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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 computationMon, 14 Nov 2011 13:14:12 -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/14/t132129447976aw0ont6c5gbv9.htm/, Retrieved Fri, 29 Mar 2024 11:19:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=142155, Retrieved Fri, 29 Mar 2024 11:19:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact76
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Time needed to su...] [2010-09-25 09:42:08] [b98453cac15ba1066b407e146608df68]
- R  D    [Central Tendency] [] [2011-11-14 18:14:12] [87b6e955a128bfb8d1e350b3ce0d281e] [Current]
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Dataseries X:
14.69
20.15
11.78
21.47
17.54
21.47
18.55
14.33
8.78
17.66
19.64
13.25
16.17
9.66
20.45
24.21
19.65
21.33
14.47
16.22
16.66
19.87
14.55
19.41
20.63
9.12
8.36
19.36
25.78
14.66
27.55
22.63
30.33
22.22
11.99
9.47
10.33
15.36
14.99
17.31
18.94
16.54
18.21
11.74
17.41
9.99
21.14
19.70
14.87
19.65
27.65
13.45
20.00
13.47
18.54
20.00
11.47
28.65
24.14
19.87
17.65
13.69
15.47
11.63
10.24
13.54
11.00
19.74
21.25
29.54
11.41
10.87
8.47
12.69
10.14
18.63
22.54
17.65
16.41
17.65
19.87
21.45
22.65
20.69
23.74
20.96
18.35
17.84
20.54
21.63
27.61
19.47
23.52
25.64
19.33
20.64
18.98
15.67
23.74
22.89
24.66
29.40
19.87
17.55
15.94
21.74
23.51
24.84
18.47
21.01
16.74
27.45
19.54
17.74
21.65
24.74
26.89
23.22
20.16
21.88




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=142155&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=142155&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=142155&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 time1 seconds
R Server'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean18.58250.46450796608909140.0046960581855
Geometric Mean17.8279919459628
Harmonic Mean17.0043489348149
Quadratic Mean19.260987946278
Winsorized Mean ( 1 / 40 )18.57683333333330.46298450257704940.1240932038364
Winsorized Mean ( 2 / 40 )18.57966666666670.46158773202979640.2516474711406
Winsorized Mean ( 3 / 40 )18.56941666666670.45650310861694840.6775251168076
Winsorized Mean ( 4 / 40 )18.547750.44855920079477541.3496144257801
Winsorized Mean ( 5 / 40 )18.5540.44694008521938441.5133943309037
Winsorized Mean ( 6 / 40 )18.56750.44370955451455741.846067570742
Winsorized Mean ( 7 / 40 )18.57041666666670.44130714286016542.080480606567
Winsorized Mean ( 8 / 40 )18.539750.43406139219225342.7122760362627
Winsorized Mean ( 9 / 40 )18.463250.42013908532223743.9455662303808
Winsorized Mean ( 10 / 40 )18.49658333333330.41126583468162944.9747627289585
Winsorized Mean ( 11 / 40 )18.43516666666670.39910179235745346.1916408788145
Winsorized Mean ( 12 / 40 )18.46616666666670.3914383657286747.1751577858024
Winsorized Mean ( 13 / 40 )18.4640.38929215372568347.429674149073
Winsorized Mean ( 14 / 40 )18.43016666666670.37960655186700248.5507075049743
Winsorized Mean ( 15 / 40 )18.43516666666670.37642706956613548.9740726880105
Winsorized Mean ( 16 / 40 )18.38716666666670.36897877811894249.8325859292088
Winsorized Mean ( 17 / 40 )18.41691666666670.36453644244274750.5214692480551
Winsorized Mean ( 18 / 40 )18.48891666666670.34529406936610253.5454220242155
Winsorized Mean ( 19 / 40 )18.5760.33287573071769655.804609005136
Winsorized Mean ( 20 / 40 )18.5610.32246923289279157.5589796071207
Winsorized Mean ( 21 / 40 )18.506750.31511869540202958.7294574077525
Winsorized Mean ( 22 / 40 )18.47558333333330.30831828555528459.9237353050878
Winsorized Mean ( 23 / 40 )18.50050.30403626612760.8496487464166
Winsorized Mean ( 24 / 40 )18.61050.28537779888288165.2135522554708
Winsorized Mean ( 25 / 40 )18.5730.27411889914478267.7552699136962
Winsorized Mean ( 26 / 40 )18.51666666666670.26386744224609870.1741242081582
Winsorized Mean ( 27 / 40 )18.50991666666670.25740045248375671.9109717487183
Winsorized Mean ( 28 / 40 )18.49591666666670.25431876091733572.7272993936876
Winsorized Mean ( 29 / 40 )18.53458333333330.24838153694835274.6214213868376
Winsorized Mean ( 30 / 40 )18.52458333333330.2405159864074677.02017487499
Winsorized Mean ( 31 / 40 )18.62016666666670.22888916939736181.3501430220201
Winsorized Mean ( 32 / 40 )18.64416666666670.22483487820097982.9238186523745
Winsorized Mean ( 33 / 40 )18.66616666666670.21490018474265686.8597050720059
Winsorized Mean ( 34 / 40 )18.720.20366525922485291.9155288007791
Winsorized Mean ( 35 / 40 )18.7550.1926915359096197.331727164175
Winsorized Mean ( 36 / 40 )18.7310.186973627164106100.179903893932
Winsorized Mean ( 37 / 40 )18.77416666666670.178831430232055104.982477869271
Winsorized Mean ( 38 / 40 )18.72983333333330.165609264046435113.096531411924
Winsorized Mean ( 39 / 40 )18.75258333333330.159679497614597117.438892365472
Winsorized Mean ( 40 / 40 )18.77591666666670.15642117495805120.034366649542
Trimmed Mean ( 1 / 40 )18.56957627118640.45344138399139740.9525396815981
Trimmed Mean ( 2 / 40 )18.56206896551720.44285777203916541.9142897279348
Trimmed Mean ( 3 / 40 )18.55280701754390.43191294162609542.9549689983703
Trimmed Mean ( 4 / 40 )18.5468750.42183281284847543.9673596626116
Trimmed Mean ( 5 / 40 )18.54663636363640.4131824710906344.8872778041163
Trimmed Mean ( 6 / 40 )18.5450.40396664875412945.9072551092881
Trimmed Mean ( 7 / 40 )18.54075471698110.39442803103254347.0066862855683
Trimmed Mean ( 8 / 40 )18.53586538461540.38424719108527748.2394297594271
Trimmed Mean ( 9 / 40 )18.53529411764710.37425522251005449.5258128753276
Trimmed Mean ( 10 / 40 )18.54490.36558353782865250.7268464826005
Trimmed Mean ( 11 / 40 )18.55081632653060.35734900305237251.9123214786522
Trimmed Mean ( 12 / 40 )18.56395833333330.35001799700492453.0371537811873
Trimmed Mean ( 13 / 40 )18.57436170212770.34291570661972154.1659694891894
Trimmed Mean ( 14 / 40 )18.58543478260870.33516329473652155.4518799477105
Trimmed Mean ( 15 / 40 )18.60022222222220.32774918007242556.7513920801023
Trimmed Mean ( 16 / 40 )18.61522727272730.3197313877707858.2214570878252
Trimmed Mean ( 17 / 40 )18.63511627906980.31157363902594559.809669191937
Trimmed Mean ( 18 / 40 )18.65345238095240.30283502161558861.5960871415679
Trimmed Mean ( 19 / 40 )18.66682926829270.29553914609217763.161951691065
Trimmed Mean ( 20 / 40 )18.6740.28885750505716264.6477923303555
Trimmed Mean ( 21 / 40 )18.68269230769230.28251585305725566.1297130958029
Trimmed Mean ( 22 / 40 )18.69592105263160.27608898753790367.7170111685997
Trimmed Mean ( 23 / 40 )18.71216216216220.26946456914970769.4420131789802
Trimmed Mean ( 24 / 40 )18.72750.26227939907060771.4028630016742
Trimmed Mean ( 25 / 40 )18.73585714285710.25650094078479473.044009450931
Trimmed Mean ( 26 / 40 )18.74735294117650.25117508013341874.6385864840507
Trimmed Mean ( 27 / 40 )18.76348484848480.24617573767394776.2198786353859
Trimmed Mean ( 28 / 40 )18.781093750.2410432349814777.9158716130065
Trimmed Mean ( 29 / 40 )18.80080645161290.23523274008699679.9242760368296
Trimmed Mean ( 30 / 40 )18.81916666666670.22909738038371782.1448356814306
Trimmed Mean ( 31 / 40 )18.83948275862070.22278396134138984.5639095614765
Trimmed Mean ( 32 / 40 )18.85464285714290.21700918112807586.8840790934795
Trimmed Mean ( 33 / 40 )18.86925925925930.21052260217701889.6305625340552
Trimmed Mean ( 34 / 40 )18.88346153846150.20416309775229992.4920406594335
Trimmed Mean ( 35 / 40 )18.8950.19822791458936695.3195721154685
Trimmed Mean ( 36 / 40 )18.9050.19273208354700398.089532640732
Trimmed Mean ( 37 / 40 )18.91760869565220.18669906157376101.326747634338
Trimmed Mean ( 38 / 40 )18.92818181818180.18056853855821104.825469427388
Trimmed Mean ( 39 / 40 )18.94309523809520.175224922022916108.107311559356
Trimmed Mean ( 40 / 40 )18.957750.169409414376791111.904937926503
Median19.345
Midrange19.345
Midmean - Weighted Average at Xnp18.7544262295082
Midmean - Weighted Average at X(n+1)p18.8191666666667
Midmean - Empirical Distribution Function18.7544262295082
Midmean - Empirical Distribution Function - Averaging18.8191666666667
Midmean - Empirical Distribution Function - Interpolation18.8191666666667
Midmean - Closest Observation18.7544262295082
Midmean - True Basic - Statistics Graphics Toolkit18.8191666666667
Midmean - MS Excel (old versions)18.8008064516129
Number of observations120

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 18.5825 & 0.464507966089091 & 40.0046960581855 \tabularnewline
Geometric Mean & 17.8279919459628 &  &  \tabularnewline
Harmonic Mean & 17.0043489348149 &  &  \tabularnewline
Quadratic Mean & 19.260987946278 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 18.5768333333333 & 0.462984502577049 & 40.1240932038364 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 18.5796666666667 & 0.461587732029796 & 40.2516474711406 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 18.5694166666667 & 0.456503108616948 & 40.6775251168076 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 18.54775 & 0.448559200794775 & 41.3496144257801 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 18.554 & 0.446940085219384 & 41.5133943309037 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 18.5675 & 0.443709554514557 & 41.846067570742 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 18.5704166666667 & 0.441307142860165 & 42.080480606567 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 18.53975 & 0.434061392192253 & 42.7122760362627 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 18.46325 & 0.420139085322237 & 43.9455662303808 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 18.4965833333333 & 0.411265834681629 & 44.9747627289585 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 18.4351666666667 & 0.399101792357453 & 46.1916408788145 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 18.4661666666667 & 0.39143836572867 & 47.1751577858024 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 18.464 & 0.389292153725683 & 47.429674149073 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 18.4301666666667 & 0.379606551867002 & 48.5507075049743 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 18.4351666666667 & 0.376427069566135 & 48.9740726880105 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 18.3871666666667 & 0.368978778118942 & 49.8325859292088 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 18.4169166666667 & 0.364536442442747 & 50.5214692480551 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 18.4889166666667 & 0.345294069366102 & 53.5454220242155 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 18.576 & 0.332875730717696 & 55.804609005136 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 18.561 & 0.322469232892791 & 57.5589796071207 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 18.50675 & 0.315118695402029 & 58.7294574077525 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 18.4755833333333 & 0.308318285555284 & 59.9237353050878 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 18.5005 & 0.304036266127 & 60.8496487464166 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 18.6105 & 0.285377798882881 & 65.2135522554708 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 18.573 & 0.274118899144782 & 67.7552699136962 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 18.5166666666667 & 0.263867442246098 & 70.1741242081582 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 18.5099166666667 & 0.257400452483756 & 71.9109717487183 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 18.4959166666667 & 0.254318760917335 & 72.7272993936876 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 18.5345833333333 & 0.248381536948352 & 74.6214213868376 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 18.5245833333333 & 0.24051598640746 & 77.02017487499 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 18.6201666666667 & 0.228889169397361 & 81.3501430220201 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 18.6441666666667 & 0.224834878200979 & 82.9238186523745 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 18.6661666666667 & 0.214900184742656 & 86.8597050720059 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 18.72 & 0.203665259224852 & 91.9155288007791 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 18.755 & 0.19269153590961 & 97.331727164175 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 18.731 & 0.186973627164106 & 100.179903893932 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 18.7741666666667 & 0.178831430232055 & 104.982477869271 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 18.7298333333333 & 0.165609264046435 & 113.096531411924 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 18.7525833333333 & 0.159679497614597 & 117.438892365472 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 18.7759166666667 & 0.15642117495805 & 120.034366649542 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 18.5695762711864 & 0.453441383991397 & 40.9525396815981 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 18.5620689655172 & 0.442857772039165 & 41.9142897279348 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 18.5528070175439 & 0.431912941626095 & 42.9549689983703 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 18.546875 & 0.421832812848475 & 43.9673596626116 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 18.5466363636364 & 0.41318247109063 & 44.8872778041163 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 18.545 & 0.403966648754129 & 45.9072551092881 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 18.5407547169811 & 0.394428031032543 & 47.0066862855683 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 18.5358653846154 & 0.384247191085277 & 48.2394297594271 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 18.5352941176471 & 0.374255222510054 & 49.5258128753276 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 18.5449 & 0.365583537828652 & 50.7268464826005 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 18.5508163265306 & 0.357349003052372 & 51.9123214786522 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 18.5639583333333 & 0.350017997004924 & 53.0371537811873 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 18.5743617021277 & 0.342915706619721 & 54.1659694891894 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 18.5854347826087 & 0.335163294736521 & 55.4518799477105 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 18.6002222222222 & 0.327749180072425 & 56.7513920801023 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 18.6152272727273 & 0.31973138777078 & 58.2214570878252 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 18.6351162790698 & 0.311573639025945 & 59.809669191937 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 18.6534523809524 & 0.302835021615588 & 61.5960871415679 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 18.6668292682927 & 0.295539146092177 & 63.161951691065 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 18.674 & 0.288857505057162 & 64.6477923303555 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 18.6826923076923 & 0.282515853057255 & 66.1297130958029 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 18.6959210526316 & 0.276088987537903 & 67.7170111685997 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 18.7121621621622 & 0.269464569149707 & 69.4420131789802 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 18.7275 & 0.262279399070607 & 71.4028630016742 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 18.7358571428571 & 0.256500940784794 & 73.044009450931 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 18.7473529411765 & 0.251175080133418 & 74.6385864840507 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 18.7634848484848 & 0.246175737673947 & 76.2198786353859 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 18.78109375 & 0.24104323498147 & 77.9158716130065 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 18.8008064516129 & 0.235232740086996 & 79.9242760368296 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 18.8191666666667 & 0.229097380383717 & 82.1448356814306 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 18.8394827586207 & 0.222783961341389 & 84.5639095614765 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 18.8546428571429 & 0.217009181128075 & 86.8840790934795 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 18.8692592592593 & 0.210522602177018 & 89.6305625340552 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 18.8834615384615 & 0.204163097752299 & 92.4920406594335 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 18.895 & 0.198227914589366 & 95.3195721154685 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 18.905 & 0.192732083547003 & 98.089532640732 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 18.9176086956522 & 0.18669906157376 & 101.326747634338 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 18.9281818181818 & 0.18056853855821 & 104.825469427388 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 18.9430952380952 & 0.175224922022916 & 108.107311559356 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 18.95775 & 0.169409414376791 & 111.904937926503 \tabularnewline
Median & 19.345 &  &  \tabularnewline
Midrange & 19.345 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 18.7544262295082 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 18.8191666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 18.7544262295082 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 18.8191666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 18.8191666666667 &  &  \tabularnewline
Midmean - Closest Observation & 18.7544262295082 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 18.8191666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 18.8008064516129 &  &  \tabularnewline
Number of observations & 120 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=142155&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]18.5825[/C][C]0.464507966089091[/C][C]40.0046960581855[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]17.8279919459628[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]17.0043489348149[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]19.260987946278[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]18.5768333333333[/C][C]0.462984502577049[/C][C]40.1240932038364[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]18.5796666666667[/C][C]0.461587732029796[/C][C]40.2516474711406[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]18.5694166666667[/C][C]0.456503108616948[/C][C]40.6775251168076[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]18.54775[/C][C]0.448559200794775[/C][C]41.3496144257801[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]18.554[/C][C]0.446940085219384[/C][C]41.5133943309037[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]18.5675[/C][C]0.443709554514557[/C][C]41.846067570742[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]18.5704166666667[/C][C]0.441307142860165[/C][C]42.080480606567[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]18.53975[/C][C]0.434061392192253[/C][C]42.7122760362627[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]18.46325[/C][C]0.420139085322237[/C][C]43.9455662303808[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]18.4965833333333[/C][C]0.411265834681629[/C][C]44.9747627289585[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]18.4351666666667[/C][C]0.399101792357453[/C][C]46.1916408788145[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]18.4661666666667[/C][C]0.39143836572867[/C][C]47.1751577858024[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]18.464[/C][C]0.389292153725683[/C][C]47.429674149073[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]18.4301666666667[/C][C]0.379606551867002[/C][C]48.5507075049743[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]18.4351666666667[/C][C]0.376427069566135[/C][C]48.9740726880105[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]18.3871666666667[/C][C]0.368978778118942[/C][C]49.8325859292088[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]18.4169166666667[/C][C]0.364536442442747[/C][C]50.5214692480551[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]18.4889166666667[/C][C]0.345294069366102[/C][C]53.5454220242155[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]18.576[/C][C]0.332875730717696[/C][C]55.804609005136[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]18.561[/C][C]0.322469232892791[/C][C]57.5589796071207[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]18.50675[/C][C]0.315118695402029[/C][C]58.7294574077525[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]18.4755833333333[/C][C]0.308318285555284[/C][C]59.9237353050878[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]18.5005[/C][C]0.304036266127[/C][C]60.8496487464166[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]18.6105[/C][C]0.285377798882881[/C][C]65.2135522554708[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]18.573[/C][C]0.274118899144782[/C][C]67.7552699136962[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]18.5166666666667[/C][C]0.263867442246098[/C][C]70.1741242081582[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]18.5099166666667[/C][C]0.257400452483756[/C][C]71.9109717487183[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]18.4959166666667[/C][C]0.254318760917335[/C][C]72.7272993936876[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]18.5345833333333[/C][C]0.248381536948352[/C][C]74.6214213868376[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]18.5245833333333[/C][C]0.24051598640746[/C][C]77.02017487499[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]18.6201666666667[/C][C]0.228889169397361[/C][C]81.3501430220201[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]18.6441666666667[/C][C]0.224834878200979[/C][C]82.9238186523745[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]18.6661666666667[/C][C]0.214900184742656[/C][C]86.8597050720059[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]18.72[/C][C]0.203665259224852[/C][C]91.9155288007791[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]18.755[/C][C]0.19269153590961[/C][C]97.331727164175[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]18.731[/C][C]0.186973627164106[/C][C]100.179903893932[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]18.7741666666667[/C][C]0.178831430232055[/C][C]104.982477869271[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]18.7298333333333[/C][C]0.165609264046435[/C][C]113.096531411924[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]18.7525833333333[/C][C]0.159679497614597[/C][C]117.438892365472[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]18.7759166666667[/C][C]0.15642117495805[/C][C]120.034366649542[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]18.5695762711864[/C][C]0.453441383991397[/C][C]40.9525396815981[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]18.5620689655172[/C][C]0.442857772039165[/C][C]41.9142897279348[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]18.5528070175439[/C][C]0.431912941626095[/C][C]42.9549689983703[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]18.546875[/C][C]0.421832812848475[/C][C]43.9673596626116[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]18.5466363636364[/C][C]0.41318247109063[/C][C]44.8872778041163[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]18.545[/C][C]0.403966648754129[/C][C]45.9072551092881[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]18.5407547169811[/C][C]0.394428031032543[/C][C]47.0066862855683[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]18.5358653846154[/C][C]0.384247191085277[/C][C]48.2394297594271[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]18.5352941176471[/C][C]0.374255222510054[/C][C]49.5258128753276[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]18.5449[/C][C]0.365583537828652[/C][C]50.7268464826005[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]18.5508163265306[/C][C]0.357349003052372[/C][C]51.9123214786522[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]18.5639583333333[/C][C]0.350017997004924[/C][C]53.0371537811873[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]18.5743617021277[/C][C]0.342915706619721[/C][C]54.1659694891894[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]18.5854347826087[/C][C]0.335163294736521[/C][C]55.4518799477105[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]18.6002222222222[/C][C]0.327749180072425[/C][C]56.7513920801023[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]18.6152272727273[/C][C]0.31973138777078[/C][C]58.2214570878252[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]18.6351162790698[/C][C]0.311573639025945[/C][C]59.809669191937[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]18.6534523809524[/C][C]0.302835021615588[/C][C]61.5960871415679[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]18.6668292682927[/C][C]0.295539146092177[/C][C]63.161951691065[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]18.674[/C][C]0.288857505057162[/C][C]64.6477923303555[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]18.6826923076923[/C][C]0.282515853057255[/C][C]66.1297130958029[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]18.6959210526316[/C][C]0.276088987537903[/C][C]67.7170111685997[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]18.7121621621622[/C][C]0.269464569149707[/C][C]69.4420131789802[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]18.7275[/C][C]0.262279399070607[/C][C]71.4028630016742[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]18.7358571428571[/C][C]0.256500940784794[/C][C]73.044009450931[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]18.7473529411765[/C][C]0.251175080133418[/C][C]74.6385864840507[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]18.7634848484848[/C][C]0.246175737673947[/C][C]76.2198786353859[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]18.78109375[/C][C]0.24104323498147[/C][C]77.9158716130065[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]18.8008064516129[/C][C]0.235232740086996[/C][C]79.9242760368296[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]18.8191666666667[/C][C]0.229097380383717[/C][C]82.1448356814306[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]18.8394827586207[/C][C]0.222783961341389[/C][C]84.5639095614765[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]18.8546428571429[/C][C]0.217009181128075[/C][C]86.8840790934795[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]18.8692592592593[/C][C]0.210522602177018[/C][C]89.6305625340552[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]18.8834615384615[/C][C]0.204163097752299[/C][C]92.4920406594335[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]18.895[/C][C]0.198227914589366[/C][C]95.3195721154685[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]18.905[/C][C]0.192732083547003[/C][C]98.089532640732[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]18.9176086956522[/C][C]0.18669906157376[/C][C]101.326747634338[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]18.9281818181818[/C][C]0.18056853855821[/C][C]104.825469427388[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]18.9430952380952[/C][C]0.175224922022916[/C][C]108.107311559356[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]18.95775[/C][C]0.169409414376791[/C][C]111.904937926503[/C][/ROW]
[ROW][C]Median[/C][C]19.345[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]19.345[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]18.7544262295082[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]18.8191666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]18.7544262295082[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]18.8191666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]18.8191666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]18.7544262295082[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]18.8191666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]18.8008064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]120[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=142155&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=142155&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 Mean18.58250.46450796608909140.0046960581855
Geometric Mean17.8279919459628
Harmonic Mean17.0043489348149
Quadratic Mean19.260987946278
Winsorized Mean ( 1 / 40 )18.57683333333330.46298450257704940.1240932038364
Winsorized Mean ( 2 / 40 )18.57966666666670.46158773202979640.2516474711406
Winsorized Mean ( 3 / 40 )18.56941666666670.45650310861694840.6775251168076
Winsorized Mean ( 4 / 40 )18.547750.44855920079477541.3496144257801
Winsorized Mean ( 5 / 40 )18.5540.44694008521938441.5133943309037
Winsorized Mean ( 6 / 40 )18.56750.44370955451455741.846067570742
Winsorized Mean ( 7 / 40 )18.57041666666670.44130714286016542.080480606567
Winsorized Mean ( 8 / 40 )18.539750.43406139219225342.7122760362627
Winsorized Mean ( 9 / 40 )18.463250.42013908532223743.9455662303808
Winsorized Mean ( 10 / 40 )18.49658333333330.41126583468162944.9747627289585
Winsorized Mean ( 11 / 40 )18.43516666666670.39910179235745346.1916408788145
Winsorized Mean ( 12 / 40 )18.46616666666670.3914383657286747.1751577858024
Winsorized Mean ( 13 / 40 )18.4640.38929215372568347.429674149073
Winsorized Mean ( 14 / 40 )18.43016666666670.37960655186700248.5507075049743
Winsorized Mean ( 15 / 40 )18.43516666666670.37642706956613548.9740726880105
Winsorized Mean ( 16 / 40 )18.38716666666670.36897877811894249.8325859292088
Winsorized Mean ( 17 / 40 )18.41691666666670.36453644244274750.5214692480551
Winsorized Mean ( 18 / 40 )18.48891666666670.34529406936610253.5454220242155
Winsorized Mean ( 19 / 40 )18.5760.33287573071769655.804609005136
Winsorized Mean ( 20 / 40 )18.5610.32246923289279157.5589796071207
Winsorized Mean ( 21 / 40 )18.506750.31511869540202958.7294574077525
Winsorized Mean ( 22 / 40 )18.47558333333330.30831828555528459.9237353050878
Winsorized Mean ( 23 / 40 )18.50050.30403626612760.8496487464166
Winsorized Mean ( 24 / 40 )18.61050.28537779888288165.2135522554708
Winsorized Mean ( 25 / 40 )18.5730.27411889914478267.7552699136962
Winsorized Mean ( 26 / 40 )18.51666666666670.26386744224609870.1741242081582
Winsorized Mean ( 27 / 40 )18.50991666666670.25740045248375671.9109717487183
Winsorized Mean ( 28 / 40 )18.49591666666670.25431876091733572.7272993936876
Winsorized Mean ( 29 / 40 )18.53458333333330.24838153694835274.6214213868376
Winsorized Mean ( 30 / 40 )18.52458333333330.2405159864074677.02017487499
Winsorized Mean ( 31 / 40 )18.62016666666670.22888916939736181.3501430220201
Winsorized Mean ( 32 / 40 )18.64416666666670.22483487820097982.9238186523745
Winsorized Mean ( 33 / 40 )18.66616666666670.21490018474265686.8597050720059
Winsorized Mean ( 34 / 40 )18.720.20366525922485291.9155288007791
Winsorized Mean ( 35 / 40 )18.7550.1926915359096197.331727164175
Winsorized Mean ( 36 / 40 )18.7310.186973627164106100.179903893932
Winsorized Mean ( 37 / 40 )18.77416666666670.178831430232055104.982477869271
Winsorized Mean ( 38 / 40 )18.72983333333330.165609264046435113.096531411924
Winsorized Mean ( 39 / 40 )18.75258333333330.159679497614597117.438892365472
Winsorized Mean ( 40 / 40 )18.77591666666670.15642117495805120.034366649542
Trimmed Mean ( 1 / 40 )18.56957627118640.45344138399139740.9525396815981
Trimmed Mean ( 2 / 40 )18.56206896551720.44285777203916541.9142897279348
Trimmed Mean ( 3 / 40 )18.55280701754390.43191294162609542.9549689983703
Trimmed Mean ( 4 / 40 )18.5468750.42183281284847543.9673596626116
Trimmed Mean ( 5 / 40 )18.54663636363640.4131824710906344.8872778041163
Trimmed Mean ( 6 / 40 )18.5450.40396664875412945.9072551092881
Trimmed Mean ( 7 / 40 )18.54075471698110.39442803103254347.0066862855683
Trimmed Mean ( 8 / 40 )18.53586538461540.38424719108527748.2394297594271
Trimmed Mean ( 9 / 40 )18.53529411764710.37425522251005449.5258128753276
Trimmed Mean ( 10 / 40 )18.54490.36558353782865250.7268464826005
Trimmed Mean ( 11 / 40 )18.55081632653060.35734900305237251.9123214786522
Trimmed Mean ( 12 / 40 )18.56395833333330.35001799700492453.0371537811873
Trimmed Mean ( 13 / 40 )18.57436170212770.34291570661972154.1659694891894
Trimmed Mean ( 14 / 40 )18.58543478260870.33516329473652155.4518799477105
Trimmed Mean ( 15 / 40 )18.60022222222220.32774918007242556.7513920801023
Trimmed Mean ( 16 / 40 )18.61522727272730.3197313877707858.2214570878252
Trimmed Mean ( 17 / 40 )18.63511627906980.31157363902594559.809669191937
Trimmed Mean ( 18 / 40 )18.65345238095240.30283502161558861.5960871415679
Trimmed Mean ( 19 / 40 )18.66682926829270.29553914609217763.161951691065
Trimmed Mean ( 20 / 40 )18.6740.28885750505716264.6477923303555
Trimmed Mean ( 21 / 40 )18.68269230769230.28251585305725566.1297130958029
Trimmed Mean ( 22 / 40 )18.69592105263160.27608898753790367.7170111685997
Trimmed Mean ( 23 / 40 )18.71216216216220.26946456914970769.4420131789802
Trimmed Mean ( 24 / 40 )18.72750.26227939907060771.4028630016742
Trimmed Mean ( 25 / 40 )18.73585714285710.25650094078479473.044009450931
Trimmed Mean ( 26 / 40 )18.74735294117650.25117508013341874.6385864840507
Trimmed Mean ( 27 / 40 )18.76348484848480.24617573767394776.2198786353859
Trimmed Mean ( 28 / 40 )18.781093750.2410432349814777.9158716130065
Trimmed Mean ( 29 / 40 )18.80080645161290.23523274008699679.9242760368296
Trimmed Mean ( 30 / 40 )18.81916666666670.22909738038371782.1448356814306
Trimmed Mean ( 31 / 40 )18.83948275862070.22278396134138984.5639095614765
Trimmed Mean ( 32 / 40 )18.85464285714290.21700918112807586.8840790934795
Trimmed Mean ( 33 / 40 )18.86925925925930.21052260217701889.6305625340552
Trimmed Mean ( 34 / 40 )18.88346153846150.20416309775229992.4920406594335
Trimmed Mean ( 35 / 40 )18.8950.19822791458936695.3195721154685
Trimmed Mean ( 36 / 40 )18.9050.19273208354700398.089532640732
Trimmed Mean ( 37 / 40 )18.91760869565220.18669906157376101.326747634338
Trimmed Mean ( 38 / 40 )18.92818181818180.18056853855821104.825469427388
Trimmed Mean ( 39 / 40 )18.94309523809520.175224922022916108.107311559356
Trimmed Mean ( 40 / 40 )18.957750.169409414376791111.904937926503
Median19.345
Midrange19.345
Midmean - Weighted Average at Xnp18.7544262295082
Midmean - Weighted Average at X(n+1)p18.8191666666667
Midmean - Empirical Distribution Function18.7544262295082
Midmean - Empirical Distribution Function - Averaging18.8191666666667
Midmean - Empirical Distribution Function - Interpolation18.8191666666667
Midmean - Closest Observation18.7544262295082
Midmean - True Basic - Statistics Graphics Toolkit18.8191666666667
Midmean - MS Excel (old versions)18.8008064516129
Number of observations120



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')