Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 26 Nov 2010 10:45:03 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/26/t1290768303y10sd1efclstg8f.htm/, Retrieved Fri, 03 May 2024 23:42:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=101746, Retrieved Fri, 03 May 2024 23:42:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
-  M D    [Central Tendency] [] [2010-11-26 10:45:03] [d42b17bf3b3c0d56878eb3f5a4351e6d] [Current]
-    D      [Central Tendency] [] [2010-11-26 16:01:16] [1ec36cc0fd92fd0f07d0b885ce2c369b]
Feedback Forum

Post a new message
Dataseries X:
10,1
10
10
10
10
10
10
9,9
9,9
9,9
9,9
9,9
9,8
9,7
9,6
9,5
9,4
9,2
9,1
8,8
8,5
8,2
8
7,9
7,7
7,6
7,5
7,5
7,4
7,3
7,2
7,2
7,3
7,4
7,3
7,4
7,4
7,5
7,5
7,5
7,6
7,5
7,6
7,7
7,8
7,9
8
8,1
8,2
8,2
8,3
8,4
8,5
8,6
8,7
8,8
8,8
8,8
8,9
8,9
9
9
9
9,1
9,1
9,1
9,1
9,1
9
9,1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101746&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101746&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101746&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean8.598571428571430.11192819454235376.822211451984
Geometric Mean8.54824708812669
Harmonic Mean8.49811383279144
Quadratic Mean8.64869106529174
Winsorized Mean ( 1 / 23 )8.597142857142860.11165926112284076.9944451601272
Winsorized Mean ( 2 / 23 )8.60.11115803012133477.3673300130695
Winsorized Mean ( 3 / 23 )8.60.11115803012133477.3673300130695
Winsorized Mean ( 4 / 23 )8.60.11115803012133477.3673300130695
Winsorized Mean ( 5 / 23 )8.607142857142860.10998440372347178.2578489836012
Winsorized Mean ( 6 / 23 )8.607142857142860.10998440372347178.2578489836012
Winsorized Mean ( 7 / 23 )8.597142857142860.10819374211383079.4606295075538
Winsorized Mean ( 8 / 23 )8.597142857142860.10819374211383079.4606295075539
Winsorized Mean ( 9 / 23 )8.610.10618843363028381.0822770959924
Winsorized Mean ( 10 / 23 )8.610.10618843363028381.0822770959924
Winsorized Mean ( 11 / 23 )8.610.10618843363028381.0822770959924
Winsorized Mean ( 12 / 23 )8.592857142857140.10322584595723983.2432717133331
Winsorized Mean ( 13 / 23 )8.574285714285710.10013832491671385.6244172390256
Winsorized Mean ( 14 / 23 )8.554285714285710.096944749889840888.2387723317253
Winsorized Mean ( 15 / 23 )8.554285714285710.090310843791645994.7204715971995
Winsorized Mean ( 16 / 23 )8.531428571428570.086919749693150398.1529353403198
Winsorized Mean ( 17 / 23 )8.482857142857140.0802421652702137105.715705879712
Winsorized Mean ( 18 / 23 )8.482857142857140.0729437637148786116.293110073327
Winsorized Mean ( 19 / 23 )8.482857142857140.0729437637148786116.293110073327
Winsorized Mean ( 20 / 23 )8.511428571428570.0685714285714286124.125
Winsorized Mean ( 21 / 23 )8.541428571428570.0641392396163421133.170094041032
Winsorized Mean ( 22 / 23 )8.541428571428570.0641392396163421133.170094041032
Winsorized Mean ( 23 / 23 )8.574285714285710.059455281463775144.214029488867
Trimmed Mean ( 1 / 23 )8.597058823529410.11116295192137577.3374462888503
Trimmed Mean ( 2 / 23 )8.59696969696970.11049728022409377.8025457236116
Trimmed Mean ( 3 / 23 )8.59531250.10993391069066078.186179732895
Trimmed Mean ( 4 / 23 )8.593548387096770.10917388378062778.7143233299695
Trimmed Mean ( 5 / 23 )8.591666666666670.10817676647980579.4224762511326
Trimmed Mean ( 6 / 23 )8.587931034482760.10724165163956580.0801824961303
Trimmed Mean ( 7 / 23 )8.583928571428570.10601325528841280.9703328897481
Trimmed Mean ( 8 / 23 )8.581481481481480.10488002110275181.8218893479647
Trimmed Mean ( 9 / 23 )8.578846153846150.10338671339805482.9782268135008
Trimmed Mean ( 10 / 23 )8.5740.10189270066584584.1473426847151
Trimmed Mean ( 11 / 23 )8.568750.099918240069476685.7576153667424
Trimmed Mean ( 12 / 23 )8.563043478260870.097324532838804587.9844292953716
Trimmed Mean ( 13 / 23 )8.559090909090910.094640645688096790.4377907278735
Trimmed Mean ( 14 / 23 )8.557142857142860.091835259837354493.1792741948796
Trimmed Mean ( 15 / 23 )8.55750.088859403496442696.3038200041777
Trimmed Mean ( 16 / 23 )8.55789473684210.08646952274301698.9700702093133
Trimmed Mean ( 17 / 23 )8.561111111111110.0839763551167523101.946686054766
Trimmed Mean ( 18 / 23 )8.570588235294120.0820340144839182104.476030939267
Trimmed Mean ( 19 / 23 )8.581250.0810014809701331105.939421072611
Trimmed Mean ( 20 / 23 )8.593333333333330.0792106653293337108.487074279769
Trimmed Mean ( 21 / 23 )8.603571428571430.0777463898440747110.662005603430
Trimmed Mean ( 22 / 23 )8.611538461538460.076726672340984112.236569093829
Trimmed Mean ( 23 / 23 )8.620833333333330.0746924046607797115.417804159411
Median8.75
Midrange8.65
Midmean - Weighted Average at Xnp8.4918918918919
Midmean - Weighted Average at X(n+1)p8.51052631578948
Midmean - Empirical Distribution Function8.51052631578948
Midmean - Empirical Distribution Function - Averaging8.51052631578948
Midmean - Empirical Distribution Function - Interpolation8.57058823529412
Midmean - Closest Observation8.51052631578948
Midmean - True Basic - Statistics Graphics Toolkit8.51052631578948
Midmean - MS Excel (old versions)8.51052631578948
Number of observations70

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.59857142857143 & 0.111928194542353 & 76.822211451984 \tabularnewline
Geometric Mean & 8.54824708812669 &  &  \tabularnewline
Harmonic Mean & 8.49811383279144 &  &  \tabularnewline
Quadratic Mean & 8.64869106529174 &  &  \tabularnewline
Winsorized Mean ( 1 / 23 ) & 8.59714285714286 & 0.111659261122840 & 76.9944451601272 \tabularnewline
Winsorized Mean ( 2 / 23 ) & 8.6 & 0.111158030121334 & 77.3673300130695 \tabularnewline
Winsorized Mean ( 3 / 23 ) & 8.6 & 0.111158030121334 & 77.3673300130695 \tabularnewline
Winsorized Mean ( 4 / 23 ) & 8.6 & 0.111158030121334 & 77.3673300130695 \tabularnewline
Winsorized Mean ( 5 / 23 ) & 8.60714285714286 & 0.109984403723471 & 78.2578489836012 \tabularnewline
Winsorized Mean ( 6 / 23 ) & 8.60714285714286 & 0.109984403723471 & 78.2578489836012 \tabularnewline
Winsorized Mean ( 7 / 23 ) & 8.59714285714286 & 0.108193742113830 & 79.4606295075538 \tabularnewline
Winsorized Mean ( 8 / 23 ) & 8.59714285714286 & 0.108193742113830 & 79.4606295075539 \tabularnewline
Winsorized Mean ( 9 / 23 ) & 8.61 & 0.106188433630283 & 81.0822770959924 \tabularnewline
Winsorized Mean ( 10 / 23 ) & 8.61 & 0.106188433630283 & 81.0822770959924 \tabularnewline
Winsorized Mean ( 11 / 23 ) & 8.61 & 0.106188433630283 & 81.0822770959924 \tabularnewline
Winsorized Mean ( 12 / 23 ) & 8.59285714285714 & 0.103225845957239 & 83.2432717133331 \tabularnewline
Winsorized Mean ( 13 / 23 ) & 8.57428571428571 & 0.100138324916713 & 85.6244172390256 \tabularnewline
Winsorized Mean ( 14 / 23 ) & 8.55428571428571 & 0.0969447498898408 & 88.2387723317253 \tabularnewline
Winsorized Mean ( 15 / 23 ) & 8.55428571428571 & 0.0903108437916459 & 94.7204715971995 \tabularnewline
Winsorized Mean ( 16 / 23 ) & 8.53142857142857 & 0.0869197496931503 & 98.1529353403198 \tabularnewline
Winsorized Mean ( 17 / 23 ) & 8.48285714285714 & 0.0802421652702137 & 105.715705879712 \tabularnewline
Winsorized Mean ( 18 / 23 ) & 8.48285714285714 & 0.0729437637148786 & 116.293110073327 \tabularnewline
Winsorized Mean ( 19 / 23 ) & 8.48285714285714 & 0.0729437637148786 & 116.293110073327 \tabularnewline
Winsorized Mean ( 20 / 23 ) & 8.51142857142857 & 0.0685714285714286 & 124.125 \tabularnewline
Winsorized Mean ( 21 / 23 ) & 8.54142857142857 & 0.0641392396163421 & 133.170094041032 \tabularnewline
Winsorized Mean ( 22 / 23 ) & 8.54142857142857 & 0.0641392396163421 & 133.170094041032 \tabularnewline
Winsorized Mean ( 23 / 23 ) & 8.57428571428571 & 0.059455281463775 & 144.214029488867 \tabularnewline
Trimmed Mean ( 1 / 23 ) & 8.59705882352941 & 0.111162951921375 & 77.3374462888503 \tabularnewline
Trimmed Mean ( 2 / 23 ) & 8.5969696969697 & 0.110497280224093 & 77.8025457236116 \tabularnewline
Trimmed Mean ( 3 / 23 ) & 8.5953125 & 0.109933910690660 & 78.186179732895 \tabularnewline
Trimmed Mean ( 4 / 23 ) & 8.59354838709677 & 0.109173883780627 & 78.7143233299695 \tabularnewline
Trimmed Mean ( 5 / 23 ) & 8.59166666666667 & 0.108176766479805 & 79.4224762511326 \tabularnewline
Trimmed Mean ( 6 / 23 ) & 8.58793103448276 & 0.107241651639565 & 80.0801824961303 \tabularnewline
Trimmed Mean ( 7 / 23 ) & 8.58392857142857 & 0.106013255288412 & 80.9703328897481 \tabularnewline
Trimmed Mean ( 8 / 23 ) & 8.58148148148148 & 0.104880021102751 & 81.8218893479647 \tabularnewline
Trimmed Mean ( 9 / 23 ) & 8.57884615384615 & 0.103386713398054 & 82.9782268135008 \tabularnewline
Trimmed Mean ( 10 / 23 ) & 8.574 & 0.101892700665845 & 84.1473426847151 \tabularnewline
Trimmed Mean ( 11 / 23 ) & 8.56875 & 0.0999182400694766 & 85.7576153667424 \tabularnewline
Trimmed Mean ( 12 / 23 ) & 8.56304347826087 & 0.0973245328388045 & 87.9844292953716 \tabularnewline
Trimmed Mean ( 13 / 23 ) & 8.55909090909091 & 0.0946406456880967 & 90.4377907278735 \tabularnewline
Trimmed Mean ( 14 / 23 ) & 8.55714285714286 & 0.0918352598373544 & 93.1792741948796 \tabularnewline
Trimmed Mean ( 15 / 23 ) & 8.5575 & 0.0888594034964426 & 96.3038200041777 \tabularnewline
Trimmed Mean ( 16 / 23 ) & 8.5578947368421 & 0.086469522743016 & 98.9700702093133 \tabularnewline
Trimmed Mean ( 17 / 23 ) & 8.56111111111111 & 0.0839763551167523 & 101.946686054766 \tabularnewline
Trimmed Mean ( 18 / 23 ) & 8.57058823529412 & 0.0820340144839182 & 104.476030939267 \tabularnewline
Trimmed Mean ( 19 / 23 ) & 8.58125 & 0.0810014809701331 & 105.939421072611 \tabularnewline
Trimmed Mean ( 20 / 23 ) & 8.59333333333333 & 0.0792106653293337 & 108.487074279769 \tabularnewline
Trimmed Mean ( 21 / 23 ) & 8.60357142857143 & 0.0777463898440747 & 110.662005603430 \tabularnewline
Trimmed Mean ( 22 / 23 ) & 8.61153846153846 & 0.076726672340984 & 112.236569093829 \tabularnewline
Trimmed Mean ( 23 / 23 ) & 8.62083333333333 & 0.0746924046607797 & 115.417804159411 \tabularnewline
Median & 8.75 &  &  \tabularnewline
Midrange & 8.65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.4918918918919 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.51052631578948 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.51052631578948 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.51052631578948 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.57058823529412 &  &  \tabularnewline
Midmean - Closest Observation & 8.51052631578948 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.51052631578948 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.51052631578948 &  &  \tabularnewline
Number of observations & 70 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101746&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]8.59857142857143[/C][C]0.111928194542353[/C][C]76.822211451984[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8.54824708812669[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8.49811383279144[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.64869106529174[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 23 )[/C][C]8.59714285714286[/C][C]0.111659261122840[/C][C]76.9944451601272[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 23 )[/C][C]8.6[/C][C]0.111158030121334[/C][C]77.3673300130695[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 23 )[/C][C]8.6[/C][C]0.111158030121334[/C][C]77.3673300130695[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 23 )[/C][C]8.6[/C][C]0.111158030121334[/C][C]77.3673300130695[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 23 )[/C][C]8.60714285714286[/C][C]0.109984403723471[/C][C]78.2578489836012[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 23 )[/C][C]8.60714285714286[/C][C]0.109984403723471[/C][C]78.2578489836012[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 23 )[/C][C]8.59714285714286[/C][C]0.108193742113830[/C][C]79.4606295075538[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 23 )[/C][C]8.59714285714286[/C][C]0.108193742113830[/C][C]79.4606295075539[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 23 )[/C][C]8.61[/C][C]0.106188433630283[/C][C]81.0822770959924[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 23 )[/C][C]8.61[/C][C]0.106188433630283[/C][C]81.0822770959924[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 23 )[/C][C]8.61[/C][C]0.106188433630283[/C][C]81.0822770959924[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 23 )[/C][C]8.59285714285714[/C][C]0.103225845957239[/C][C]83.2432717133331[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 23 )[/C][C]8.57428571428571[/C][C]0.100138324916713[/C][C]85.6244172390256[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 23 )[/C][C]8.55428571428571[/C][C]0.0969447498898408[/C][C]88.2387723317253[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 23 )[/C][C]8.55428571428571[/C][C]0.0903108437916459[/C][C]94.7204715971995[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 23 )[/C][C]8.53142857142857[/C][C]0.0869197496931503[/C][C]98.1529353403198[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 23 )[/C][C]8.48285714285714[/C][C]0.0802421652702137[/C][C]105.715705879712[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 23 )[/C][C]8.48285714285714[/C][C]0.0729437637148786[/C][C]116.293110073327[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 23 )[/C][C]8.48285714285714[/C][C]0.0729437637148786[/C][C]116.293110073327[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 23 )[/C][C]8.51142857142857[/C][C]0.0685714285714286[/C][C]124.125[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 23 )[/C][C]8.54142857142857[/C][C]0.0641392396163421[/C][C]133.170094041032[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 23 )[/C][C]8.54142857142857[/C][C]0.0641392396163421[/C][C]133.170094041032[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 23 )[/C][C]8.57428571428571[/C][C]0.059455281463775[/C][C]144.214029488867[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 23 )[/C][C]8.59705882352941[/C][C]0.111162951921375[/C][C]77.3374462888503[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 23 )[/C][C]8.5969696969697[/C][C]0.110497280224093[/C][C]77.8025457236116[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 23 )[/C][C]8.5953125[/C][C]0.109933910690660[/C][C]78.186179732895[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 23 )[/C][C]8.59354838709677[/C][C]0.109173883780627[/C][C]78.7143233299695[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 23 )[/C][C]8.59166666666667[/C][C]0.108176766479805[/C][C]79.4224762511326[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 23 )[/C][C]8.58793103448276[/C][C]0.107241651639565[/C][C]80.0801824961303[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 23 )[/C][C]8.58392857142857[/C][C]0.106013255288412[/C][C]80.9703328897481[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 23 )[/C][C]8.58148148148148[/C][C]0.104880021102751[/C][C]81.8218893479647[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 23 )[/C][C]8.57884615384615[/C][C]0.103386713398054[/C][C]82.9782268135008[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 23 )[/C][C]8.574[/C][C]0.101892700665845[/C][C]84.1473426847151[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 23 )[/C][C]8.56875[/C][C]0.0999182400694766[/C][C]85.7576153667424[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 23 )[/C][C]8.56304347826087[/C][C]0.0973245328388045[/C][C]87.9844292953716[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 23 )[/C][C]8.55909090909091[/C][C]0.0946406456880967[/C][C]90.4377907278735[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 23 )[/C][C]8.55714285714286[/C][C]0.0918352598373544[/C][C]93.1792741948796[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 23 )[/C][C]8.5575[/C][C]0.0888594034964426[/C][C]96.3038200041777[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 23 )[/C][C]8.5578947368421[/C][C]0.086469522743016[/C][C]98.9700702093133[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 23 )[/C][C]8.56111111111111[/C][C]0.0839763551167523[/C][C]101.946686054766[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 23 )[/C][C]8.57058823529412[/C][C]0.0820340144839182[/C][C]104.476030939267[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 23 )[/C][C]8.58125[/C][C]0.0810014809701331[/C][C]105.939421072611[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 23 )[/C][C]8.59333333333333[/C][C]0.0792106653293337[/C][C]108.487074279769[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 23 )[/C][C]8.60357142857143[/C][C]0.0777463898440747[/C][C]110.662005603430[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 23 )[/C][C]8.61153846153846[/C][C]0.076726672340984[/C][C]112.236569093829[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 23 )[/C][C]8.62083333333333[/C][C]0.0746924046607797[/C][C]115.417804159411[/C][/ROW]
[ROW][C]Median[/C][C]8.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.4918918918919[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.51052631578948[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.51052631578948[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.51052631578948[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.57058823529412[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.51052631578948[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.51052631578948[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.51052631578948[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]70[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101746&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101746&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 Mean8.598571428571430.11192819454235376.822211451984
Geometric Mean8.54824708812669
Harmonic Mean8.49811383279144
Quadratic Mean8.64869106529174
Winsorized Mean ( 1 / 23 )8.597142857142860.11165926112284076.9944451601272
Winsorized Mean ( 2 / 23 )8.60.11115803012133477.3673300130695
Winsorized Mean ( 3 / 23 )8.60.11115803012133477.3673300130695
Winsorized Mean ( 4 / 23 )8.60.11115803012133477.3673300130695
Winsorized Mean ( 5 / 23 )8.607142857142860.10998440372347178.2578489836012
Winsorized Mean ( 6 / 23 )8.607142857142860.10998440372347178.2578489836012
Winsorized Mean ( 7 / 23 )8.597142857142860.10819374211383079.4606295075538
Winsorized Mean ( 8 / 23 )8.597142857142860.10819374211383079.4606295075539
Winsorized Mean ( 9 / 23 )8.610.10618843363028381.0822770959924
Winsorized Mean ( 10 / 23 )8.610.10618843363028381.0822770959924
Winsorized Mean ( 11 / 23 )8.610.10618843363028381.0822770959924
Winsorized Mean ( 12 / 23 )8.592857142857140.10322584595723983.2432717133331
Winsorized Mean ( 13 / 23 )8.574285714285710.10013832491671385.6244172390256
Winsorized Mean ( 14 / 23 )8.554285714285710.096944749889840888.2387723317253
Winsorized Mean ( 15 / 23 )8.554285714285710.090310843791645994.7204715971995
Winsorized Mean ( 16 / 23 )8.531428571428570.086919749693150398.1529353403198
Winsorized Mean ( 17 / 23 )8.482857142857140.0802421652702137105.715705879712
Winsorized Mean ( 18 / 23 )8.482857142857140.0729437637148786116.293110073327
Winsorized Mean ( 19 / 23 )8.482857142857140.0729437637148786116.293110073327
Winsorized Mean ( 20 / 23 )8.511428571428570.0685714285714286124.125
Winsorized Mean ( 21 / 23 )8.541428571428570.0641392396163421133.170094041032
Winsorized Mean ( 22 / 23 )8.541428571428570.0641392396163421133.170094041032
Winsorized Mean ( 23 / 23 )8.574285714285710.059455281463775144.214029488867
Trimmed Mean ( 1 / 23 )8.597058823529410.11116295192137577.3374462888503
Trimmed Mean ( 2 / 23 )8.59696969696970.11049728022409377.8025457236116
Trimmed Mean ( 3 / 23 )8.59531250.10993391069066078.186179732895
Trimmed Mean ( 4 / 23 )8.593548387096770.10917388378062778.7143233299695
Trimmed Mean ( 5 / 23 )8.591666666666670.10817676647980579.4224762511326
Trimmed Mean ( 6 / 23 )8.587931034482760.10724165163956580.0801824961303
Trimmed Mean ( 7 / 23 )8.583928571428570.10601325528841280.9703328897481
Trimmed Mean ( 8 / 23 )8.581481481481480.10488002110275181.8218893479647
Trimmed Mean ( 9 / 23 )8.578846153846150.10338671339805482.9782268135008
Trimmed Mean ( 10 / 23 )8.5740.10189270066584584.1473426847151
Trimmed Mean ( 11 / 23 )8.568750.099918240069476685.7576153667424
Trimmed Mean ( 12 / 23 )8.563043478260870.097324532838804587.9844292953716
Trimmed Mean ( 13 / 23 )8.559090909090910.094640645688096790.4377907278735
Trimmed Mean ( 14 / 23 )8.557142857142860.091835259837354493.1792741948796
Trimmed Mean ( 15 / 23 )8.55750.088859403496442696.3038200041777
Trimmed Mean ( 16 / 23 )8.55789473684210.08646952274301698.9700702093133
Trimmed Mean ( 17 / 23 )8.561111111111110.0839763551167523101.946686054766
Trimmed Mean ( 18 / 23 )8.570588235294120.0820340144839182104.476030939267
Trimmed Mean ( 19 / 23 )8.581250.0810014809701331105.939421072611
Trimmed Mean ( 20 / 23 )8.593333333333330.0792106653293337108.487074279769
Trimmed Mean ( 21 / 23 )8.603571428571430.0777463898440747110.662005603430
Trimmed Mean ( 22 / 23 )8.611538461538460.076726672340984112.236569093829
Trimmed Mean ( 23 / 23 )8.620833333333330.0746924046607797115.417804159411
Median8.75
Midrange8.65
Midmean - Weighted Average at Xnp8.4918918918919
Midmean - Weighted Average at X(n+1)p8.51052631578948
Midmean - Empirical Distribution Function8.51052631578948
Midmean - Empirical Distribution Function - Averaging8.51052631578948
Midmean - Empirical Distribution Function - Interpolation8.57058823529412
Midmean - Closest Observation8.51052631578948
Midmean - True Basic - Statistics Graphics Toolkit8.51052631578948
Midmean - MS Excel (old versions)8.51052631578948
Number of observations70



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')