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*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Wed, 12 Oct 2016 13:11:12 +0100

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/2016/Oct/12/t1476274307shz9wm2a05698jg.htm/, Retrieved Sun, 05 May 2024 15:04:19 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 05 May 2024 15:04:19 +0200

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Estimated Impact

Dataseries X:

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-0,4
0
0,2
-0,6
0,5
-0,3
-1,2
0
0,9
0,5
-0,5
0,1
-0,9
1,1
-0,6
-0,2
0,1
-0,2
3,5
-0,9
-1,3
-0,3
-0,4
1,3
-0,7
0,5
-0,6
0,8
-0,2
0,3
3,8
-1,1
-1,7
0,1
-0,9
1,9
-1,4
1,4
-0,2
0,6
0,5
0,6
3,4
-1,4
-1,6
-1,2
-1,7
1,9
-0,8
1
-0,9
1,1
-0,6
0,6
4,1
-1,1
-2
-1,3
-1,7
1,6
-1,2
1,2
-0,8
0,7
1,2
-0,2
4,4
-1,1
-2,2
-0,7
-1,7
1,6

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	0.0652777777777778	0.169392726015161	0.385363523649387
Geometric Mean	NaN
Harmonic Mean	0
Quadratic Mean	1.42882041480999
Winsorized Mean ( 1 / 24 )	0.0638888888888889	0.167431409303698	0.381582459077336
Winsorized Mean ( 2 / 24 )	0.0638888888888889	0.163314954838816	0.391200481008883
Winsorized Mean ( 3 / 24 )	0.0513888888888889	0.159395290362703	0.322399041853456
Winsorized Mean ( 4 / 24 )	0.0458333333333333	0.157716707609419	0.29060544078081
Winsorized Mean ( 5 / 24 )	-0.0583333333333333	0.130692000753806	-0.446342033153353
Winsorized Mean ( 6 / 24 )	-0.05	0.129250881224615	-0.38684455785728
Winsorized Mean ( 7 / 24 )	-0.0597222222222222	0.120130662468132	-0.497143868144949
Winsorized Mean ( 8 / 24 )	-0.0597222222222222	0.120130662468132	-0.497143868144949
Winsorized Mean ( 9 / 24 )	-0.0722222222222222	0.113474474083271	-0.636462277579917
Winsorized Mean ( 10 / 24 )	-0.0861111111111111	0.110983396866864	-0.775891831950416
Winsorized Mean ( 11 / 24 )	-0.0861111111111111	0.106025537190822	-0.812173306475503
Winsorized Mean ( 12 / 24 )	-0.0861111111111111	0.106025537190822	-0.812173306475503
Winsorized Mean ( 13 / 24 )	-0.104166666666667	0.102995766584226	-1.01136842922067
Winsorized Mean ( 14 / 24 )	-0.0847222222222222	0.100149725982291	-0.845955606880077
Winsorized Mean ( 15 / 24 )	-0.105555555555556	0.0967364344492629	-1.09116648919822
Winsorized Mean ( 16 / 24 )	-0.127777777777778	0.0932213912493904	-1.37069159841158
Winsorized Mean ( 17 / 24 )	-0.104166666666667	0.0828964486875513	-1.25658780702761
Winsorized Mean ( 18 / 24 )	-0.129166666666667	0.079129593493902	-1.63234336186272
Winsorized Mean ( 19 / 24 )	-0.155555555555556	0.0753159461240902	-2.06537345091918
Winsorized Mean ( 20 / 24 )	-0.155555555555556	0.0753159461240902	-2.06537345091918
Winsorized Mean ( 21 / 24 )	-0.126388888888889	0.0713439358415259	-1.77154354323306
Winsorized Mean ( 22 / 24 )	-0.156944444444444	0.0670419714404347	-2.34098790761077
Winsorized Mean ( 23 / 24 )	-0.125	0.0628219407860936	-1.98975068958185
Winsorized Mean ( 24 / 24 )	-0.125	0.0628219407860936	-1.98975068958185
Trimmed Mean ( 1 / 24 )	0.0357142857142857	0.159385929721904	0.224074269144083
Trimmed Mean ( 2 / 24 )	0.00588235294117647	0.149610004468175	0.0393179116736658
Trimmed Mean ( 3 / 24 )	-0.0257575757575758	0.140434069111389	-0.183414010008821
Trimmed Mean ( 4 / 24 )	-0.0546875	0.131118692584768	-0.41708393305283
Trimmed Mean ( 5 / 24 )	-0.0838709677419355	0.120179522607152	-0.697880686513429
Trimmed Mean ( 6 / 24 )	-0.09	0.116534226683411	-0.772305292285532
Trimmed Mean ( 7 / 24 )	-0.0982758620689655	0.112484222979493	-0.873685744238835
Trimmed Mean ( 8 / 24 )	-0.105357142857143	0.109971060031842	-0.958044260250262
Trimmed Mean ( 9 / 24 )	-0.112962962962963	0.106826606253348	-1.05744221336641
Trimmed Mean ( 10 / 24 )	-0.119230769230769	0.10450048032749	-1.14095905451455
Trimmed Mean ( 11 / 24 )	-0.124	0.102122775248667	-1.21422473780273
Trimmed Mean ( 12 / 24 )	-0.129166666666667	0.100175304379697	-1.28940628098401
Trimmed Mean ( 13 / 24 )	-0.134782608695652	0.0976149089401051	-1.38075843289833
Trimmed Mean ( 14 / 24 )	-0.138636363636364	0.0949694459094719	-1.45979964723093
Trimmed Mean ( 15 / 24 )	-0.145238095238095	0.0920916059707483	-1.57710459826521
Trimmed Mean ( 16 / 24 )	-0.15	0.0890836541454011	-1.68381058723941
Trimmed Mean ( 17 / 24 )	-0.152631578947368	0.0859005381133001	-1.77684077771494
Trimmed Mean ( 18 / 24 )	-0.158333333333333	0.0840799883708629	-1.88312744091913
Trimmed Mean ( 19 / 24 )	-0.161764705882353	0.0824118073288514	-1.962882639339
Trimmed Mean ( 20 / 24 )	-0.1625	0.0809158762682458	-2.00825854571843
Trimmed Mean ( 21 / 24 )	-0.163333333333333	0.0785622724425726	-2.07903015347127
Trimmed Mean ( 22 / 24 )	-0.167857142857143	0.0761253441845151	-2.20500996948251
Trimmed Mean ( 23 / 24 )	-0.169230769230769	0.0737499373181962	-2.29465644832508
Trimmed Mean ( 24 / 24 )	-0.175	0.0712847931829113	-2.45494154063074
Median	-0.2
Midrange	1.1
Midmean - Weighted Average at Xnp	-0.178378378378378
Midmean - Weighted Average at X(n+1)p	-0.178378378378378
Midmean - Empirical Distribution Function	-0.178378378378378
Midmean - Empirical Distribution Function - Averaging	-0.178378378378378
Midmean - Empirical Distribution Function - Interpolation	-0.178378378378378
Midmean - Closest Observation	-0.178378378378378
Midmean - True Basic - Statistics Graphics Toolkit	-0.178378378378378
Midmean - MS Excel (old versions)	-0.152631578947368
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.0652777777777778 & 0.169392726015161 & 0.385363523649387 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 1.42882041480999 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 0.0638888888888889 & 0.167431409303698 & 0.381582459077336 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 0.0638888888888889 & 0.163314954838816 & 0.391200481008883 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 0.0513888888888889 & 0.159395290362703 & 0.322399041853456 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 0.0458333333333333 & 0.157716707609419 & 0.29060544078081 \tabularnewline
Winsorized Mean ( 5 / 24 ) & -0.0583333333333333 & 0.130692000753806 & -0.446342033153353 \tabularnewline
Winsorized Mean ( 6 / 24 ) & -0.05 & 0.129250881224615 & -0.38684455785728 \tabularnewline
Winsorized Mean ( 7 / 24 ) & -0.0597222222222222 & 0.120130662468132 & -0.497143868144949 \tabularnewline
Winsorized Mean ( 8 / 24 ) & -0.0597222222222222 & 0.120130662468132 & -0.497143868144949 \tabularnewline
Winsorized Mean ( 9 / 24 ) & -0.0722222222222222 & 0.113474474083271 & -0.636462277579917 \tabularnewline
Winsorized Mean ( 10 / 24 ) & -0.0861111111111111 & 0.110983396866864 & -0.775891831950416 \tabularnewline
Winsorized Mean ( 11 / 24 ) & -0.0861111111111111 & 0.106025537190822 & -0.812173306475503 \tabularnewline
Winsorized Mean ( 12 / 24 ) & -0.0861111111111111 & 0.106025537190822 & -0.812173306475503 \tabularnewline
Winsorized Mean ( 13 / 24 ) & -0.104166666666667 & 0.102995766584226 & -1.01136842922067 \tabularnewline
Winsorized Mean ( 14 / 24 ) & -0.0847222222222222 & 0.100149725982291 & -0.845955606880077 \tabularnewline
Winsorized Mean ( 15 / 24 ) & -0.105555555555556 & 0.0967364344492629 & -1.09116648919822 \tabularnewline
Winsorized Mean ( 16 / 24 ) & -0.127777777777778 & 0.0932213912493904 & -1.37069159841158 \tabularnewline
Winsorized Mean ( 17 / 24 ) & -0.104166666666667 & 0.0828964486875513 & -1.25658780702761 \tabularnewline
Winsorized Mean ( 18 / 24 ) & -0.129166666666667 & 0.079129593493902 & -1.63234336186272 \tabularnewline
Winsorized Mean ( 19 / 24 ) & -0.155555555555556 & 0.0753159461240902 & -2.06537345091918 \tabularnewline
Winsorized Mean ( 20 / 24 ) & -0.155555555555556 & 0.0753159461240902 & -2.06537345091918 \tabularnewline
Winsorized Mean ( 21 / 24 ) & -0.126388888888889 & 0.0713439358415259 & -1.77154354323306 \tabularnewline
Winsorized Mean ( 22 / 24 ) & -0.156944444444444 & 0.0670419714404347 & -2.34098790761077 \tabularnewline
Winsorized Mean ( 23 / 24 ) & -0.125 & 0.0628219407860936 & -1.98975068958185 \tabularnewline
Winsorized Mean ( 24 / 24 ) & -0.125 & 0.0628219407860936 & -1.98975068958185 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 0.0357142857142857 & 0.159385929721904 & 0.224074269144083 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 0.00588235294117647 & 0.149610004468175 & 0.0393179116736658 \tabularnewline
Trimmed Mean ( 3 / 24 ) & -0.0257575757575758 & 0.140434069111389 & -0.183414010008821 \tabularnewline
Trimmed Mean ( 4 / 24 ) & -0.0546875 & 0.131118692584768 & -0.41708393305283 \tabularnewline
Trimmed Mean ( 5 / 24 ) & -0.0838709677419355 & 0.120179522607152 & -0.697880686513429 \tabularnewline
Trimmed Mean ( 6 / 24 ) & -0.09 & 0.116534226683411 & -0.772305292285532 \tabularnewline
Trimmed Mean ( 7 / 24 ) & -0.0982758620689655 & 0.112484222979493 & -0.873685744238835 \tabularnewline
Trimmed Mean ( 8 / 24 ) & -0.105357142857143 & 0.109971060031842 & -0.958044260250262 \tabularnewline
Trimmed Mean ( 9 / 24 ) & -0.112962962962963 & 0.106826606253348 & -1.05744221336641 \tabularnewline
Trimmed Mean ( 10 / 24 ) & -0.119230769230769 & 0.10450048032749 & -1.14095905451455 \tabularnewline
Trimmed Mean ( 11 / 24 ) & -0.124 & 0.102122775248667 & -1.21422473780273 \tabularnewline
Trimmed Mean ( 12 / 24 ) & -0.129166666666667 & 0.100175304379697 & -1.28940628098401 \tabularnewline
Trimmed Mean ( 13 / 24 ) & -0.134782608695652 & 0.0976149089401051 & -1.38075843289833 \tabularnewline
Trimmed Mean ( 14 / 24 ) & -0.138636363636364 & 0.0949694459094719 & -1.45979964723093 \tabularnewline
Trimmed Mean ( 15 / 24 ) & -0.145238095238095 & 0.0920916059707483 & -1.57710459826521 \tabularnewline
Trimmed Mean ( 16 / 24 ) & -0.15 & 0.0890836541454011 & -1.68381058723941 \tabularnewline
Trimmed Mean ( 17 / 24 ) & -0.152631578947368 & 0.0859005381133001 & -1.77684077771494 \tabularnewline
Trimmed Mean ( 18 / 24 ) & -0.158333333333333 & 0.0840799883708629 & -1.88312744091913 \tabularnewline
Trimmed Mean ( 19 / 24 ) & -0.161764705882353 & 0.0824118073288514 & -1.962882639339 \tabularnewline
Trimmed Mean ( 20 / 24 ) & -0.1625 & 0.0809158762682458 & -2.00825854571843 \tabularnewline
Trimmed Mean ( 21 / 24 ) & -0.163333333333333 & 0.0785622724425726 & -2.07903015347127 \tabularnewline
Trimmed Mean ( 22 / 24 ) & -0.167857142857143 & 0.0761253441845151 & -2.20500996948251 \tabularnewline
Trimmed Mean ( 23 / 24 ) & -0.169230769230769 & 0.0737499373181962 & -2.29465644832508 \tabularnewline
Trimmed Mean ( 24 / 24 ) & -0.175 & 0.0712847931829113 & -2.45494154063074 \tabularnewline
Median & -0.2 &  &  \tabularnewline
Midrange & 1.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -0.178378378378378 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -0.178378378378378 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -0.178378378378378 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -0.178378378378378 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -0.178378378378378 &  &  \tabularnewline
Midmean - Closest Observation & -0.178378378378378 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -0.178378378378378 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -0.152631578947368 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.0652777777777778[/C][C]0.169392726015161[/C][C]0.385363523649387[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.42882041480999[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]0.0638888888888889[/C][C]0.167431409303698[/C][C]0.381582459077336[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]0.0638888888888889[/C][C]0.163314954838816[/C][C]0.391200481008883[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]0.0513888888888889[/C][C]0.159395290362703[/C][C]0.322399041853456[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]0.0458333333333333[/C][C]0.157716707609419[/C][C]0.29060544078081[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]-0.0583333333333333[/C][C]0.130692000753806[/C][C]-0.446342033153353[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]-0.05[/C][C]0.129250881224615[/C][C]-0.38684455785728[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]-0.0597222222222222[/C][C]0.120130662468132[/C][C]-0.497143868144949[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]-0.0597222222222222[/C][C]0.120130662468132[/C][C]-0.497143868144949[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]-0.0722222222222222[/C][C]0.113474474083271[/C][C]-0.636462277579917[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]-0.0861111111111111[/C][C]0.110983396866864[/C][C]-0.775891831950416[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]-0.0861111111111111[/C][C]0.106025537190822[/C][C]-0.812173306475503[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]-0.0861111111111111[/C][C]0.106025537190822[/C][C]-0.812173306475503[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]-0.104166666666667[/C][C]0.102995766584226[/C][C]-1.01136842922067[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]-0.0847222222222222[/C][C]0.100149725982291[/C][C]-0.845955606880077[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]-0.105555555555556[/C][C]0.0967364344492629[/C][C]-1.09116648919822[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]-0.127777777777778[/C][C]0.0932213912493904[/C][C]-1.37069159841158[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]-0.104166666666667[/C][C]0.0828964486875513[/C][C]-1.25658780702761[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]-0.129166666666667[/C][C]0.079129593493902[/C][C]-1.63234336186272[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]-0.155555555555556[/C][C]0.0753159461240902[/C][C]-2.06537345091918[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]-0.155555555555556[/C][C]0.0753159461240902[/C][C]-2.06537345091918[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]-0.126388888888889[/C][C]0.0713439358415259[/C][C]-1.77154354323306[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]-0.156944444444444[/C][C]0.0670419714404347[/C][C]-2.34098790761077[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]-0.125[/C][C]0.0628219407860936[/C][C]-1.98975068958185[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]-0.125[/C][C]0.0628219407860936[/C][C]-1.98975068958185[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]0.0357142857142857[/C][C]0.159385929721904[/C][C]0.224074269144083[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]0.00588235294117647[/C][C]0.149610004468175[/C][C]0.0393179116736658[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]-0.0257575757575758[/C][C]0.140434069111389[/C][C]-0.183414010008821[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]-0.0546875[/C][C]0.131118692584768[/C][C]-0.41708393305283[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]-0.0838709677419355[/C][C]0.120179522607152[/C][C]-0.697880686513429[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]-0.09[/C][C]0.116534226683411[/C][C]-0.772305292285532[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]-0.0982758620689655[/C][C]0.112484222979493[/C][C]-0.873685744238835[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]-0.105357142857143[/C][C]0.109971060031842[/C][C]-0.958044260250262[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]-0.112962962962963[/C][C]0.106826606253348[/C][C]-1.05744221336641[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]-0.119230769230769[/C][C]0.10450048032749[/C][C]-1.14095905451455[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]-0.124[/C][C]0.102122775248667[/C][C]-1.21422473780273[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]-0.129166666666667[/C][C]0.100175304379697[/C][C]-1.28940628098401[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]-0.134782608695652[/C][C]0.0976149089401051[/C][C]-1.38075843289833[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]-0.138636363636364[/C][C]0.0949694459094719[/C][C]-1.45979964723093[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]-0.145238095238095[/C][C]0.0920916059707483[/C][C]-1.57710459826521[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]-0.15[/C][C]0.0890836541454011[/C][C]-1.68381058723941[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]-0.152631578947368[/C][C]0.0859005381133001[/C][C]-1.77684077771494[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]-0.158333333333333[/C][C]0.0840799883708629[/C][C]-1.88312744091913[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]-0.161764705882353[/C][C]0.0824118073288514[/C][C]-1.962882639339[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]-0.1625[/C][C]0.0809158762682458[/C][C]-2.00825854571843[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]-0.163333333333333[/C][C]0.0785622724425726[/C][C]-2.07903015347127[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]-0.167857142857143[/C][C]0.0761253441845151[/C][C]-2.20500996948251[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]-0.169230769230769[/C][C]0.0737499373181962[/C][C]-2.29465644832508[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]-0.175[/C][C]0.0712847931829113[/C][C]-2.45494154063074[/C][/ROW]
[ROW][C]Median[/C][C]-0.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-0.178378378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-0.178378378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-0.178378378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-0.178378378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-0.178378378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-0.178378378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-0.178378378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-0.152631578947368[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.0652777777777778	0.169392726015161	0.385363523649387
Geometric Mean	NaN
Harmonic Mean	0
Quadratic Mean	1.42882041480999
Winsorized Mean ( 1 / 24 )	0.0638888888888889	0.167431409303698	0.381582459077336
Winsorized Mean ( 2 / 24 )	0.0638888888888889	0.163314954838816	0.391200481008883
Winsorized Mean ( 3 / 24 )	0.0513888888888889	0.159395290362703	0.322399041853456
Winsorized Mean ( 4 / 24 )	0.0458333333333333	0.157716707609419	0.29060544078081
Winsorized Mean ( 5 / 24 )	-0.0583333333333333	0.130692000753806	-0.446342033153353
Winsorized Mean ( 6 / 24 )	-0.05	0.129250881224615	-0.38684455785728
Winsorized Mean ( 7 / 24 )	-0.0597222222222222	0.120130662468132	-0.497143868144949
Winsorized Mean ( 8 / 24 )	-0.0597222222222222	0.120130662468132	-0.497143868144949
Winsorized Mean ( 9 / 24 )	-0.0722222222222222	0.113474474083271	-0.636462277579917
Winsorized Mean ( 10 / 24 )	-0.0861111111111111	0.110983396866864	-0.775891831950416
Winsorized Mean ( 11 / 24 )	-0.0861111111111111	0.106025537190822	-0.812173306475503
Winsorized Mean ( 12 / 24 )	-0.0861111111111111	0.106025537190822	-0.812173306475503
Winsorized Mean ( 13 / 24 )	-0.104166666666667	0.102995766584226	-1.01136842922067
Winsorized Mean ( 14 / 24 )	-0.0847222222222222	0.100149725982291	-0.845955606880077
Winsorized Mean ( 15 / 24 )	-0.105555555555556	0.0967364344492629	-1.09116648919822
Winsorized Mean ( 16 / 24 )	-0.127777777777778	0.0932213912493904	-1.37069159841158
Winsorized Mean ( 17 / 24 )	-0.104166666666667	0.0828964486875513	-1.25658780702761
Winsorized Mean ( 18 / 24 )	-0.129166666666667	0.079129593493902	-1.63234336186272
Winsorized Mean ( 19 / 24 )	-0.155555555555556	0.0753159461240902	-2.06537345091918
Winsorized Mean ( 20 / 24 )	-0.155555555555556	0.0753159461240902	-2.06537345091918
Winsorized Mean ( 21 / 24 )	-0.126388888888889	0.0713439358415259	-1.77154354323306
Winsorized Mean ( 22 / 24 )	-0.156944444444444	0.0670419714404347	-2.34098790761077
Winsorized Mean ( 23 / 24 )	-0.125	0.0628219407860936	-1.98975068958185
Winsorized Mean ( 24 / 24 )	-0.125	0.0628219407860936	-1.98975068958185
Trimmed Mean ( 1 / 24 )	0.0357142857142857	0.159385929721904	0.224074269144083
Trimmed Mean ( 2 / 24 )	0.00588235294117647	0.149610004468175	0.0393179116736658
Trimmed Mean ( 3 / 24 )	-0.0257575757575758	0.140434069111389	-0.183414010008821
Trimmed Mean ( 4 / 24 )	-0.0546875	0.131118692584768	-0.41708393305283
Trimmed Mean ( 5 / 24 )	-0.0838709677419355	0.120179522607152	-0.697880686513429
Trimmed Mean ( 6 / 24 )	-0.09	0.116534226683411	-0.772305292285532
Trimmed Mean ( 7 / 24 )	-0.0982758620689655	0.112484222979493	-0.873685744238835
Trimmed Mean ( 8 / 24 )	-0.105357142857143	0.109971060031842	-0.958044260250262
Trimmed Mean ( 9 / 24 )	-0.112962962962963	0.106826606253348	-1.05744221336641
Trimmed Mean ( 10 / 24 )	-0.119230769230769	0.10450048032749	-1.14095905451455
Trimmed Mean ( 11 / 24 )	-0.124	0.102122775248667	-1.21422473780273
Trimmed Mean ( 12 / 24 )	-0.129166666666667	0.100175304379697	-1.28940628098401
Trimmed Mean ( 13 / 24 )	-0.134782608695652	0.0976149089401051	-1.38075843289833
Trimmed Mean ( 14 / 24 )	-0.138636363636364	0.0949694459094719	-1.45979964723093
Trimmed Mean ( 15 / 24 )	-0.145238095238095	0.0920916059707483	-1.57710459826521
Trimmed Mean ( 16 / 24 )	-0.15	0.0890836541454011	-1.68381058723941
Trimmed Mean ( 17 / 24 )	-0.152631578947368	0.0859005381133001	-1.77684077771494
Trimmed Mean ( 18 / 24 )	-0.158333333333333	0.0840799883708629	-1.88312744091913
Trimmed Mean ( 19 / 24 )	-0.161764705882353	0.0824118073288514	-1.962882639339
Trimmed Mean ( 20 / 24 )	-0.1625	0.0809158762682458	-2.00825854571843
Trimmed Mean ( 21 / 24 )	-0.163333333333333	0.0785622724425726	-2.07903015347127
Trimmed Mean ( 22 / 24 )	-0.167857142857143	0.0761253441845151	-2.20500996948251
Trimmed Mean ( 23 / 24 )	-0.169230769230769	0.0737499373181962	-2.29465644832508
Trimmed Mean ( 24 / 24 )	-0.175	0.0712847931829113	-2.45494154063074
Median	-0.2
Midrange	1.1
Midmean - Weighted Average at Xnp	-0.178378378378378
Midmean - Weighted Average at X(n+1)p	-0.178378378378378
Midmean - Empirical Distribution Function	-0.178378378378378
Midmean - Empirical Distribution Function - Averaging	-0.178378378378378
Midmean - Empirical Distribution Function - Interpolation	-0.178378378378378
Midmean - Closest Observation	-0.178378378378378
Midmean - True Basic - Statistics Graphics Toolkit	-0.178378378378378
Midmean - MS Excel (old versions)	-0.152631578947368
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