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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 computationSat, 11 Dec 2010 11:12:58 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/11/t129206587015ite1pdsw6l6xp.htm/, Retrieved Sat, 27 Apr 2024 18:51:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=108060, Retrieved Sat, 27 Apr 2024 18:51:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact128
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]
-  M D  [Central Tendency] [Mini-tutorial Uni...] [2010-11-14 20:27:58] [6ca0fc48dd5333d51a15728999009c83]
-    D    [Central Tendency] [Mini-tutorial Uni...] [2010-11-14 20:54:36] [6ca0fc48dd5333d51a15728999009c83]
-    D        [Central Tendency] [Univariate analys...] [2010-12-11 11:12:58] [b4ba846736d082ffaee409a197f454c7] [Current]
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Dataseries X:
69
53
43
60
49
62
45
50
75
82
60
59
21
62
54
47
59
37
43
48
79
62
16
38
58
60
67
55
47
59
49
47
57
39
49
26
53
75
65
49
48
45
31
61
49
69
54
80
57
34
69
44
70
51
66
18
74
59
48
55
44
56
65
77
46
70
39
55
44
45
45
49
65
45
71
48
41
40
64
56
52
41
42
54
40
40
51
48
80
38
57
28
51
46
58
67
72
26
54
53
64
47
43
66
54
62
52
64
55
57
74
32
38
66
37
26
64
28
66
65
48
44
64
39
50
66
48
70
66
61
31
61
54
34
62
47
52
37
46
38
63
34
46
40
30
35
51
56
68
39
44
58




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108060&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108060&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108060&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean52.07236842105261.0890989194757747.8123405412221
Geometric Mean50.1266913823368
Harmonic Mean47.8358517275049
Quadratic Mean53.7646552848127
Winsorized Mean ( 1 / 50 )52.07236842105261.0839662099477548.0387376868165
Winsorized Mean ( 2 / 50 )52.11184210526321.0760774161838448.4275957487062
Winsorized Mean ( 3 / 50 )52.19078947368421.0551510835172949.4628591952054
Winsorized Mean ( 4 / 50 )52.13815789473681.0465819044160949.8175610286572
Winsorized Mean ( 5 / 50 )52.07236842105261.0365868015171250.2344505494774
Winsorized Mean ( 6 / 50 )52.15131578947371.0238426321874850.9368472751037
Winsorized Mean ( 7 / 50 )52.10526315789471.0171566712458651.2263888453624
Winsorized Mean ( 8 / 50 )52.21052631578951.0011596438794852.1500508285317
Winsorized Mean ( 9 / 50 )52.15131578947370.97604453653358453.4312870339798
Winsorized Mean ( 10 / 50 )52.08552631578950.96735419790758453.8432834926979
Winsorized Mean ( 11 / 50 )52.08552631578950.9478353132357354.9520845957715
Winsorized Mean ( 12 / 50 )52.24342105263160.92645167947727756.3908752176999
Winsorized Mean ( 13 / 50 )52.24342105263160.92645167947727756.3908752176999
Winsorized Mean ( 14 / 50 )52.15131578947370.9149888466209156.9966683004613
Winsorized Mean ( 15 / 50 )52.250.90225744151175257.9103009806758
Winsorized Mean ( 16 / 50 )52.46052631578950.87662022372224859.844074886882
Winsorized Mean ( 17 / 50 )52.34868421052630.86291370670316460.6650280368462
Winsorized Mean ( 18 / 50 )52.23026315789470.84897732312733761.521387833419
Winsorized Mean ( 19 / 50 )52.35526315789470.83442864611232362.7438468247975
Winsorized Mean ( 20 / 50 )52.22368421052630.81945440496789363.7298230309379
Winsorized Mean ( 21 / 50 )52.22368421052630.81945440496789363.7298230309379
Winsorized Mean ( 22 / 50 )52.22368421052630.81945440496789363.7298230309379
Winsorized Mean ( 23 / 50 )52.3750.80240209365529865.272760893991
Winsorized Mean ( 24 / 50 )52.3750.80240209365529865.272760893991
Winsorized Mean ( 25 / 50 )52.3750.80240209365529865.272760893991
Winsorized Mean ( 26 / 50 )52.20394736842110.78353007660882766.6266030199675
Winsorized Mean ( 27 / 50 )52.38157894736840.76408205362686968.5549133090206
Winsorized Mean ( 28 / 50 )52.38157894736840.76408205362686968.5549133090206
Winsorized Mean ( 29 / 50 )52.38157894736840.76408205362686968.5549133090206
Winsorized Mean ( 30 / 50 )52.18421052631580.74288897111756870.24496601129
Winsorized Mean ( 31 / 50 )52.38815789473680.72114223701795772.6460817374538
Winsorized Mean ( 32 / 50 )52.38815789473680.72114223701795772.6460817374538
Winsorized Mean ( 33 / 50 )52.60526315789470.69887363286748575.2714949941019
Winsorized Mean ( 34 / 50 )52.82894736842110.67687080611124978.0487899484591
Winsorized Mean ( 35 / 50 )52.59868421052630.65211802469078980.6582278345499
Winsorized Mean ( 36 / 50 )52.36184210526320.62755572561398483.4377569482514
Winsorized Mean ( 37 / 50 )52.60526315789470.60403819243249687.089299678304
Winsorized Mean ( 38 / 50 )52.60526315789470.60403819243249687.089299678304
Winsorized Mean ( 39 / 50 )52.60526315789470.60403819243249687.089299678304
Winsorized Mean ( 40 / 50 )52.60526315789470.60403819243249687.089299678304
Winsorized Mean ( 41 / 50 )52.33552631578950.57671683461857290.7473532490222
Winsorized Mean ( 42 / 50 )52.61184210526320.55083584117225295.5127429495113
Winsorized Mean ( 43 / 50 )52.61184210526320.55083584117225295.5127429495113
Winsorized Mean ( 44 / 50 )52.32236842105260.52213149141372100.209179644355
Winsorized Mean ( 45 / 50 )52.32236842105260.52213149141372100.209179644355
Winsorized Mean ( 46 / 50 )52.32236842105260.52213149141372100.209179644355
Winsorized Mean ( 47 / 50 )52.32236842105260.463987330741423112.766804079423
Winsorized Mean ( 48 / 50 )52.32236842105260.463987330741423112.766804079423
Winsorized Mean ( 49 / 50 )52.32236842105260.463987330741423112.766804079423
Winsorized Mean ( 50 / 50 )52.32236842105260.463987330741423112.766804079423
Trimmed Mean ( 1 / 50 )52.11333333333331.0581963747277549.2473179628318
Trimmed Mean ( 2 / 50 )52.15540540540541.0301000741184550.631396614586
Trimmed Mean ( 3 / 50 )52.17808219178081.0039922638625251.9706018361571
Trimmed Mean ( 4 / 50 )52.17361111111110.98390948813307953.0268401111855
Trimmed Mean ( 5 / 50 )52.18309859154930.96469594678026854.0927934503235
Trimmed Mean ( 6 / 50 )52.20714285714290.94632390004677355.1683655612655
Trimmed Mean ( 7 / 50 )52.21739130434780.92913735048273356.1998624608281
Trimmed Mean ( 8 / 50 )52.23529411764710.9116909099378857.2949598907443
Trimmed Mean ( 9 / 50 )52.23880597014930.89551677699959158.3336988338445
Trimmed Mean ( 10 / 50 )52.250.88196355021583759.2428110971403
Trimmed Mean ( 11 / 50 )52.26923076923080.86843463046952760.187870146278
Trimmed Mean ( 12 / 50 )52.28906250.85639330398536861.0572995569491
Trimmed Mean ( 13 / 50 )52.29365079365080.84606033484559661.8084179577976
Trimmed Mean ( 14 / 50 )52.29838709677420.83468129941033462.6567135668677
Trimmed Mean ( 15 / 50 )52.31147540983610.82355266228969163.5192839573811
Trimmed Mean ( 16 / 50 )52.31666666666670.81279882101048964.366071055105
Trimmed Mean ( 17 / 50 )52.30508474576270.80384672685450665.0684800949993
Trimmed Mean ( 18 / 50 )52.3017241379310.79543485957683365.75236615322
Trimmed Mean ( 19 / 50 )52.30701754385970.7875690769202766.415783804517
Trimmed Mean ( 20 / 50 )52.30357142857140.78031187929949867.0290595543995
Trimmed Mean ( 21 / 50 )52.30909090909090.77370737039491367.6083657861388
Trimmed Mean ( 22 / 50 )52.31481481481480.76626791609491268.2722240041366
Trimmed Mean ( 23 / 50 )52.32075471698110.75789313702782469.0344748629916
Trimmed Mean ( 24 / 50 )52.31730769230770.75018847806951469.7388845892937
Trimmed Mean ( 25 / 50 )52.31372549019610.74147983753920370.553132859031
Trimmed Mean ( 26 / 50 )52.310.73163646655420371.4972563442129
Trimmed Mean ( 27 / 50 )52.31632653061220.72242737531008272.4174198245974
Trimmed Mean ( 28 / 50 )52.31250.71394513340226173.2724372679845
Trimmed Mean ( 29 / 50 )52.30851063829790.70427439546019274.2729126253668
Trimmed Mean ( 30 / 50 )52.3043478260870.69324416006526375.4486670629334
Trimmed Mean ( 31 / 50 )52.31111111111110.68288227452470676.6034103718979
Trimmed Mean ( 32 / 50 )52.30681818181820.67329993241724477.6872470401551
Trimmed Mean ( 33 / 50 )52.30232558139540.66226609425596978.9747897937536
Trimmed Mean ( 34 / 50 )52.28571428571430.6519249550654880.2020445443182
Trimmed Mean ( 35 / 50 )52.25609756097560.6422378294466581.3656486196076
Trimmed Mean ( 36 / 50 )52.23750.63376605664626982.4239472155195
Trimmed Mean ( 37 / 50 )52.23076923076920.62656346621644183.360700147695
Trimmed Mean ( 38 / 50 )52.21052631578950.62050228365885584.1423596508377
Trimmed Mean ( 39 / 50 )52.18918918918920.61321847921360585.1070066513926
Trimmed Mean ( 40 / 50 )52.16666666666670.60449541808448286.2978694395596
Trimmed Mean ( 41 / 50 )52.14285714285710.59406509681073187.7729686911229
Trimmed Mean ( 42 / 50 )52.13235294117650.58511849867449289.0970855634805
Trimmed Mean ( 43 / 50 )52.10606060606060.5774022638529190.242217372626
Trimmed Mean ( 44 / 50 )52.0781250.5679540206682791.6942623959655
Trimmed Mean ( 45 / 50 )52.06451612903230.56040278242711792.9055275270755
Trimmed Mean ( 46 / 50 )52.050.55102626389567494.4601072769458
Trimmed Mean ( 47 / 50 )52.03448275862070.53941192533294796.4652064866806
Trimmed Mean ( 48 / 50 )52.01785714285710.53360515549102997.4837979123155
Trimmed Mean ( 49 / 50 )520.52605090984469198.8497482408161
Trimmed Mean ( 50 / 50 )51.98076923076920.516317732083734100.675932668412
Median52
Midrange49
Midmean - Weighted Average at Xnp52.3544303797468
Midmean - Weighted Average at X(n+1)p52.3544303797468
Midmean - Empirical Distribution Function52.3544303797468
Midmean - Empirical Distribution Function - Averaging52.3544303797468
Midmean - Empirical Distribution Function - Interpolation52.3544303797468
Midmean - Closest Observation52.3544303797468
Midmean - True Basic - Statistics Graphics Toolkit52.3544303797468
Midmean - MS Excel (old versions)52.3544303797468
Number of observations152

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 52.0723684210526 & 1.08909891947577 & 47.8123405412221 \tabularnewline
Geometric Mean & 50.1266913823368 &  &  \tabularnewline
Harmonic Mean & 47.8358517275049 &  &  \tabularnewline
Quadratic Mean & 53.7646552848127 &  &  \tabularnewline
Winsorized Mean ( 1 / 50 ) & 52.0723684210526 & 1.08396620994775 & 48.0387376868165 \tabularnewline
Winsorized Mean ( 2 / 50 ) & 52.1118421052632 & 1.07607741618384 & 48.4275957487062 \tabularnewline
Winsorized Mean ( 3 / 50 ) & 52.1907894736842 & 1.05515108351729 & 49.4628591952054 \tabularnewline
Winsorized Mean ( 4 / 50 ) & 52.1381578947368 & 1.04658190441609 & 49.8175610286572 \tabularnewline
Winsorized Mean ( 5 / 50 ) & 52.0723684210526 & 1.03658680151712 & 50.2344505494774 \tabularnewline
Winsorized Mean ( 6 / 50 ) & 52.1513157894737 & 1.02384263218748 & 50.9368472751037 \tabularnewline
Winsorized Mean ( 7 / 50 ) & 52.1052631578947 & 1.01715667124586 & 51.2263888453624 \tabularnewline
Winsorized Mean ( 8 / 50 ) & 52.2105263157895 & 1.00115964387948 & 52.1500508285317 \tabularnewline
Winsorized Mean ( 9 / 50 ) & 52.1513157894737 & 0.976044536533584 & 53.4312870339798 \tabularnewline
Winsorized Mean ( 10 / 50 ) & 52.0855263157895 & 0.967354197907584 & 53.8432834926979 \tabularnewline
Winsorized Mean ( 11 / 50 ) & 52.0855263157895 & 0.94783531323573 & 54.9520845957715 \tabularnewline
Winsorized Mean ( 12 / 50 ) & 52.2434210526316 & 0.926451679477277 & 56.3908752176999 \tabularnewline
Winsorized Mean ( 13 / 50 ) & 52.2434210526316 & 0.926451679477277 & 56.3908752176999 \tabularnewline
Winsorized Mean ( 14 / 50 ) & 52.1513157894737 & 0.91498884662091 & 56.9966683004613 \tabularnewline
Winsorized Mean ( 15 / 50 ) & 52.25 & 0.902257441511752 & 57.9103009806758 \tabularnewline
Winsorized Mean ( 16 / 50 ) & 52.4605263157895 & 0.876620223722248 & 59.844074886882 \tabularnewline
Winsorized Mean ( 17 / 50 ) & 52.3486842105263 & 0.862913706703164 & 60.6650280368462 \tabularnewline
Winsorized Mean ( 18 / 50 ) & 52.2302631578947 & 0.848977323127337 & 61.521387833419 \tabularnewline
Winsorized Mean ( 19 / 50 ) & 52.3552631578947 & 0.834428646112323 & 62.7438468247975 \tabularnewline
Winsorized Mean ( 20 / 50 ) & 52.2236842105263 & 0.819454404967893 & 63.7298230309379 \tabularnewline
Winsorized Mean ( 21 / 50 ) & 52.2236842105263 & 0.819454404967893 & 63.7298230309379 \tabularnewline
Winsorized Mean ( 22 / 50 ) & 52.2236842105263 & 0.819454404967893 & 63.7298230309379 \tabularnewline
Winsorized Mean ( 23 / 50 ) & 52.375 & 0.802402093655298 & 65.272760893991 \tabularnewline
Winsorized Mean ( 24 / 50 ) & 52.375 & 0.802402093655298 & 65.272760893991 \tabularnewline
Winsorized Mean ( 25 / 50 ) & 52.375 & 0.802402093655298 & 65.272760893991 \tabularnewline
Winsorized Mean ( 26 / 50 ) & 52.2039473684211 & 0.783530076608827 & 66.6266030199675 \tabularnewline
Winsorized Mean ( 27 / 50 ) & 52.3815789473684 & 0.764082053626869 & 68.5549133090206 \tabularnewline
Winsorized Mean ( 28 / 50 ) & 52.3815789473684 & 0.764082053626869 & 68.5549133090206 \tabularnewline
Winsorized Mean ( 29 / 50 ) & 52.3815789473684 & 0.764082053626869 & 68.5549133090206 \tabularnewline
Winsorized Mean ( 30 / 50 ) & 52.1842105263158 & 0.742888971117568 & 70.24496601129 \tabularnewline
Winsorized Mean ( 31 / 50 ) & 52.3881578947368 & 0.721142237017957 & 72.6460817374538 \tabularnewline
Winsorized Mean ( 32 / 50 ) & 52.3881578947368 & 0.721142237017957 & 72.6460817374538 \tabularnewline
Winsorized Mean ( 33 / 50 ) & 52.6052631578947 & 0.698873632867485 & 75.2714949941019 \tabularnewline
Winsorized Mean ( 34 / 50 ) & 52.8289473684211 & 0.676870806111249 & 78.0487899484591 \tabularnewline
Winsorized Mean ( 35 / 50 ) & 52.5986842105263 & 0.652118024690789 & 80.6582278345499 \tabularnewline
Winsorized Mean ( 36 / 50 ) & 52.3618421052632 & 0.627555725613984 & 83.4377569482514 \tabularnewline
Winsorized Mean ( 37 / 50 ) & 52.6052631578947 & 0.604038192432496 & 87.089299678304 \tabularnewline
Winsorized Mean ( 38 / 50 ) & 52.6052631578947 & 0.604038192432496 & 87.089299678304 \tabularnewline
Winsorized Mean ( 39 / 50 ) & 52.6052631578947 & 0.604038192432496 & 87.089299678304 \tabularnewline
Winsorized Mean ( 40 / 50 ) & 52.6052631578947 & 0.604038192432496 & 87.089299678304 \tabularnewline
Winsorized Mean ( 41 / 50 ) & 52.3355263157895 & 0.576716834618572 & 90.7473532490222 \tabularnewline
Winsorized Mean ( 42 / 50 ) & 52.6118421052632 & 0.550835841172252 & 95.5127429495113 \tabularnewline
Winsorized Mean ( 43 / 50 ) & 52.6118421052632 & 0.550835841172252 & 95.5127429495113 \tabularnewline
Winsorized Mean ( 44 / 50 ) & 52.3223684210526 & 0.52213149141372 & 100.209179644355 \tabularnewline
Winsorized Mean ( 45 / 50 ) & 52.3223684210526 & 0.52213149141372 & 100.209179644355 \tabularnewline
Winsorized Mean ( 46 / 50 ) & 52.3223684210526 & 0.52213149141372 & 100.209179644355 \tabularnewline
Winsorized Mean ( 47 / 50 ) & 52.3223684210526 & 0.463987330741423 & 112.766804079423 \tabularnewline
Winsorized Mean ( 48 / 50 ) & 52.3223684210526 & 0.463987330741423 & 112.766804079423 \tabularnewline
Winsorized Mean ( 49 / 50 ) & 52.3223684210526 & 0.463987330741423 & 112.766804079423 \tabularnewline
Winsorized Mean ( 50 / 50 ) & 52.3223684210526 & 0.463987330741423 & 112.766804079423 \tabularnewline
Trimmed Mean ( 1 / 50 ) & 52.1133333333333 & 1.05819637472775 & 49.2473179628318 \tabularnewline
Trimmed Mean ( 2 / 50 ) & 52.1554054054054 & 1.03010007411845 & 50.631396614586 \tabularnewline
Trimmed Mean ( 3 / 50 ) & 52.1780821917808 & 1.00399226386252 & 51.9706018361571 \tabularnewline
Trimmed Mean ( 4 / 50 ) & 52.1736111111111 & 0.983909488133079 & 53.0268401111855 \tabularnewline
Trimmed Mean ( 5 / 50 ) & 52.1830985915493 & 0.964695946780268 & 54.0927934503235 \tabularnewline
Trimmed Mean ( 6 / 50 ) & 52.2071428571429 & 0.946323900046773 & 55.1683655612655 \tabularnewline
Trimmed Mean ( 7 / 50 ) & 52.2173913043478 & 0.929137350482733 & 56.1998624608281 \tabularnewline
Trimmed Mean ( 8 / 50 ) & 52.2352941176471 & 0.91169090993788 & 57.2949598907443 \tabularnewline
Trimmed Mean ( 9 / 50 ) & 52.2388059701493 & 0.895516776999591 & 58.3336988338445 \tabularnewline
Trimmed Mean ( 10 / 50 ) & 52.25 & 0.881963550215837 & 59.2428110971403 \tabularnewline
Trimmed Mean ( 11 / 50 ) & 52.2692307692308 & 0.868434630469527 & 60.187870146278 \tabularnewline
Trimmed Mean ( 12 / 50 ) & 52.2890625 & 0.856393303985368 & 61.0572995569491 \tabularnewline
Trimmed Mean ( 13 / 50 ) & 52.2936507936508 & 0.846060334845596 & 61.8084179577976 \tabularnewline
Trimmed Mean ( 14 / 50 ) & 52.2983870967742 & 0.834681299410334 & 62.6567135668677 \tabularnewline
Trimmed Mean ( 15 / 50 ) & 52.3114754098361 & 0.823552662289691 & 63.5192839573811 \tabularnewline
Trimmed Mean ( 16 / 50 ) & 52.3166666666667 & 0.812798821010489 & 64.366071055105 \tabularnewline
Trimmed Mean ( 17 / 50 ) & 52.3050847457627 & 0.803846726854506 & 65.0684800949993 \tabularnewline
Trimmed Mean ( 18 / 50 ) & 52.301724137931 & 0.795434859576833 & 65.75236615322 \tabularnewline
Trimmed Mean ( 19 / 50 ) & 52.3070175438597 & 0.78756907692027 & 66.415783804517 \tabularnewline
Trimmed Mean ( 20 / 50 ) & 52.3035714285714 & 0.780311879299498 & 67.0290595543995 \tabularnewline
Trimmed Mean ( 21 / 50 ) & 52.3090909090909 & 0.773707370394913 & 67.6083657861388 \tabularnewline
Trimmed Mean ( 22 / 50 ) & 52.3148148148148 & 0.766267916094912 & 68.2722240041366 \tabularnewline
Trimmed Mean ( 23 / 50 ) & 52.3207547169811 & 0.757893137027824 & 69.0344748629916 \tabularnewline
Trimmed Mean ( 24 / 50 ) & 52.3173076923077 & 0.750188478069514 & 69.7388845892937 \tabularnewline
Trimmed Mean ( 25 / 50 ) & 52.3137254901961 & 0.741479837539203 & 70.553132859031 \tabularnewline
Trimmed Mean ( 26 / 50 ) & 52.31 & 0.731636466554203 & 71.4972563442129 \tabularnewline
Trimmed Mean ( 27 / 50 ) & 52.3163265306122 & 0.722427375310082 & 72.4174198245974 \tabularnewline
Trimmed Mean ( 28 / 50 ) & 52.3125 & 0.713945133402261 & 73.2724372679845 \tabularnewline
Trimmed Mean ( 29 / 50 ) & 52.3085106382979 & 0.704274395460192 & 74.2729126253668 \tabularnewline
Trimmed Mean ( 30 / 50 ) & 52.304347826087 & 0.693244160065263 & 75.4486670629334 \tabularnewline
Trimmed Mean ( 31 / 50 ) & 52.3111111111111 & 0.682882274524706 & 76.6034103718979 \tabularnewline
Trimmed Mean ( 32 / 50 ) & 52.3068181818182 & 0.673299932417244 & 77.6872470401551 \tabularnewline
Trimmed Mean ( 33 / 50 ) & 52.3023255813954 & 0.662266094255969 & 78.9747897937536 \tabularnewline
Trimmed Mean ( 34 / 50 ) & 52.2857142857143 & 0.65192495506548 & 80.2020445443182 \tabularnewline
Trimmed Mean ( 35 / 50 ) & 52.2560975609756 & 0.64223782944665 & 81.3656486196076 \tabularnewline
Trimmed Mean ( 36 / 50 ) & 52.2375 & 0.633766056646269 & 82.4239472155195 \tabularnewline
Trimmed Mean ( 37 / 50 ) & 52.2307692307692 & 0.626563466216441 & 83.360700147695 \tabularnewline
Trimmed Mean ( 38 / 50 ) & 52.2105263157895 & 0.620502283658855 & 84.1423596508377 \tabularnewline
Trimmed Mean ( 39 / 50 ) & 52.1891891891892 & 0.613218479213605 & 85.1070066513926 \tabularnewline
Trimmed Mean ( 40 / 50 ) & 52.1666666666667 & 0.604495418084482 & 86.2978694395596 \tabularnewline
Trimmed Mean ( 41 / 50 ) & 52.1428571428571 & 0.594065096810731 & 87.7729686911229 \tabularnewline
Trimmed Mean ( 42 / 50 ) & 52.1323529411765 & 0.585118498674492 & 89.0970855634805 \tabularnewline
Trimmed Mean ( 43 / 50 ) & 52.1060606060606 & 0.57740226385291 & 90.242217372626 \tabularnewline
Trimmed Mean ( 44 / 50 ) & 52.078125 & 0.56795402066827 & 91.6942623959655 \tabularnewline
Trimmed Mean ( 45 / 50 ) & 52.0645161290323 & 0.560402782427117 & 92.9055275270755 \tabularnewline
Trimmed Mean ( 46 / 50 ) & 52.05 & 0.551026263895674 & 94.4601072769458 \tabularnewline
Trimmed Mean ( 47 / 50 ) & 52.0344827586207 & 0.539411925332947 & 96.4652064866806 \tabularnewline
Trimmed Mean ( 48 / 50 ) & 52.0178571428571 & 0.533605155491029 & 97.4837979123155 \tabularnewline
Trimmed Mean ( 49 / 50 ) & 52 & 0.526050909844691 & 98.8497482408161 \tabularnewline
Trimmed Mean ( 50 / 50 ) & 51.9807692307692 & 0.516317732083734 & 100.675932668412 \tabularnewline
Median & 52 &  &  \tabularnewline
Midrange & 49 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 52.3544303797468 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 52.3544303797468 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 52.3544303797468 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 52.3544303797468 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 52.3544303797468 &  &  \tabularnewline
Midmean - Closest Observation & 52.3544303797468 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 52.3544303797468 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 52.3544303797468 &  &  \tabularnewline
Number of observations & 152 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108060&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]52.0723684210526[/C][C]1.08909891947577[/C][C]47.8123405412221[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]50.1266913823368[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]47.8358517275049[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]53.7646552848127[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 50 )[/C][C]52.0723684210526[/C][C]1.08396620994775[/C][C]48.0387376868165[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 50 )[/C][C]52.1118421052632[/C][C]1.07607741618384[/C][C]48.4275957487062[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 50 )[/C][C]52.1907894736842[/C][C]1.05515108351729[/C][C]49.4628591952054[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 50 )[/C][C]52.1381578947368[/C][C]1.04658190441609[/C][C]49.8175610286572[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 50 )[/C][C]52.0723684210526[/C][C]1.03658680151712[/C][C]50.2344505494774[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 50 )[/C][C]52.1513157894737[/C][C]1.02384263218748[/C][C]50.9368472751037[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 50 )[/C][C]52.1052631578947[/C][C]1.01715667124586[/C][C]51.2263888453624[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 50 )[/C][C]52.2105263157895[/C][C]1.00115964387948[/C][C]52.1500508285317[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 50 )[/C][C]52.1513157894737[/C][C]0.976044536533584[/C][C]53.4312870339798[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 50 )[/C][C]52.0855263157895[/C][C]0.967354197907584[/C][C]53.8432834926979[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 50 )[/C][C]52.0855263157895[/C][C]0.94783531323573[/C][C]54.9520845957715[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 50 )[/C][C]52.2434210526316[/C][C]0.926451679477277[/C][C]56.3908752176999[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 50 )[/C][C]52.2434210526316[/C][C]0.926451679477277[/C][C]56.3908752176999[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 50 )[/C][C]52.1513157894737[/C][C]0.91498884662091[/C][C]56.9966683004613[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 50 )[/C][C]52.25[/C][C]0.902257441511752[/C][C]57.9103009806758[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 50 )[/C][C]52.4605263157895[/C][C]0.876620223722248[/C][C]59.844074886882[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 50 )[/C][C]52.3486842105263[/C][C]0.862913706703164[/C][C]60.6650280368462[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 50 )[/C][C]52.2302631578947[/C][C]0.848977323127337[/C][C]61.521387833419[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 50 )[/C][C]52.3552631578947[/C][C]0.834428646112323[/C][C]62.7438468247975[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 50 )[/C][C]52.2236842105263[/C][C]0.819454404967893[/C][C]63.7298230309379[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 50 )[/C][C]52.2236842105263[/C][C]0.819454404967893[/C][C]63.7298230309379[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 50 )[/C][C]52.2236842105263[/C][C]0.819454404967893[/C][C]63.7298230309379[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 50 )[/C][C]52.375[/C][C]0.802402093655298[/C][C]65.272760893991[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 50 )[/C][C]52.375[/C][C]0.802402093655298[/C][C]65.272760893991[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 50 )[/C][C]52.375[/C][C]0.802402093655298[/C][C]65.272760893991[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 50 )[/C][C]52.2039473684211[/C][C]0.783530076608827[/C][C]66.6266030199675[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 50 )[/C][C]52.3815789473684[/C][C]0.764082053626869[/C][C]68.5549133090206[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 50 )[/C][C]52.3815789473684[/C][C]0.764082053626869[/C][C]68.5549133090206[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 50 )[/C][C]52.3815789473684[/C][C]0.764082053626869[/C][C]68.5549133090206[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 50 )[/C][C]52.1842105263158[/C][C]0.742888971117568[/C][C]70.24496601129[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 50 )[/C][C]52.3881578947368[/C][C]0.721142237017957[/C][C]72.6460817374538[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 50 )[/C][C]52.3881578947368[/C][C]0.721142237017957[/C][C]72.6460817374538[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 50 )[/C][C]52.6052631578947[/C][C]0.698873632867485[/C][C]75.2714949941019[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 50 )[/C][C]52.8289473684211[/C][C]0.676870806111249[/C][C]78.0487899484591[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 50 )[/C][C]52.5986842105263[/C][C]0.652118024690789[/C][C]80.6582278345499[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 50 )[/C][C]52.3618421052632[/C][C]0.627555725613984[/C][C]83.4377569482514[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 50 )[/C][C]52.6052631578947[/C][C]0.604038192432496[/C][C]87.089299678304[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 50 )[/C][C]52.6052631578947[/C][C]0.604038192432496[/C][C]87.089299678304[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 50 )[/C][C]52.6052631578947[/C][C]0.604038192432496[/C][C]87.089299678304[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 50 )[/C][C]52.6052631578947[/C][C]0.604038192432496[/C][C]87.089299678304[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 50 )[/C][C]52.3355263157895[/C][C]0.576716834618572[/C][C]90.7473532490222[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 50 )[/C][C]52.6118421052632[/C][C]0.550835841172252[/C][C]95.5127429495113[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 50 )[/C][C]52.6118421052632[/C][C]0.550835841172252[/C][C]95.5127429495113[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 50 )[/C][C]52.3223684210526[/C][C]0.52213149141372[/C][C]100.209179644355[/C][/ROW]
[ROW][C]Winsorized Mean ( 45 / 50 )[/C][C]52.3223684210526[/C][C]0.52213149141372[/C][C]100.209179644355[/C][/ROW]
[ROW][C]Winsorized Mean ( 46 / 50 )[/C][C]52.3223684210526[/C][C]0.52213149141372[/C][C]100.209179644355[/C][/ROW]
[ROW][C]Winsorized Mean ( 47 / 50 )[/C][C]52.3223684210526[/C][C]0.463987330741423[/C][C]112.766804079423[/C][/ROW]
[ROW][C]Winsorized Mean ( 48 / 50 )[/C][C]52.3223684210526[/C][C]0.463987330741423[/C][C]112.766804079423[/C][/ROW]
[ROW][C]Winsorized Mean ( 49 / 50 )[/C][C]52.3223684210526[/C][C]0.463987330741423[/C][C]112.766804079423[/C][/ROW]
[ROW][C]Winsorized Mean ( 50 / 50 )[/C][C]52.3223684210526[/C][C]0.463987330741423[/C][C]112.766804079423[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 50 )[/C][C]52.1133333333333[/C][C]1.05819637472775[/C][C]49.2473179628318[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 50 )[/C][C]52.1554054054054[/C][C]1.03010007411845[/C][C]50.631396614586[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 50 )[/C][C]52.1780821917808[/C][C]1.00399226386252[/C][C]51.9706018361571[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 50 )[/C][C]52.1736111111111[/C][C]0.983909488133079[/C][C]53.0268401111855[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 50 )[/C][C]52.1830985915493[/C][C]0.964695946780268[/C][C]54.0927934503235[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 50 )[/C][C]52.2071428571429[/C][C]0.946323900046773[/C][C]55.1683655612655[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 50 )[/C][C]52.2173913043478[/C][C]0.929137350482733[/C][C]56.1998624608281[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 50 )[/C][C]52.2352941176471[/C][C]0.91169090993788[/C][C]57.2949598907443[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 50 )[/C][C]52.2388059701493[/C][C]0.895516776999591[/C][C]58.3336988338445[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 50 )[/C][C]52.25[/C][C]0.881963550215837[/C][C]59.2428110971403[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 50 )[/C][C]52.2692307692308[/C][C]0.868434630469527[/C][C]60.187870146278[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 50 )[/C][C]52.2890625[/C][C]0.856393303985368[/C][C]61.0572995569491[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 50 )[/C][C]52.2936507936508[/C][C]0.846060334845596[/C][C]61.8084179577976[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 50 )[/C][C]52.2983870967742[/C][C]0.834681299410334[/C][C]62.6567135668677[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 50 )[/C][C]52.3114754098361[/C][C]0.823552662289691[/C][C]63.5192839573811[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 50 )[/C][C]52.3166666666667[/C][C]0.812798821010489[/C][C]64.366071055105[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 50 )[/C][C]52.3050847457627[/C][C]0.803846726854506[/C][C]65.0684800949993[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 50 )[/C][C]52.301724137931[/C][C]0.795434859576833[/C][C]65.75236615322[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 50 )[/C][C]52.3070175438597[/C][C]0.78756907692027[/C][C]66.415783804517[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 50 )[/C][C]52.3035714285714[/C][C]0.780311879299498[/C][C]67.0290595543995[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 50 )[/C][C]52.3090909090909[/C][C]0.773707370394913[/C][C]67.6083657861388[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 50 )[/C][C]52.3148148148148[/C][C]0.766267916094912[/C][C]68.2722240041366[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 50 )[/C][C]52.3207547169811[/C][C]0.757893137027824[/C][C]69.0344748629916[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 50 )[/C][C]52.3173076923077[/C][C]0.750188478069514[/C][C]69.7388845892937[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 50 )[/C][C]52.3137254901961[/C][C]0.741479837539203[/C][C]70.553132859031[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 50 )[/C][C]52.31[/C][C]0.731636466554203[/C][C]71.4972563442129[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 50 )[/C][C]52.3163265306122[/C][C]0.722427375310082[/C][C]72.4174198245974[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 50 )[/C][C]52.3125[/C][C]0.713945133402261[/C][C]73.2724372679845[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 50 )[/C][C]52.3085106382979[/C][C]0.704274395460192[/C][C]74.2729126253668[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 50 )[/C][C]52.304347826087[/C][C]0.693244160065263[/C][C]75.4486670629334[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 50 )[/C][C]52.3111111111111[/C][C]0.682882274524706[/C][C]76.6034103718979[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 50 )[/C][C]52.3068181818182[/C][C]0.673299932417244[/C][C]77.6872470401551[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 50 )[/C][C]52.3023255813954[/C][C]0.662266094255969[/C][C]78.9747897937536[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 50 )[/C][C]52.2857142857143[/C][C]0.65192495506548[/C][C]80.2020445443182[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 50 )[/C][C]52.2560975609756[/C][C]0.64223782944665[/C][C]81.3656486196076[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 50 )[/C][C]52.2375[/C][C]0.633766056646269[/C][C]82.4239472155195[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 50 )[/C][C]52.2307692307692[/C][C]0.626563466216441[/C][C]83.360700147695[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 50 )[/C][C]52.2105263157895[/C][C]0.620502283658855[/C][C]84.1423596508377[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 50 )[/C][C]52.1891891891892[/C][C]0.613218479213605[/C][C]85.1070066513926[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 50 )[/C][C]52.1666666666667[/C][C]0.604495418084482[/C][C]86.2978694395596[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 50 )[/C][C]52.1428571428571[/C][C]0.594065096810731[/C][C]87.7729686911229[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 50 )[/C][C]52.1323529411765[/C][C]0.585118498674492[/C][C]89.0970855634805[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 50 )[/C][C]52.1060606060606[/C][C]0.57740226385291[/C][C]90.242217372626[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 50 )[/C][C]52.078125[/C][C]0.56795402066827[/C][C]91.6942623959655[/C][/ROW]
[ROW][C]Trimmed Mean ( 45 / 50 )[/C][C]52.0645161290323[/C][C]0.560402782427117[/C][C]92.9055275270755[/C][/ROW]
[ROW][C]Trimmed Mean ( 46 / 50 )[/C][C]52.05[/C][C]0.551026263895674[/C][C]94.4601072769458[/C][/ROW]
[ROW][C]Trimmed Mean ( 47 / 50 )[/C][C]52.0344827586207[/C][C]0.539411925332947[/C][C]96.4652064866806[/C][/ROW]
[ROW][C]Trimmed Mean ( 48 / 50 )[/C][C]52.0178571428571[/C][C]0.533605155491029[/C][C]97.4837979123155[/C][/ROW]
[ROW][C]Trimmed Mean ( 49 / 50 )[/C][C]52[/C][C]0.526050909844691[/C][C]98.8497482408161[/C][/ROW]
[ROW][C]Trimmed Mean ( 50 / 50 )[/C][C]51.9807692307692[/C][C]0.516317732083734[/C][C]100.675932668412[/C][/ROW]
[ROW][C]Median[/C][C]52[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]49[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]52.3544303797468[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]52.3544303797468[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]52.3544303797468[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]52.3544303797468[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]52.3544303797468[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]52.3544303797468[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]52.3544303797468[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]52.3544303797468[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]152[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108060&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108060&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 Mean52.07236842105261.0890989194757747.8123405412221
Geometric Mean50.1266913823368
Harmonic Mean47.8358517275049
Quadratic Mean53.7646552848127
Winsorized Mean ( 1 / 50 )52.07236842105261.0839662099477548.0387376868165
Winsorized Mean ( 2 / 50 )52.11184210526321.0760774161838448.4275957487062
Winsorized Mean ( 3 / 50 )52.19078947368421.0551510835172949.4628591952054
Winsorized Mean ( 4 / 50 )52.13815789473681.0465819044160949.8175610286572
Winsorized Mean ( 5 / 50 )52.07236842105261.0365868015171250.2344505494774
Winsorized Mean ( 6 / 50 )52.15131578947371.0238426321874850.9368472751037
Winsorized Mean ( 7 / 50 )52.10526315789471.0171566712458651.2263888453624
Winsorized Mean ( 8 / 50 )52.21052631578951.0011596438794852.1500508285317
Winsorized Mean ( 9 / 50 )52.15131578947370.97604453653358453.4312870339798
Winsorized Mean ( 10 / 50 )52.08552631578950.96735419790758453.8432834926979
Winsorized Mean ( 11 / 50 )52.08552631578950.9478353132357354.9520845957715
Winsorized Mean ( 12 / 50 )52.24342105263160.92645167947727756.3908752176999
Winsorized Mean ( 13 / 50 )52.24342105263160.92645167947727756.3908752176999
Winsorized Mean ( 14 / 50 )52.15131578947370.9149888466209156.9966683004613
Winsorized Mean ( 15 / 50 )52.250.90225744151175257.9103009806758
Winsorized Mean ( 16 / 50 )52.46052631578950.87662022372224859.844074886882
Winsorized Mean ( 17 / 50 )52.34868421052630.86291370670316460.6650280368462
Winsorized Mean ( 18 / 50 )52.23026315789470.84897732312733761.521387833419
Winsorized Mean ( 19 / 50 )52.35526315789470.83442864611232362.7438468247975
Winsorized Mean ( 20 / 50 )52.22368421052630.81945440496789363.7298230309379
Winsorized Mean ( 21 / 50 )52.22368421052630.81945440496789363.7298230309379
Winsorized Mean ( 22 / 50 )52.22368421052630.81945440496789363.7298230309379
Winsorized Mean ( 23 / 50 )52.3750.80240209365529865.272760893991
Winsorized Mean ( 24 / 50 )52.3750.80240209365529865.272760893991
Winsorized Mean ( 25 / 50 )52.3750.80240209365529865.272760893991
Winsorized Mean ( 26 / 50 )52.20394736842110.78353007660882766.6266030199675
Winsorized Mean ( 27 / 50 )52.38157894736840.76408205362686968.5549133090206
Winsorized Mean ( 28 / 50 )52.38157894736840.76408205362686968.5549133090206
Winsorized Mean ( 29 / 50 )52.38157894736840.76408205362686968.5549133090206
Winsorized Mean ( 30 / 50 )52.18421052631580.74288897111756870.24496601129
Winsorized Mean ( 31 / 50 )52.38815789473680.72114223701795772.6460817374538
Winsorized Mean ( 32 / 50 )52.38815789473680.72114223701795772.6460817374538
Winsorized Mean ( 33 / 50 )52.60526315789470.69887363286748575.2714949941019
Winsorized Mean ( 34 / 50 )52.82894736842110.67687080611124978.0487899484591
Winsorized Mean ( 35 / 50 )52.59868421052630.65211802469078980.6582278345499
Winsorized Mean ( 36 / 50 )52.36184210526320.62755572561398483.4377569482514
Winsorized Mean ( 37 / 50 )52.60526315789470.60403819243249687.089299678304
Winsorized Mean ( 38 / 50 )52.60526315789470.60403819243249687.089299678304
Winsorized Mean ( 39 / 50 )52.60526315789470.60403819243249687.089299678304
Winsorized Mean ( 40 / 50 )52.60526315789470.60403819243249687.089299678304
Winsorized Mean ( 41 / 50 )52.33552631578950.57671683461857290.7473532490222
Winsorized Mean ( 42 / 50 )52.61184210526320.55083584117225295.5127429495113
Winsorized Mean ( 43 / 50 )52.61184210526320.55083584117225295.5127429495113
Winsorized Mean ( 44 / 50 )52.32236842105260.52213149141372100.209179644355
Winsorized Mean ( 45 / 50 )52.32236842105260.52213149141372100.209179644355
Winsorized Mean ( 46 / 50 )52.32236842105260.52213149141372100.209179644355
Winsorized Mean ( 47 / 50 )52.32236842105260.463987330741423112.766804079423
Winsorized Mean ( 48 / 50 )52.32236842105260.463987330741423112.766804079423
Winsorized Mean ( 49 / 50 )52.32236842105260.463987330741423112.766804079423
Winsorized Mean ( 50 / 50 )52.32236842105260.463987330741423112.766804079423
Trimmed Mean ( 1 / 50 )52.11333333333331.0581963747277549.2473179628318
Trimmed Mean ( 2 / 50 )52.15540540540541.0301000741184550.631396614586
Trimmed Mean ( 3 / 50 )52.17808219178081.0039922638625251.9706018361571
Trimmed Mean ( 4 / 50 )52.17361111111110.98390948813307953.0268401111855
Trimmed Mean ( 5 / 50 )52.18309859154930.96469594678026854.0927934503235
Trimmed Mean ( 6 / 50 )52.20714285714290.94632390004677355.1683655612655
Trimmed Mean ( 7 / 50 )52.21739130434780.92913735048273356.1998624608281
Trimmed Mean ( 8 / 50 )52.23529411764710.9116909099378857.2949598907443
Trimmed Mean ( 9 / 50 )52.23880597014930.89551677699959158.3336988338445
Trimmed Mean ( 10 / 50 )52.250.88196355021583759.2428110971403
Trimmed Mean ( 11 / 50 )52.26923076923080.86843463046952760.187870146278
Trimmed Mean ( 12 / 50 )52.28906250.85639330398536861.0572995569491
Trimmed Mean ( 13 / 50 )52.29365079365080.84606033484559661.8084179577976
Trimmed Mean ( 14 / 50 )52.29838709677420.83468129941033462.6567135668677
Trimmed Mean ( 15 / 50 )52.31147540983610.82355266228969163.5192839573811
Trimmed Mean ( 16 / 50 )52.31666666666670.81279882101048964.366071055105
Trimmed Mean ( 17 / 50 )52.30508474576270.80384672685450665.0684800949993
Trimmed Mean ( 18 / 50 )52.3017241379310.79543485957683365.75236615322
Trimmed Mean ( 19 / 50 )52.30701754385970.7875690769202766.415783804517
Trimmed Mean ( 20 / 50 )52.30357142857140.78031187929949867.0290595543995
Trimmed Mean ( 21 / 50 )52.30909090909090.77370737039491367.6083657861388
Trimmed Mean ( 22 / 50 )52.31481481481480.76626791609491268.2722240041366
Trimmed Mean ( 23 / 50 )52.32075471698110.75789313702782469.0344748629916
Trimmed Mean ( 24 / 50 )52.31730769230770.75018847806951469.7388845892937
Trimmed Mean ( 25 / 50 )52.31372549019610.74147983753920370.553132859031
Trimmed Mean ( 26 / 50 )52.310.73163646655420371.4972563442129
Trimmed Mean ( 27 / 50 )52.31632653061220.72242737531008272.4174198245974
Trimmed Mean ( 28 / 50 )52.31250.71394513340226173.2724372679845
Trimmed Mean ( 29 / 50 )52.30851063829790.70427439546019274.2729126253668
Trimmed Mean ( 30 / 50 )52.3043478260870.69324416006526375.4486670629334
Trimmed Mean ( 31 / 50 )52.31111111111110.68288227452470676.6034103718979
Trimmed Mean ( 32 / 50 )52.30681818181820.67329993241724477.6872470401551
Trimmed Mean ( 33 / 50 )52.30232558139540.66226609425596978.9747897937536
Trimmed Mean ( 34 / 50 )52.28571428571430.6519249550654880.2020445443182
Trimmed Mean ( 35 / 50 )52.25609756097560.6422378294466581.3656486196076
Trimmed Mean ( 36 / 50 )52.23750.63376605664626982.4239472155195
Trimmed Mean ( 37 / 50 )52.23076923076920.62656346621644183.360700147695
Trimmed Mean ( 38 / 50 )52.21052631578950.62050228365885584.1423596508377
Trimmed Mean ( 39 / 50 )52.18918918918920.61321847921360585.1070066513926
Trimmed Mean ( 40 / 50 )52.16666666666670.60449541808448286.2978694395596
Trimmed Mean ( 41 / 50 )52.14285714285710.59406509681073187.7729686911229
Trimmed Mean ( 42 / 50 )52.13235294117650.58511849867449289.0970855634805
Trimmed Mean ( 43 / 50 )52.10606060606060.5774022638529190.242217372626
Trimmed Mean ( 44 / 50 )52.0781250.5679540206682791.6942623959655
Trimmed Mean ( 45 / 50 )52.06451612903230.56040278242711792.9055275270755
Trimmed Mean ( 46 / 50 )52.050.55102626389567494.4601072769458
Trimmed Mean ( 47 / 50 )52.03448275862070.53941192533294796.4652064866806
Trimmed Mean ( 48 / 50 )52.01785714285710.53360515549102997.4837979123155
Trimmed Mean ( 49 / 50 )520.52605090984469198.8497482408161
Trimmed Mean ( 50 / 50 )51.98076923076920.516317732083734100.675932668412
Median52
Midrange49
Midmean - Weighted Average at Xnp52.3544303797468
Midmean - Weighted Average at X(n+1)p52.3544303797468
Midmean - Empirical Distribution Function52.3544303797468
Midmean - Empirical Distribution Function - Averaging52.3544303797468
Midmean - Empirical Distribution Function - Interpolation52.3544303797468
Midmean - Closest Observation52.3544303797468
Midmean - True Basic - Statistics Graphics Toolkit52.3544303797468
Midmean - MS Excel (old versions)52.3544303797468
Number of observations152



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')