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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 01 Jun 2009 05:39:01 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/01/t1243856376crkobxmja089pll.htm/, Retrieved Mon, 13 May 2024 03:00:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=40908, Retrieved Mon, 13 May 2024 03:00:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact99
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Dorien Storms opg...] [2009-06-01 11:39:01] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
65
65,05
65,84
66,6
67,55
68,07
69,06
69,06
69,11
69,29
69,38
69,28
69,75
69,9
70,21
70,48
71,55
72,18
72,64
72,77
72,74
73,13
73,44
73,34
73,34
73,81
74,26
74,72
75,11
75,26
75,89
75,91
76,43
76,56
76,76
76,76
76,56
76,82
77,09
77,51
77,76
77,86
77,89
77,94
77,99
78,17
78,91
78,87
78,88
79,08
79,41
79,51
79,73
80,38
80,56
80,46
80,45
80,58
80,68
80,52
81,49
81,66
81,95
82,3
82,4
83,14
83,17
83,11
83,21
83,33
83,88
83,8
83,73




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40908&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40908&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40908&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean76.04123287671230.609850704875916124.688275784127
Geometric Mean75.8615757274944
Harmonic Mean75.6784703581152
Quadratic Mean76.2171055927179
Winsorized Mean ( 1 / 24 )76.04082191780820.609484110562643124.762599385260
Winsorized Mean ( 2 / 24 )76.06054794520550.603890383700164125.950917580715
Winsorized Mean ( 3 / 24 )76.07534246575340.593912775723098128.091776394489
Winsorized Mean ( 4 / 24 )76.12082191780820.581700413559145130.859150420852
Winsorized Mean ( 5 / 24 )76.1536986301370.574108086852994132.646970795304
Winsorized Mean ( 6 / 24 )76.2326027397260.558463558295059136.504166847444
Winsorized Mean ( 7 / 24 )76.22972602739730.557970132415968136.619724961493
Winsorized Mean ( 8 / 24 )76.1573972602740.544120575271406139.964193087694
Winsorized Mean ( 9 / 24 )76.16602739726030.538416159839942141.463115482831
Winsorized Mean ( 10 / 24 )76.11945205479450.530720049144163143.426750463911
Winsorized Mean ( 11 / 24 )76.08931506849310.521722112126613145.842611037401
Winsorized Mean ( 12 / 24 )76.12219178082190.506850905526321150.186555752082
Winsorized Mean ( 13 / 24 )76.00465753424660.481817576104819157.745713945711
Winsorized Mean ( 14 / 24 )76.04493150684930.468866801715234162.188773503813
Winsorized Mean ( 15 / 24 )76.0963013698630.458801400964503165.858912396282
Winsorized Mean ( 16 / 24 )76.32205479452050.419054616545143182.129134917426
Winsorized Mean ( 17 / 24 )76.4547945205480.39443672675742193.832849058115
Winsorized Mean ( 18 / 24 )76.56575342465750.377347947232225202.904915705128
Winsorized Mean ( 19 / 24 )76.57356164383560.37099927639362206.398142843258
Winsorized Mean ( 20 / 24 )76.4036986301370.345175572802763221.347350885096
Winsorized Mean ( 21 / 24 )76.44397260273970.321767186823348237.575413942715
Winsorized Mean ( 22 / 24 )76.47712328767120.308792295672215247.665257066039
Winsorized Mean ( 23 / 24 )76.37315068493150.295310949598087258.619434155334
Winsorized Mean ( 24 / 24 )76.35013698630140.283560243086563269.255436358876
Trimmed Mean ( 1 / 24 )76.0863380281690.596991257007273127.449668877215
Trimmed Mean ( 2 / 24 )76.13449275362320.582100055566215130.792794169322
Trimmed Mean ( 3 / 24 )76.1747761194030.567884357921099134.137831156791
Trimmed Mean ( 4 / 24 )76.2120.555371246243309137.227126026995
Trimmed Mean ( 5 / 24 )76.23841269841270.544735226783606139.954989047731
Trimmed Mean ( 6 / 24 )76.25868852459020.534150082029091142.766407963290
Trimmed Mean ( 7 / 24 )76.26406779661020.525526766352928145.119283506472
Trimmed Mean ( 8 / 24 )76.2703508771930.514913792144247148.122563506372
Trimmed Mean ( 9 / 24 )76.28909090909090.505009335695771151.064714088868
Trimmed Mean ( 10 / 24 )76.30792452830190.493857432764019154.514075248847
Trimmed Mean ( 11 / 24 )76.33490196078430.481441330495967158.554941434185
Trimmed Mean ( 12 / 24 )76.36816326530610.467603591188407163.318170998682
Trimmed Mean ( 13 / 24 )76.40.453270161204031168.552899659349
Trimmed Mean ( 14 / 24 )76.44933333333330.440106323241982173.706509759233
Trimmed Mean ( 15 / 24 )76.49837209302320.425787125990439179.663421985993
Trimmed Mean ( 16 / 24 )76.54609756097560.409198484554924187.063492290870
Trimmed Mean ( 17 / 24 )76.57230769230770.397213210871039192.773819189936
Trimmed Mean ( 18 / 24 )76.5859459459460.386924125893071197.935307779466
Trimmed Mean ( 19 / 24 )76.58828571428570.376753599730598203.28481471458
Trimmed Mean ( 20 / 24 )76.590.363753058927053210.554930385780
Trimmed Mean ( 21 / 24 )76.6119354838710.352043319473594217.620762122195
Trimmed Mean ( 22 / 24 )76.63206896551720.341549417736647224.365977472123
Trimmed Mean ( 23 / 24 )76.65111111111110.329378821962232.714145537731
Trimmed Mean ( 24 / 24 )76.68640.314288020770757244.000391144196
Median76.76
Midrange74.44
Midmean - Weighted Average at Xnp76.4786111111111
Midmean - Weighted Average at X(n+1)p76.5859459459459
Midmean - Empirical Distribution Function76.5859459459459
Midmean - Empirical Distribution Function - Averaging76.5859459459459
Midmean - Empirical Distribution Function - Interpolation76.5859459459459
Midmean - Closest Observation76.47
Midmean - True Basic - Statistics Graphics Toolkit76.5859459459459
Midmean - MS Excel (old versions)76.5859459459459
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 76.0412328767123 & 0.609850704875916 & 124.688275784127 \tabularnewline
Geometric Mean & 75.8615757274944 &  &  \tabularnewline
Harmonic Mean & 75.6784703581152 &  &  \tabularnewline
Quadratic Mean & 76.2171055927179 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 76.0408219178082 & 0.609484110562643 & 124.762599385260 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 76.0605479452055 & 0.603890383700164 & 125.950917580715 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 76.0753424657534 & 0.593912775723098 & 128.091776394489 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 76.1208219178082 & 0.581700413559145 & 130.859150420852 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 76.153698630137 & 0.574108086852994 & 132.646970795304 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 76.232602739726 & 0.558463558295059 & 136.504166847444 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 76.2297260273973 & 0.557970132415968 & 136.619724961493 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 76.157397260274 & 0.544120575271406 & 139.964193087694 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 76.1660273972603 & 0.538416159839942 & 141.463115482831 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 76.1194520547945 & 0.530720049144163 & 143.426750463911 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 76.0893150684931 & 0.521722112126613 & 145.842611037401 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 76.1221917808219 & 0.506850905526321 & 150.186555752082 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 76.0046575342466 & 0.481817576104819 & 157.745713945711 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 76.0449315068493 & 0.468866801715234 & 162.188773503813 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 76.096301369863 & 0.458801400964503 & 165.858912396282 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 76.3220547945205 & 0.419054616545143 & 182.129134917426 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 76.454794520548 & 0.39443672675742 & 193.832849058115 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 76.5657534246575 & 0.377347947232225 & 202.904915705128 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 76.5735616438356 & 0.37099927639362 & 206.398142843258 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 76.403698630137 & 0.345175572802763 & 221.347350885096 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 76.4439726027397 & 0.321767186823348 & 237.575413942715 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 76.4771232876712 & 0.308792295672215 & 247.665257066039 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 76.3731506849315 & 0.295310949598087 & 258.619434155334 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 76.3501369863014 & 0.283560243086563 & 269.255436358876 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 76.086338028169 & 0.596991257007273 & 127.449668877215 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 76.1344927536232 & 0.582100055566215 & 130.792794169322 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 76.174776119403 & 0.567884357921099 & 134.137831156791 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 76.212 & 0.555371246243309 & 137.227126026995 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 76.2384126984127 & 0.544735226783606 & 139.954989047731 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 76.2586885245902 & 0.534150082029091 & 142.766407963290 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 76.2640677966102 & 0.525526766352928 & 145.119283506472 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 76.270350877193 & 0.514913792144247 & 148.122563506372 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 76.2890909090909 & 0.505009335695771 & 151.064714088868 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 76.3079245283019 & 0.493857432764019 & 154.514075248847 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 76.3349019607843 & 0.481441330495967 & 158.554941434185 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 76.3681632653061 & 0.467603591188407 & 163.318170998682 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 76.4 & 0.453270161204031 & 168.552899659349 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 76.4493333333333 & 0.440106323241982 & 173.706509759233 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 76.4983720930232 & 0.425787125990439 & 179.663421985993 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 76.5460975609756 & 0.409198484554924 & 187.063492290870 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 76.5723076923077 & 0.397213210871039 & 192.773819189936 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 76.585945945946 & 0.386924125893071 & 197.935307779466 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 76.5882857142857 & 0.376753599730598 & 203.28481471458 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 76.59 & 0.363753058927053 & 210.554930385780 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 76.611935483871 & 0.352043319473594 & 217.620762122195 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 76.6320689655172 & 0.341549417736647 & 224.365977472123 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 76.6511111111111 & 0.329378821962 & 232.714145537731 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 76.6864 & 0.314288020770757 & 244.000391144196 \tabularnewline
Median & 76.76 &  &  \tabularnewline
Midrange & 74.44 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 76.4786111111111 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 76.5859459459459 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 76.5859459459459 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 76.5859459459459 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 76.5859459459459 &  &  \tabularnewline
Midmean - Closest Observation & 76.47 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 76.5859459459459 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 76.5859459459459 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40908&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]76.0412328767123[/C][C]0.609850704875916[/C][C]124.688275784127[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]75.8615757274944[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]75.6784703581152[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]76.2171055927179[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]76.0408219178082[/C][C]0.609484110562643[/C][C]124.762599385260[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]76.0605479452055[/C][C]0.603890383700164[/C][C]125.950917580715[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]76.0753424657534[/C][C]0.593912775723098[/C][C]128.091776394489[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]76.1208219178082[/C][C]0.581700413559145[/C][C]130.859150420852[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]76.153698630137[/C][C]0.574108086852994[/C][C]132.646970795304[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]76.232602739726[/C][C]0.558463558295059[/C][C]136.504166847444[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]76.2297260273973[/C][C]0.557970132415968[/C][C]136.619724961493[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]76.157397260274[/C][C]0.544120575271406[/C][C]139.964193087694[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]76.1660273972603[/C][C]0.538416159839942[/C][C]141.463115482831[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]76.1194520547945[/C][C]0.530720049144163[/C][C]143.426750463911[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]76.0893150684931[/C][C]0.521722112126613[/C][C]145.842611037401[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]76.1221917808219[/C][C]0.506850905526321[/C][C]150.186555752082[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]76.0046575342466[/C][C]0.481817576104819[/C][C]157.745713945711[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]76.0449315068493[/C][C]0.468866801715234[/C][C]162.188773503813[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]76.096301369863[/C][C]0.458801400964503[/C][C]165.858912396282[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]76.3220547945205[/C][C]0.419054616545143[/C][C]182.129134917426[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]76.454794520548[/C][C]0.39443672675742[/C][C]193.832849058115[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]76.5657534246575[/C][C]0.377347947232225[/C][C]202.904915705128[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]76.5735616438356[/C][C]0.37099927639362[/C][C]206.398142843258[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]76.403698630137[/C][C]0.345175572802763[/C][C]221.347350885096[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]76.4439726027397[/C][C]0.321767186823348[/C][C]237.575413942715[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]76.4771232876712[/C][C]0.308792295672215[/C][C]247.665257066039[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]76.3731506849315[/C][C]0.295310949598087[/C][C]258.619434155334[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]76.3501369863014[/C][C]0.283560243086563[/C][C]269.255436358876[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]76.086338028169[/C][C]0.596991257007273[/C][C]127.449668877215[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]76.1344927536232[/C][C]0.582100055566215[/C][C]130.792794169322[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]76.174776119403[/C][C]0.567884357921099[/C][C]134.137831156791[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]76.212[/C][C]0.555371246243309[/C][C]137.227126026995[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]76.2384126984127[/C][C]0.544735226783606[/C][C]139.954989047731[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]76.2586885245902[/C][C]0.534150082029091[/C][C]142.766407963290[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]76.2640677966102[/C][C]0.525526766352928[/C][C]145.119283506472[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]76.270350877193[/C][C]0.514913792144247[/C][C]148.122563506372[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]76.2890909090909[/C][C]0.505009335695771[/C][C]151.064714088868[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]76.3079245283019[/C][C]0.493857432764019[/C][C]154.514075248847[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]76.3349019607843[/C][C]0.481441330495967[/C][C]158.554941434185[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]76.3681632653061[/C][C]0.467603591188407[/C][C]163.318170998682[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]76.4[/C][C]0.453270161204031[/C][C]168.552899659349[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]76.4493333333333[/C][C]0.440106323241982[/C][C]173.706509759233[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]76.4983720930232[/C][C]0.425787125990439[/C][C]179.663421985993[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]76.5460975609756[/C][C]0.409198484554924[/C][C]187.063492290870[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]76.5723076923077[/C][C]0.397213210871039[/C][C]192.773819189936[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]76.585945945946[/C][C]0.386924125893071[/C][C]197.935307779466[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]76.5882857142857[/C][C]0.376753599730598[/C][C]203.28481471458[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]76.59[/C][C]0.363753058927053[/C][C]210.554930385780[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]76.611935483871[/C][C]0.352043319473594[/C][C]217.620762122195[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]76.6320689655172[/C][C]0.341549417736647[/C][C]224.365977472123[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]76.6511111111111[/C][C]0.329378821962[/C][C]232.714145537731[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]76.6864[/C][C]0.314288020770757[/C][C]244.000391144196[/C][/ROW]
[ROW][C]Median[/C][C]76.76[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]74.44[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]76.4786111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]76.5859459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]76.5859459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]76.5859459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]76.5859459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]76.47[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]76.5859459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]76.5859459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40908&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40908&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 Mean76.04123287671230.609850704875916124.688275784127
Geometric Mean75.8615757274944
Harmonic Mean75.6784703581152
Quadratic Mean76.2171055927179
Winsorized Mean ( 1 / 24 )76.04082191780820.609484110562643124.762599385260
Winsorized Mean ( 2 / 24 )76.06054794520550.603890383700164125.950917580715
Winsorized Mean ( 3 / 24 )76.07534246575340.593912775723098128.091776394489
Winsorized Mean ( 4 / 24 )76.12082191780820.581700413559145130.859150420852
Winsorized Mean ( 5 / 24 )76.1536986301370.574108086852994132.646970795304
Winsorized Mean ( 6 / 24 )76.2326027397260.558463558295059136.504166847444
Winsorized Mean ( 7 / 24 )76.22972602739730.557970132415968136.619724961493
Winsorized Mean ( 8 / 24 )76.1573972602740.544120575271406139.964193087694
Winsorized Mean ( 9 / 24 )76.16602739726030.538416159839942141.463115482831
Winsorized Mean ( 10 / 24 )76.11945205479450.530720049144163143.426750463911
Winsorized Mean ( 11 / 24 )76.08931506849310.521722112126613145.842611037401
Winsorized Mean ( 12 / 24 )76.12219178082190.506850905526321150.186555752082
Winsorized Mean ( 13 / 24 )76.00465753424660.481817576104819157.745713945711
Winsorized Mean ( 14 / 24 )76.04493150684930.468866801715234162.188773503813
Winsorized Mean ( 15 / 24 )76.0963013698630.458801400964503165.858912396282
Winsorized Mean ( 16 / 24 )76.32205479452050.419054616545143182.129134917426
Winsorized Mean ( 17 / 24 )76.4547945205480.39443672675742193.832849058115
Winsorized Mean ( 18 / 24 )76.56575342465750.377347947232225202.904915705128
Winsorized Mean ( 19 / 24 )76.57356164383560.37099927639362206.398142843258
Winsorized Mean ( 20 / 24 )76.4036986301370.345175572802763221.347350885096
Winsorized Mean ( 21 / 24 )76.44397260273970.321767186823348237.575413942715
Winsorized Mean ( 22 / 24 )76.47712328767120.308792295672215247.665257066039
Winsorized Mean ( 23 / 24 )76.37315068493150.295310949598087258.619434155334
Winsorized Mean ( 24 / 24 )76.35013698630140.283560243086563269.255436358876
Trimmed Mean ( 1 / 24 )76.0863380281690.596991257007273127.449668877215
Trimmed Mean ( 2 / 24 )76.13449275362320.582100055566215130.792794169322
Trimmed Mean ( 3 / 24 )76.1747761194030.567884357921099134.137831156791
Trimmed Mean ( 4 / 24 )76.2120.555371246243309137.227126026995
Trimmed Mean ( 5 / 24 )76.23841269841270.544735226783606139.954989047731
Trimmed Mean ( 6 / 24 )76.25868852459020.534150082029091142.766407963290
Trimmed Mean ( 7 / 24 )76.26406779661020.525526766352928145.119283506472
Trimmed Mean ( 8 / 24 )76.2703508771930.514913792144247148.122563506372
Trimmed Mean ( 9 / 24 )76.28909090909090.505009335695771151.064714088868
Trimmed Mean ( 10 / 24 )76.30792452830190.493857432764019154.514075248847
Trimmed Mean ( 11 / 24 )76.33490196078430.481441330495967158.554941434185
Trimmed Mean ( 12 / 24 )76.36816326530610.467603591188407163.318170998682
Trimmed Mean ( 13 / 24 )76.40.453270161204031168.552899659349
Trimmed Mean ( 14 / 24 )76.44933333333330.440106323241982173.706509759233
Trimmed Mean ( 15 / 24 )76.49837209302320.425787125990439179.663421985993
Trimmed Mean ( 16 / 24 )76.54609756097560.409198484554924187.063492290870
Trimmed Mean ( 17 / 24 )76.57230769230770.397213210871039192.773819189936
Trimmed Mean ( 18 / 24 )76.5859459459460.386924125893071197.935307779466
Trimmed Mean ( 19 / 24 )76.58828571428570.376753599730598203.28481471458
Trimmed Mean ( 20 / 24 )76.590.363753058927053210.554930385780
Trimmed Mean ( 21 / 24 )76.6119354838710.352043319473594217.620762122195
Trimmed Mean ( 22 / 24 )76.63206896551720.341549417736647224.365977472123
Trimmed Mean ( 23 / 24 )76.65111111111110.329378821962232.714145537731
Trimmed Mean ( 24 / 24 )76.68640.314288020770757244.000391144196
Median76.76
Midrange74.44
Midmean - Weighted Average at Xnp76.4786111111111
Midmean - Weighted Average at X(n+1)p76.5859459459459
Midmean - Empirical Distribution Function76.5859459459459
Midmean - Empirical Distribution Function - Averaging76.5859459459459
Midmean - Empirical Distribution Function - Interpolation76.5859459459459
Midmean - Closest Observation76.47
Midmean - True Basic - Statistics Graphics Toolkit76.5859459459459
Midmean - MS Excel (old versions)76.5859459459459
Number of observations73



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')