3111052631579[/C][C]0.64366407252494[/C][C]71.9491847377631[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 74 )[/C][C]46.3497340425532[/C][C]0.642645654650951[/C][C]72.1233135354004[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 74 )[/C][C]46.3889784946237[/C][C]0.641616241165591[/C][C]72.300193664598[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 74 )[/C][C]46.4307065217391[/C][C]0.640585275643758[/C][C]72.4816949235657[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 74 )[/C][C]46.472967032967[/C][C]0.639527608340679[/C][C]72.6676478495525[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 74 )[/C][C]46.5162777777778[/C][C]0.63833306849553[/C][C]72.871483671386[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 74 )[/C][C]46.5606741573034[/C][C]0.636991778570586[/C][C]73.0946233902514[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 74 )[/C][C]46.6038068181818[/C][C]0.635881276936329[/C][C]73.2901069877676[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 74 )[/C][C]46.6497701149425[/C][C]0.634765071183922[/C][C]73.4913942695909[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 74 )[/C][C]46.6961046511628[/C][C]0.633655699972457[/C][C]73.6931817281727[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 74 )[/C][C]46.7431764705882[/C][C]0.632474443907827[/C][C]73.9052414225298[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 74 )[/C][C]46.7913095238095[/C][C]0.631157535269874[/C][C]74.1357060782015[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 74 )[/C][C]46.840421686747[/C][C]0.629754383134493[/C][C]74.3788736389685[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 74 )[/C][C]46.889756097561[/C][C]0.628325240417071[/C][C]74.6265677094817[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 74 )[/C][C]46.9404320987654[/C][C]0.626837300068643[/C][C]74.8845547219751[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 74 )[/C][C]46.9914375[/C][C]0.625307678021319[/C][C]75.1493051367872[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 74 )[/C][C]47.0441139240506[/C][C]0.623624918860611[/C][C]75.4365524873544[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 74 )[/C][C]47.0967307692308[/C][C]0.621960574200565[/C][C]75.7230164142902[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 74 )[/C][C]47.1508441558442[/C][C]0.620216754261926[/C][C]76.0231706606424[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 74 )[/C][C]47.2058552631579[/C][C]0.618399897829957[/C][C]76.3354836066584[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 74 )[/C][C]47.2624666666667[/C][C]0.61635965949948[/C][C]76.6800129408965[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 74 )[/C][C]47.3204054054054[/C][C]0.614100798829614[/C][C]77.0564140212668[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 74 )[/C][C]47.3793835616438[/C][C]0.61168125344094[/C][C]77.4576354843585[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 74 )[/C][C]47.4398611111111[/C][C]0.60908405944787[/C][C]77.8872150325442[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 74 )[/C][C]47.5023943661972[/C][C]0.606222074467637[/C][C]78.3580743210516[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 74 )[/C][C]47.5654285714286[/C][C]0.603297519414289[/C][C]78.8424070060945[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 74 )[/C][C]47.6307246376812[/C][C]0.600039286397454[/C][C]79.3793435154036[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 74 )[/C][C]47.6984558823529[/C][C]0.596458355197153[/C][C]79.9694655406189[/C][/ROW]
[ROW][C]Trimmed Mean ( 45 / 74 )[/C][C]47.7678358208955[/C][C]0.592877036080668[/C][C]80.5695496939371[/C][/ROW]
[ROW][C]Trimmed Mean ( 46 / 74 )[/C][C]47.8380303030303[/C][C]0.589245926164282[/C][C]81.1851693475995[/C][/ROW]
[ROW][C]Trimmed Mean ( 47 / 74 )[/C][C]47.9105384615385[/C][C]0.585227530038182[/C][C]81.8665151627652[/C][/ROW]
[ROW][C]Trimmed Mean ( 48 / 74 )[/C][C]47.984765625[/C][C]0.580881094989574[/C][C]82.6068640189801[/C][/ROW]
[ROW][C]Trimmed Mean ( 49 / 74 )[/C][C]48.0604761904762[/C][C]0.576217098164995[/C][C]83.4068901175065[/C][/ROW]
[ROW][C]Trimmed Mean ( 50 / 74 )[/C][C]48.1358064516129[/C][C]0.571590991384228[/C][C]84.2137248087866[/C][/ROW]
[ROW][C]Trimmed Mean ( 51 / 74 )[/C][C]48.2130327868852[/C][C]0.566518601603872[/C][C]85.1040595143553[/C][/ROW]
[ROW][C]Trimmed Mean ( 52 / 74 )[/C][C]48.2928333333333[/C][C]0.560871011091766[/C][C]86.1032793250068[/C][/ROW]
[ROW][C]Trimmed Mean ( 53 / 74 )[/C][C]48.3754237288136[/C][C]0.554507802077739[/C][C]87.240294090635[/C][/ROW]
[ROW][C]Trimmed Mean ( 54 / 74 )[/C][C]48.4599137931034[/C][C]0.547557127641792[/C][C]88.502023527316[/C][/ROW]
[ROW][C]Trimmed Mean ( 55 / 74 )[/C][C]48.5416666666667[/C][C]0.541081678069297[/C][C]89.7122719805897[/C][/ROW]
[ROW][C]Trimmed Mean ( 56 / 74 )[/C][C]48.625[/C][C]0.534074708934335[/C][C]91.0453147969201[/C][/ROW]
[ROW][C]Trimmed Mean ( 57 / 74 )[/C][C]48.7114545454545[/C][C]0.52626172839983[/C][C]92.5612711636249[/C][/ROW]
[ROW][C]Trimmed Mean ( 58 / 74 )[/C][C]48.7984259259259[/C][C]0.518212325763444[/C][C]94.1668569037505[/C][/ROW]
[ROW][C]Trimmed Mean ( 59 / 74 )[/C][C]48.8852830188679[/C][C]0.510074906106076[/C][C]95.839419727701[/C][/ROW]
[ROW][C]Trimmed Mean ( 60 / 74 )[/C][C]48.9734615384615[/C][C]0.501370429042067[/C][C]97.6791982567294[/C][/ROW]
[ROW][C]Trimmed Mean ( 61 / 74 )[/C][C]48.9734615384615[/C][C]0.492134147121266[/C][C]99.5124232385241[/C][/ROW]
[ROW][C]Trimmed Mean ( 62 / 74 )[/C][C]49.1551[/C][C]0.481682939748175[/C][C]102.048663018247[/C][/ROW]
[ROW][C]Trimmed Mean ( 63 / 74 )[/C][C]49.2508163265306[/C][C]0.469917775383171[/C][C]104.807306525852[/C][/ROW]
[ROW][C]Trimmed Mean ( 64 / 74 )[/C][C]49.3489583333333[/C][C]0.456855035723517[/C][C]108.018856036423[/C][/ROW]
[ROW][C]Trimmed Mean ( 65 / 74 )[/C][C]49.4462765957447[/C][C]0.443411954229955[/C][C]111.513178939018[/C][/ROW]
[ROW][C]Trimmed Mean ( 66 / 74 )[/C][C]49.544347826087[/C][C]0.42906425769063[/C][C]115.470694512639[/C][/ROW]
[ROW][C]Trimmed Mean ( 67 / 74 )[/C][C]49.6412222222222[/C][C]0.414445219112114[/C][C]119.777524104563[/C][/ROW]
[ROW][C]Trimmed Mean ( 68 / 74 )[/C][C]49.7398863636364[/C][C]0.398470052600166[/C][C]124.82716339425[/C][/ROW]
[ROW][C]Trimmed Mean ( 69 / 74 )[/C][C]49.843023255814[/C][C]0.379744246491366[/C][C]131.254189408627[/C][/ROW]
[ROW][C]Trimmed Mean ( 70 / 74 )[/C][C]49.929880952381[/C][C]0.365636552817666[/C][C]136.556043337603[/C][/ROW]
[ROW][C]Trimmed Mean ( 71 / 74 )[/C][C]50.0206097560976[/C][C]0.349073594262602[/C][C]143.295312444825[/C][/ROW]
[ROW][C]Trimmed Mean ( 72 / 74 )[/C][C]50.1[/C][C]0.335450056649763[/C][C]149.351592008549[/C][/ROW]
[ROW][C]Trimmed Mean ( 73 / 74 )[/C][C]50.1839743589744[/C][C]0.319257502086974[/C][C]157.189647951649[/C][/ROW]
[ROW][C]Trimmed Mean ( 74 / 74 )[/C][C]50.2569736842105[/C][C]0.30591381768468[/C][C]164.284745503104[/C][/ROW]
[ROW][C]Median[/C][C]51.39[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]41.015[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]48.4987610619469[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]48.625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]48.4987610619469[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]48.625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]48.625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]48.4987610619469[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]48.625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]48.6659829059829[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]224[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=142927&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=142927&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean45.66794642857140.678138046026267.3431415567665
Geometric Mean44.3795342591813
Harmonic Mean42.9442709125863
Quadratic Mean46.7772659602321
Winsorized Mean ( 1 / 74 )45.67325892857140.67716012465345867.448240476276
Winsorized Mean ( 2 / 74 )45.67263392857140.67618632768742467.5444504841929
Winsorized Mean ( 3 / 74 )45.66540178571430.67441489701219267.7111404092973
Winsorized Mean ( 4 / 74 )45.67718750.67232454517500967.9391936941853
Winsorized Mean ( 5 / 74 )45.68053571428570.67165960148705168.0114385518337
Winsorized Mean ( 6 / 74 )45.68401785714290.67012011028045268.1728799901612
Winsorized Mean ( 7 / 74 )45.68901785714290.66892015045111668.302648419741
Winsorized Mean ( 8 / 74 )45.69580357142860.66742947847059168.4653660730421
Winsorized Mean ( 9 / 74 )45.72352678571430.66301984116176368.9625316575688
Winsorized Mean ( 10 / 74 )45.73200892857140.66192164383083369.0897621414826
Winsorized Mean ( 11 / 74 )45.74379464285710.65940752728994269.3710531799003
Winsorized Mean ( 12 / 74 )45.74165178571430.65823927379083469.4909185869232
Winsorized Mean ( 13 / 74 )45.77357142857140.65157720155999370.2504190124843
Winsorized Mean ( 14 / 74 )45.78357142857140.65034705819385470.3986753714574
Winsorized Mean ( 15 / 74 )45.77553571428570.64978217805511370.4475088117962
Winsorized Mean ( 16 / 74 )45.76982142857140.6491258411436770.5099358668749
Winsorized Mean ( 17 / 74 )45.75995535714290.64681328892081970.7467767607116
Winsorized Mean ( 18 / 74 )45.76316964285710.64531355897493170.9161755651796
Winsorized Mean ( 19 / 74 )45.73772321428570.6434681561616471.0800103724113
Winsorized Mean ( 20 / 74 )45.74397321428570.64199782401078271.2525362290285
Winsorized Mean ( 21 / 74 )45.74209821428570.64187513569152471.2632343438658
Winsorized Mean ( 22 / 74 )45.74013392857140.64174682808046771.2744215119614
Winsorized Mean ( 23 / 74 )45.78120535714290.63639124251680471.9387733496883
Winsorized Mean ( 24 / 74 )45.74691964285720.63400413112204672.1555545101817
Winsorized Mean ( 25 / 74 )45.76031250.63161325148382772.4498930199721
Winsorized Mean ( 26 / 74 )45.76727678571430.63027713592842472.6145280810436
Winsorized Mean ( 27 / 74 )45.76848214285710.62973977401322472.6784046864031
Winsorized Mean ( 28 / 74 )45.77223214285710.62828306017122772.8528827920058
Winsorized Mean ( 29 / 74 )45.79294642857140.62586981522656173.1668876090384
Winsorized Mean ( 30 / 74 )45.79026785714290.62367911323805773.4195949250345
Winsorized Mean ( 31 / 74 )45.81102678571430.62126726243034873.7380344274141
Winsorized Mean ( 32 / 74 )45.80245535714290.620260262206373.8439299564685
Winsorized Mean ( 33 / 74 )45.83486607142860.61663538136036874.3305808536507
Winsorized Mean ( 34 / 74 )45.83183035714290.61419106182447874.62145447216
Winsorized Mean ( 35 / 74 )45.84433035714290.61161296715799274.9564394786618
Winsorized Mean ( 36 / 74 )45.84111607142860.6111531856313175.0075711772255
Winsorized Mean ( 37 / 74 )45.84607142857140.61037136723050975.1117661966891
Winsorized Mean ( 38 / 74 )45.85964285714290.6084194331766375.3750461547624
Winsorized Mean ( 39 / 74 )45.8631250.60635603830536975.6372858563053
Winsorized Mean ( 40 / 74 )45.85419642857140.60523522236776875.7626039165123
Winsorized Mean ( 41 / 74 )45.88714285714290.60097628324408376.3543323364494
Winsorized Mean ( 42 / 74 )45.87589285714290.60030112061078376.421467963388
Winsorized Mean ( 43 / 74 )45.86245535714290.59887920070430476.5804778379461
Winsorized Mean ( 44 / 74 )45.87227678571430.59219790036427377.4610594828136
Winsorized Mean ( 45 / 74 )45.90642857142860.58649914992256278.2719439192534
Winsorized Mean ( 46 / 74 )45.90232142857140.58527927830858378.4280652498513
Winsorized Mean ( 47 / 74 )45.91700892857140.58280115718906378.78674975533
Winsorized Mean ( 48 / 74 )45.94058035714290.57975542100555679.241312271753
Winsorized Mean ( 49 / 74 )46.01714285714290.57176585327553880.4824957515727
Winsorized Mean ( 50 / 74 )46.03276785714290.56986201021021380.778797379671
Winsorized Mean ( 51 / 74 )46.03276785714290.56878709521917980.9314561530345
Winsorized Mean ( 52 / 74 )46.03044642857140.56865231375852980.9465561202618
Winsorized Mean ( 53 / 74 )46.05647321428570.56607303009874581.3613628726521
Winsorized Mean ( 54 / 74 )46.21316964285710.55065724316905983.9236570773103
Winsorized Mean ( 55 / 74 )46.250.54706237135140584.54246247233
Winsorized Mean ( 56 / 74 )46.24750.54535767198305384.802144309867
Winsorized Mean ( 57 / 74 )46.32129464285710.53660654040657286.322642671781
Winsorized Mean ( 58 / 74 )46.41450892857140.52600375252407288.2398817610095
Winsorized Mean ( 59 / 74 )46.46982142857140.520285745743789.3159611016196
Winsorized Mean ( 60 / 74 )46.53678571428570.51346874282486790.6321686852093
Winsorized Mean ( 61 / 74 )46.54495535714290.51227017470636590.8601703853296
Winsorized Mean ( 62 / 74 )46.55879464285710.51009937542499391.2739691242836
Winsorized Mean ( 63 / 74 )46.60098214285710.50608375553408492.0815608745984
Winsorized Mean ( 64 / 74 )46.73526785714290.49291680025300894.8137045301645
Winsorized Mean ( 65 / 74 )46.8281250.48327359071124596.897752950005
Winsorized Mean ( 66 / 74 )46.97544642857140.467659312031727100.448008240205
Winsorized Mean ( 67 / 74 )47.04424107142860.459416889919424102.399894526471
Winsorized Mean ( 68 / 74 )47.04727678571430.458671927979904102.572828018757
Winsorized Mean ( 69 / 74 )47.59558035714290.40764826568409116.756489267214
Winsorized Mean ( 70 / 74 )47.60495535714290.406793950368495117.024737742584
Winsorized Mean ( 71 / 74 )48.00750.369938238261636129.771661955224
Winsorized Mean ( 72 / 74 )47.99464285714290.369150517606348130.013749319249
Winsorized Mean ( 73 / 74 )48.37593750.334773796192792144.503357342045
Winsorized Mean ( 74 / 74 )48.61379464285710.309983592671754156.826992757436
Trimmed Mean ( 1 / 74 )45.70986486486490.67392958919284567.8258761714423
Trimmed Mean ( 2 / 74 )45.74713636363640.67049819609400868.2285748569297
Trimmed Mean ( 3 / 74 )45.78541284403670.66737516312419968.6052094442658
Trimmed Mean ( 4 / 74 )45.82689814814810.66469411702105268.9443414265945
Trimmed Mean ( 5 / 74 )45.86607476635510.66241576436362569.240614782799
Trimmed Mean ( 6 / 74 )45.90528301886790.66012365900008869.5404298770359
Trimmed Mean ( 7 / 74 )45.9446190476190.65796185537869569.8286970164483
Trimmed Mean ( 8 / 74 )45.98394230769230.65584002770384870.1145711838998
Trimmed Mean ( 9 / 74 )46.02310679611650.65378085827565870.3953109265116
Trimmed Mean ( 10 / 74 )46.05965686274510.65216984484057270.625247743561
Trimmed Mean ( 11 / 74 )46.09599009900990.65055531049156270.8563735559696
Trimmed Mean ( 12 / 74 )46.131850.64909073270531371.0714969041838
Trimmed Mean ( 13 / 74 )46.16863636363640.6476117689060471.2906073983575
Trimmed Mean ( 14 / 74 )46.20336734693880.64667766591937371.4472909486554
Trimmed Mean ( 15 / 74 )46.23798969072160.64574515821485271.60408266714
Trimmed Mean ( 16 / 74 )46.27395833333330.64474048006940471.7714487670328
Trimmed Mean ( 17 / 74 )46.31110526315790.6436640725249471.9491847377631
Trimmed Mean ( 18 / 74 )46.34973404255320.64264565465095172.1233135354004
Trimmed Mean ( 19 / 74 )46.38897849462370.64161624116559172.300193664598
Trimmed Mean ( 20 / 74 )46.43070652173910.64058527564375872.4816949235657
Trimmed Mean ( 21 / 74 )46.4729670329670.63952760834067972.6676478495525
Trimmed Mean ( 22 / 74 )46.51627777777780.6383330684955372.871483671386
Trimmed Mean ( 23 / 74 )46.56067415730340.63699177857058673.0946233902514
Trimmed Mean ( 24 / 74 )46.60380681818180.63588127693632973.2901069877676
Trimmed Mean ( 25 / 74 )46.64977011494250.63476507118392273.4913942695909
Trimmed Mean ( 26 / 74 )46.69610465116280.63365569997245773.6931817281727
Trimmed Mean ( 27 / 74 )46.74317647058820.63247444390782773.9052414225298
Trimmed Mean ( 28 / 74 )46.79130952380950.63115753526987474.1357060782015
Trimmed Mean ( 29 / 74 )46.8404216867470.62975438313449374.3788736389685
Trimmed Mean ( 30 / 74 )46.8897560975610.62832524041707174.6265677094817
Trimmed Mean ( 31 / 74 )46.94043209876540.62683730006864374.8845547219751
Trimmed Mean ( 32 / 74 )46.99143750.62530767802131975.1493051367872
Trimmed Mean ( 33 / 74 )47.04411392405060.62362491886061175.4365524873544
Trimmed Mean ( 34 / 74 )47.09673076923080.62196057420056575.7230164142902
Trimmed Mean ( 35 / 74 )47.15084415584420.62021675426192676.0231706606424
Trimmed Mean ( 36 / 74 )47.20585526315790.61839989782995776.3354836066584
Trimmed Mean ( 37 / 74 )47.26246666666670.6163596594994876.6800129408965
Trimmed Mean ( 38 / 74 )47.32040540540540.61410079882961477.0564140212668
Trimmed Mean ( 39 / 74 )47.37938356164380.6116812534409477.4576354843585
Trimmed Mean ( 40 / 74 )47.43986111111110.6090840594478777.8872150325442
Trimmed Mean ( 41 / 74 )47.50239436619720.60622207446763778.3580743210516
Trimmed Mean ( 42 / 74 )47.56542857142860.60329751941428978.8424070060945
Trimmed Mean ( 43 / 74 )47.63072463768120.60003928639745479.3793435154036
Trimmed Mean ( 44 / 74 )47.69845588235290.59645835519715379.9694655406189
Trimmed Mean ( 45 / 74 )47.76783582089550.59287703608066880.5695496939371
Trimmed Mean ( 46 / 74 )47.83803030303030.58924592616428281.1851693475995
Trimmed Mean ( 47 / 74 )47.91053846153850.58522753003818281.8665151627652
Trimmed Mean ( 48 / 74 )47.9847656250.58088109498957482.6068640189801
Trimmed Mean ( 49 / 74 )48.06047619047620.57621709816499583.4068901175065
Trimmed Mean ( 50 / 74 )48.13580645161290.57159099138422884.2137248087866
Trimmed Mean ( 51 / 74 )48.21303278688520.56651860160387285.1040595143553
Trimmed Mean ( 52 / 74 )48.29283333333330.56087101109176686.1032793250068
Trimmed Mean ( 53 / 74 )48.37542372881360.55450780207773987.240294090635
Trimmed Mean ( 54 / 74 )48.45991379310340.54755712764179288.502023527316
Trimmed Mean ( 55 / 74 )48.54166666666670.54108167806929789.7122719805897
Trimmed Mean ( 56 / 74 )48.6250.53407470893433591.0453147969201
Trimmed Mean ( 57 / 74 )48.71145454545450.5262617283998392.5612711636249
Trimmed Mean ( 58 / 74 )48.79842592592590.51821232576344494.1668569037505
Trimmed Mean ( 59 / 74 )48.88528301886790.51007490610607695.839419727701
Trimmed Mean ( 60 / 74 )48.97346153846150.50137042904206797.6791982567294
Trimmed Mean ( 61 / 74 )48.97346153846150.49213414712126699.5124232385241
Trimmed Mean ( 62 / 74 )49.15510.481682939748175102.048663018247
Trimmed Mean ( 63 / 74 )49.25081632653060.469917775383171104.807306525852
Trimmed Mean ( 64 / 74 )49.34895833333330.456855035723517108.018856036423
Trimmed Mean ( 65 / 74 )49.44627659574470.443411954229955111.513178939018
Trimmed Mean ( 66 / 74 )49.5443478260870.42906425769063115.470694512639
Trimmed Mean ( 67 / 74 )49.64122222222220.414445219112114119.777524104563
Trimmed Mean ( 68 / 74 )49.73988636363640.398470052600166124.82716339425
Trimmed Mean ( 69 / 74 )49.8430232558140.379744246491366131.254189408627
Trimmed Mean ( 70 / 74 )49.9298809523810.365636552817666136.556043337603
Trimmed Mean ( 71 / 74 )50.02060975609760.349073594262602143.295312444825
Trimmed Mean ( 72 / 74 )50.10.335450056649763149.351592008549
Trimmed Mean ( 73 / 74 )50.18397435897440.319257502086974157.189647951649
Trimmed Mean ( 74 / 74 )50.25697368421050.30591381768468164.284745503104
Median51.39
Midrange41.015
Midmean - Weighted Average at Xnp48.4987610619469
Midmean - Weighted Average at X(n+1)p48.625
Midmean - Empirical Distribution Function48.4987610619469
Midmean - Empirical Distribution Function - Averaging48.625
Midmean - Empirical Distribution Function - Interpolation48.625
Midmean - Closest Observation48.4987610619469
Midmean - True Basic - Statistics Graphics Toolkit48.625
Midmean - MS Excel (old versions)48.6659829059829
Number of observations224



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')