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*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Sun, 23 Feb 2014 07:42:25 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Feb/23/t1393159365as27g622r3htlt3.htm/, Retrieved Wed, 15 May 2024 13:50:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=233971, Retrieved Wed, 15 May 2024 13:50:26 +0000

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No (this computation is public)

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Estimated Impact

130

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Central Tendency] [] [2014-02-23 12:42:25] [96d7fff632246663047c645f81fe87bb] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ wold.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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233971&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233971&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233971&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.25459722222222	0.0199002663900571	63.0442426061726
Geometric Mean	1.24338421407537
Harmonic Mean	1.23225030496315
Quadratic Mean	1.26575339335029
Winsorized Mean ( 1 / 24 )	1.25447222222222	0.0198490781807439	63.2005280446333
Winsorized Mean ( 2 / 24 )	1.25461111111111	0.019794143586599	63.3829448403367
Winsorized Mean ( 3 / 24 )	1.25406944444444	0.0196471946094269	63.8294407611117
Winsorized Mean ( 4 / 24 )	1.25390277777778	0.0195972072493175	63.9837483895288
Winsorized Mean ( 5 / 24 )	1.25376388888889	0.0195478175906403	64.1383051113186
Winsorized Mean ( 6 / 24 )	1.25393055555556	0.0194040447035244	64.6221225891013
Winsorized Mean ( 7 / 24 )	1.252375	0.0190680811950668	65.6791308568589
Winsorized Mean ( 8 / 24 )	1.25393055555556	0.0187038040868588	67.0414718702363
Winsorized Mean ( 9 / 24 )	1.25443055555556	0.0183022017624663	68.5398714229076
Winsorized Mean ( 10 / 24 )	1.25429166666667	0.0179717157091937	69.7925388406301
Winsorized Mean ( 11 / 24 )	1.25475	0.0177603344466176	70.6490074143262
Winsorized Mean ( 12 / 24 )	1.25158333333333	0.0171593123177337	72.939014696985
Winsorized Mean ( 13 / 24 )	1.25230555555556	0.0169980855831857	73.6733292362241
Winsorized Mean ( 14 / 24 )	1.25308333333333	0.0166532193403407	75.2457112180029
Winsorized Mean ( 15 / 24 )	1.252875	0.0161327864520956	77.6601738156184
Winsorized Mean ( 16 / 24 )	1.25198611111111	0.0160006539999305	78.2459336422468
Winsorized Mean ( 17 / 24 )	1.24986111111111	0.0156897904659444	79.6607904881843
Winsorized Mean ( 18 / 24 )	1.25036111111111	0.0153328907054346	81.5476438939157
Winsorized Mean ( 19 / 24 )	1.25036111111111	0.0151828359554743	82.3535942018976
Winsorized Mean ( 20 / 24 )	1.24786111111111	0.0145930089372194	85.5108851422988
Winsorized Mean ( 21 / 24 )	1.25340277777778	0.0138288450737166	90.6368370674727
Winsorized Mean ( 22 / 24 )	1.25523611111111	0.0129962299374952	96.5846339398516
Winsorized Mean ( 23 / 24 )	1.25363888888889	0.0124237156717998	100.906920442045
Winsorized Mean ( 24 / 24 )	1.25163888888889	0.0121454298152565	103.054309969058
Trimmed Mean ( 1 / 24 )	1.25411428571429	0.0197103512742126	63.6271910260202
Trimmed Mean ( 2 / 24 )	1.25373529411765	0.0195359646468415	64.1757556784043
Trimmed Mean ( 3 / 24 )	1.25325757575758	0.0193526867677599	64.7588415395326
Trimmed Mean ( 4 / 24 )	1.252953125	0.0191880371245783	65.2986606636834
Trimmed Mean ( 5 / 24 )	1.25267741935484	0.0189964617790657	65.9426704785256
Trimmed Mean ( 6 / 24 )	1.25241666666667	0.0187689985355204	66.7279431183537
Trimmed Mean ( 7 / 24 )	1.25210344827586	0.0185211850326107	67.6038518092256
Trimmed Mean ( 8 / 24 )	1.25205357142857	0.0182919579881656	68.4483078431852
Trimmed Mean ( 9 / 24 )	1.25174074074074	0.0180823719939849	69.2243662035672
Trimmed Mean ( 10 / 24 )	1.25132692307692	0.0178969886568044	69.9182944724711
Trimmed Mean ( 11 / 24 )	1.2509	0.0177189452397191	70.5967529712752
Trimmed Mean ( 12 / 24 )	1.250375	0.0175194072985418	71.3708505483559
Trimmed Mean ( 13 / 24 )	1.25021739130435	0.0173719445384459	71.9676135586025
Trimmed Mean ( 14 / 24 )	1.24995454545455	0.0171903580128634	72.7125371396695
Trimmed Mean ( 15 / 24 )	1.24957142857143	0.0170009954910122	73.4998976519954
Trimmed Mean ( 16 / 24 )	1.249175	0.0168351695177776	74.2003220508648
Trimmed Mean ( 17 / 24 )	1.24884210526316	0.0166106585567701	75.1831783788101
Trimmed Mean ( 18 / 24 )	1.24872222222222	0.0163475453771784	76.3859156473407
Trimmed Mean ( 19 / 24 )	1.24852941176471	0.0160395142247842	77.8408494339238
Trimmed Mean ( 20 / 24 )	1.2483125	0.015612781512997	79.9545230912782
Trimmed Mean ( 21 / 24 )	1.24836666666667	0.0151417428151097	82.445375140102
Trimmed Mean ( 22 / 24 )	1.24775	0.0146527373429067	85.1547373572509
Trimmed Mean ( 23 / 24 )	1.24680769230769	0.0141551859733749	88.081336031393
Trimmed Mean ( 24 / 24 )	1.24591666666667	0.0135555642175469	91.911826514303
Median	1.2275
Midrange	1.2715
Midmean - Weighted Average at Xnp	1.23658974358974
Midmean - Weighted Average at X(n+1)p	1.24872222222222
Midmean - Empirical Distribution Function	1.23658974358974
Midmean - Empirical Distribution Function - Averaging	1.24872222222222
Midmean - Empirical Distribution Function - Interpolation	1.24872222222222
Midmean - Closest Observation	1.23658974358974
Midmean - True Basic - Statistics Graphics Toolkit	1.24872222222222
Midmean - MS Excel (old versions)	1.24095
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.25459722222222 & 0.0199002663900571 & 63.0442426061726 \tabularnewline
Geometric Mean & 1.24338421407537 &  &  \tabularnewline
Harmonic Mean & 1.23225030496315 &  &  \tabularnewline
Quadratic Mean & 1.26575339335029 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.25447222222222 & 0.0198490781807439 & 63.2005280446333 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.25461111111111 & 0.019794143586599 & 63.3829448403367 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.25406944444444 & 0.0196471946094269 & 63.8294407611117 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.25390277777778 & 0.0195972072493175 & 63.9837483895288 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.25376388888889 & 0.0195478175906403 & 64.1383051113186 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.25393055555556 & 0.0194040447035244 & 64.6221225891013 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.252375 & 0.0190680811950668 & 65.6791308568589 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.25393055555556 & 0.0187038040868588 & 67.0414718702363 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.25443055555556 & 0.0183022017624663 & 68.5398714229076 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.25429166666667 & 0.0179717157091937 & 69.7925388406301 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.25475 & 0.0177603344466176 & 70.6490074143262 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.25158333333333 & 0.0171593123177337 & 72.939014696985 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.25230555555556 & 0.0169980855831857 & 73.6733292362241 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.25308333333333 & 0.0166532193403407 & 75.2457112180029 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.252875 & 0.0161327864520956 & 77.6601738156184 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.25198611111111 & 0.0160006539999305 & 78.2459336422468 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.24986111111111 & 0.0156897904659444 & 79.6607904881843 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.25036111111111 & 0.0153328907054346 & 81.5476438939157 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.25036111111111 & 0.0151828359554743 & 82.3535942018976 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.24786111111111 & 0.0145930089372194 & 85.5108851422988 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.25340277777778 & 0.0138288450737166 & 90.6368370674727 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.25523611111111 & 0.0129962299374952 & 96.5846339398516 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.25363888888889 & 0.0124237156717998 & 100.906920442045 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.25163888888889 & 0.0121454298152565 & 103.054309969058 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.25411428571429 & 0.0197103512742126 & 63.6271910260202 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.25373529411765 & 0.0195359646468415 & 64.1757556784043 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.25325757575758 & 0.0193526867677599 & 64.7588415395326 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.252953125 & 0.0191880371245783 & 65.2986606636834 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.25267741935484 & 0.0189964617790657 & 65.9426704785256 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.25241666666667 & 0.0187689985355204 & 66.7279431183537 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.25210344827586 & 0.0185211850326107 & 67.6038518092256 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.25205357142857 & 0.0182919579881656 & 68.4483078431852 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.25174074074074 & 0.0180823719939849 & 69.2243662035672 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.25132692307692 & 0.0178969886568044 & 69.9182944724711 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.2509 & 0.0177189452397191 & 70.5967529712752 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.250375 & 0.0175194072985418 & 71.3708505483559 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.25021739130435 & 0.0173719445384459 & 71.9676135586025 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.24995454545455 & 0.0171903580128634 & 72.7125371396695 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.24957142857143 & 0.0170009954910122 & 73.4998976519954 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.249175 & 0.0168351695177776 & 74.2003220508648 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.24884210526316 & 0.0166106585567701 & 75.1831783788101 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.24872222222222 & 0.0163475453771784 & 76.3859156473407 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.24852941176471 & 0.0160395142247842 & 77.8408494339238 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.2483125 & 0.015612781512997 & 79.9545230912782 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.24836666666667 & 0.0151417428151097 & 82.445375140102 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.24775 & 0.0146527373429067 & 85.1547373572509 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.24680769230769 & 0.0141551859733749 & 88.081336031393 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.24591666666667 & 0.0135555642175469 & 91.911826514303 \tabularnewline
Median & 1.2275 &  &  \tabularnewline
Midrange & 1.2715 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.23658974358974 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.24872222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.23658974358974 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.24872222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.24872222222222 &  &  \tabularnewline
Midmean - Closest Observation & 1.23658974358974 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.24872222222222 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.24095 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233971&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]1.25459722222222[/C][C]0.0199002663900571[/C][C]63.0442426061726[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.24338421407537[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.23225030496315[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.26575339335029[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.25447222222222[/C][C]0.0198490781807439[/C][C]63.2005280446333[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.25461111111111[/C][C]0.019794143586599[/C][C]63.3829448403367[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.25406944444444[/C][C]0.0196471946094269[/C][C]63.8294407611117[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.25390277777778[/C][C]0.0195972072493175[/C][C]63.9837483895288[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.25376388888889[/C][C]0.0195478175906403[/C][C]64.1383051113186[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.25393055555556[/C][C]0.0194040447035244[/C][C]64.6221225891013[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.252375[/C][C]0.0190680811950668[/C][C]65.6791308568589[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.25393055555556[/C][C]0.0187038040868588[/C][C]67.0414718702363[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.25443055555556[/C][C]0.0183022017624663[/C][C]68.5398714229076[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.25429166666667[/C][C]0.0179717157091937[/C][C]69.7925388406301[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.25475[/C][C]0.0177603344466176[/C][C]70.6490074143262[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.25158333333333[/C][C]0.0171593123177337[/C][C]72.939014696985[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.25230555555556[/C][C]0.0169980855831857[/C][C]73.6733292362241[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.25308333333333[/C][C]0.0166532193403407[/C][C]75.2457112180029[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.252875[/C][C]0.0161327864520956[/C][C]77.6601738156184[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.25198611111111[/C][C]0.0160006539999305[/C][C]78.2459336422468[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.24986111111111[/C][C]0.0156897904659444[/C][C]79.6607904881843[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.25036111111111[/C][C]0.0153328907054346[/C][C]81.5476438939157[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.25036111111111[/C][C]0.0151828359554743[/C][C]82.3535942018976[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.24786111111111[/C][C]0.0145930089372194[/C][C]85.5108851422988[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.25340277777778[/C][C]0.0138288450737166[/C][C]90.6368370674727[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.25523611111111[/C][C]0.0129962299374952[/C][C]96.5846339398516[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.25363888888889[/C][C]0.0124237156717998[/C][C]100.906920442045[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.25163888888889[/C][C]0.0121454298152565[/C][C]103.054309969058[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.25411428571429[/C][C]0.0197103512742126[/C][C]63.6271910260202[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.25373529411765[/C][C]0.0195359646468415[/C][C]64.1757556784043[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.25325757575758[/C][C]0.0193526867677599[/C][C]64.7588415395326[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.252953125[/C][C]0.0191880371245783[/C][C]65.2986606636834[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.25267741935484[/C][C]0.0189964617790657[/C][C]65.9426704785256[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.25241666666667[/C][C]0.0187689985355204[/C][C]66.7279431183537[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.25210344827586[/C][C]0.0185211850326107[/C][C]67.6038518092256[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.25205357142857[/C][C]0.0182919579881656[/C][C]68.4483078431852[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.25174074074074[/C][C]0.0180823719939849[/C][C]69.2243662035672[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.25132692307692[/C][C]0.0178969886568044[/C][C]69.9182944724711[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.2509[/C][C]0.0177189452397191[/C][C]70.5967529712752[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.250375[/C][C]0.0175194072985418[/C][C]71.3708505483559[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.25021739130435[/C][C]0.0173719445384459[/C][C]71.9676135586025[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.24995454545455[/C][C]0.0171903580128634[/C][C]72.7125371396695[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.24957142857143[/C][C]0.0170009954910122[/C][C]73.4998976519954[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.249175[/C][C]0.0168351695177776[/C][C]74.2003220508648[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.24884210526316[/C][C]0.0166106585567701[/C][C]75.1831783788101[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.24872222222222[/C][C]0.0163475453771784[/C][C]76.3859156473407[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.24852941176471[/C][C]0.0160395142247842[/C][C]77.8408494339238[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.2483125[/C][C]0.015612781512997[/C][C]79.9545230912782[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.24836666666667[/C][C]0.0151417428151097[/C][C]82.445375140102[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.24775[/C][C]0.0146527373429067[/C][C]85.1547373572509[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.24680769230769[/C][C]0.0141551859733749[/C][C]88.081336031393[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.24591666666667[/C][C]0.0135555642175469[/C][C]91.911826514303[/C][/ROW]
[ROW][C]Median[/C][C]1.2275[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.2715[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.23658974358974[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.24872222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.23658974358974[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.24872222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.24872222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.23658974358974[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.24872222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.24095[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233971&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233971&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
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.25459722222222	0.0199002663900571	63.0442426061726
Geometric Mean	1.24338421407537
Harmonic Mean	1.23225030496315
Quadratic Mean	1.26575339335029
Winsorized Mean ( 1 / 24 )	1.25447222222222	0.0198490781807439	63.2005280446333
Winsorized Mean ( 2 / 24 )	1.25461111111111	0.019794143586599	63.3829448403367
Winsorized Mean ( 3 / 24 )	1.25406944444444	0.0196471946094269	63.8294407611117
Winsorized Mean ( 4 / 24 )	1.25390277777778	0.0195972072493175	63.9837483895288
Winsorized Mean ( 5 / 24 )	1.25376388888889	0.0195478175906403	64.1383051113186
Winsorized Mean ( 6 / 24 )	1.25393055555556	0.0194040447035244	64.6221225891013
Winsorized Mean ( 7 / 24 )	1.252375	0.0190680811950668	65.6791308568589
Winsorized Mean ( 8 / 24 )	1.25393055555556	0.0187038040868588	67.0414718702363
Winsorized Mean ( 9 / 24 )	1.25443055555556	0.0183022017624663	68.5398714229076
Winsorized Mean ( 10 / 24 )	1.25429166666667	0.0179717157091937	69.7925388406301
Winsorized Mean ( 11 / 24 )	1.25475	0.0177603344466176	70.6490074143262
Winsorized Mean ( 12 / 24 )	1.25158333333333	0.0171593123177337	72.939014696985
Winsorized Mean ( 13 / 24 )	1.25230555555556	0.0169980855831857	73.6733292362241
Winsorized Mean ( 14 / 24 )	1.25308333333333	0.0166532193403407	75.2457112180029
Winsorized Mean ( 15 / 24 )	1.252875	0.0161327864520956	77.6601738156184
Winsorized Mean ( 16 / 24 )	1.25198611111111	0.0160006539999305	78.2459336422468
Winsorized Mean ( 17 / 24 )	1.24986111111111	0.0156897904659444	79.6607904881843
Winsorized Mean ( 18 / 24 )	1.25036111111111	0.0153328907054346	81.5476438939157
Winsorized Mean ( 19 / 24 )	1.25036111111111	0.0151828359554743	82.3535942018976
Winsorized Mean ( 20 / 24 )	1.24786111111111	0.0145930089372194	85.5108851422988
Winsorized Mean ( 21 / 24 )	1.25340277777778	0.0138288450737166	90.6368370674727
Winsorized Mean ( 22 / 24 )	1.25523611111111	0.0129962299374952	96.5846339398516
Winsorized Mean ( 23 / 24 )	1.25363888888889	0.0124237156717998	100.906920442045
Winsorized Mean ( 24 / 24 )	1.25163888888889	0.0121454298152565	103.054309969058
Trimmed Mean ( 1 / 24 )	1.25411428571429	0.0197103512742126	63.6271910260202
Trimmed Mean ( 2 / 24 )	1.25373529411765	0.0195359646468415	64.1757556784043
Trimmed Mean ( 3 / 24 )	1.25325757575758	0.0193526867677599	64.7588415395326
Trimmed Mean ( 4 / 24 )	1.252953125	0.0191880371245783	65.2986606636834
Trimmed Mean ( 5 / 24 )	1.25267741935484	0.0189964617790657	65.9426704785256
Trimmed Mean ( 6 / 24 )	1.25241666666667	0.0187689985355204	66.7279431183537
Trimmed Mean ( 7 / 24 )	1.25210344827586	0.0185211850326107	67.6038518092256
Trimmed Mean ( 8 / 24 )	1.25205357142857	0.0182919579881656	68.4483078431852
Trimmed Mean ( 9 / 24 )	1.25174074074074	0.0180823719939849	69.2243662035672
Trimmed Mean ( 10 / 24 )	1.25132692307692	0.0178969886568044	69.9182944724711
Trimmed Mean ( 11 / 24 )	1.2509	0.0177189452397191	70.5967529712752
Trimmed Mean ( 12 / 24 )	1.250375	0.0175194072985418	71.3708505483559
Trimmed Mean ( 13 / 24 )	1.25021739130435	0.0173719445384459	71.9676135586025
Trimmed Mean ( 14 / 24 )	1.24995454545455	0.0171903580128634	72.7125371396695
Trimmed Mean ( 15 / 24 )	1.24957142857143	0.0170009954910122	73.4998976519954
Trimmed Mean ( 16 / 24 )	1.249175	0.0168351695177776	74.2003220508648
Trimmed Mean ( 17 / 24 )	1.24884210526316	0.0166106585567701	75.1831783788101
Trimmed Mean ( 18 / 24 )	1.24872222222222	0.0163475453771784	76.3859156473407
Trimmed Mean ( 19 / 24 )	1.24852941176471	0.0160395142247842	77.8408494339238
Trimmed Mean ( 20 / 24 )	1.2483125	0.015612781512997	79.9545230912782
Trimmed Mean ( 21 / 24 )	1.24836666666667	0.0151417428151097	82.445375140102
Trimmed Mean ( 22 / 24 )	1.24775	0.0146527373429067	85.1547373572509
Trimmed Mean ( 23 / 24 )	1.24680769230769	0.0141551859733749	88.081336031393
Trimmed Mean ( 24 / 24 )	1.24591666666667	0.0135555642175469	91.911826514303
Median	1.2275
Midrange	1.2715
Midmean - Weighted Average at Xnp	1.23658974358974
Midmean - Weighted Average at X(n+1)p	1.24872222222222
Midmean - Empirical Distribution Function	1.23658974358974
Midmean - Empirical Distribution Function - Averaging	1.24872222222222
Midmean - Empirical Distribution Function - Interpolation	1.24872222222222
Midmean - Closest Observation	1.23658974358974
Midmean - True Basic - Statistics Graphics Toolkit	1.24872222222222
Midmean - MS Excel (old versions)	1.24095
Number of observations	72

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code