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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 06 Dec 2009 07:19:54 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/06/t126010925655tk6khbb1y3854.htm/, Retrieved Sun, 05 May 2024 21:40:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64408, Retrieved Sun, 05 May 2024 21:40:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact106
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central tendecy] [2009-12-06 14:19:54] [6c304092df7982e5e12293b2743450a3] [Current]
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Dataseries X:
8.4
8.4
8.4
8.6
8.9
8.8
8.3
7.5
7.2
7.4
8.8
9.3
9.3
8.7
8.2
8.3
8.5
8.6
8.5
8.2
8.1
7.9
8.6
8.7
8.7
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8
8.2
8.1
8.1
8
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9
7.7
8
8
7.7
7.3
7.4
8.1
8.3
8.2




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64408&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64408&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64408&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.930136986301370.081338800706714397.4951304592663
Geometric Mean7.89898377115985
Harmonic Mean7.86666382992008
Quadratic Mean7.96011461334158
Winsorized Mean ( 1 / 24 )7.934246575342470.080149669214530198.9928798596225
Winsorized Mean ( 2 / 24 )7.926027397260270.0771699629773262102.708710636405
Winsorized Mean ( 3 / 24 )7.926027397260270.0754496262965982105.050585222284
Winsorized Mean ( 4 / 24 )7.936986301369860.0729229605715515108.840703108620
Winsorized Mean ( 5 / 24 )7.936986301369860.0704007567424181112.740070826364
Winsorized Mean ( 6 / 24 )7.936986301369860.0704007567424181112.740070826364
Winsorized Mean ( 7 / 24 )7.946575342465750.068498858209685116.010332875041
Winsorized Mean ( 8 / 24 )7.946575342465750.068498858209685116.010332875041
Winsorized Mean ( 9 / 24 )7.946575342465750.068498858209685116.010332875041
Winsorized Mean ( 10 / 24 )7.946575342465750.0639004348181124.358705305944
Winsorized Mean ( 11 / 24 )7.961643835616440.0612102117213603130.070516205029
Winsorized Mean ( 12 / 24 )7.961643835616440.0612102117213603130.070516205029
Winsorized Mean ( 13 / 24 )7.961643835616440.0612102117213603130.070516205029
Winsorized Mean ( 14 / 24 )7.961643835616440.0552643480197526144.064738315031
Winsorized Mean ( 15 / 24 )7.961643835616440.0552643480197526144.064738315031
Winsorized Mean ( 16 / 24 )7.961643835616440.0552643480197526144.064738315031
Winsorized Mean ( 17 / 24 )7.984931506849320.0514874352155087155.085050817294
Winsorized Mean ( 18 / 24 )7.984931506849310.0514874352155087155.085050817294
Winsorized Mean ( 19 / 24 )7.984931506849310.0439086862459055181.853118130901
Winsorized Mean ( 20 / 24 )7.984931506849310.0439086862459055181.853118130901
Winsorized Mean ( 21 / 24 )7.984931506849310.0439086862459055181.853118130901
Winsorized Mean ( 22 / 24 )8.045205479452050.0351145708984906229.113022702432
Winsorized Mean ( 23 / 24 )8.013698630136990.0308624796521335259.658288007426
Winsorized Mean ( 24 / 24 )8.013698630136990.0308624796521335259.658288007426
Trimmed Mean ( 1 / 24 )7.936619718309860.0771013975196022102.937430106790
Trimmed Mean ( 2 / 24 )7.939130434782610.073466632453048108.064439184094
Trimmed Mean ( 3 / 24 )7.946268656716420.0710561393221155111.830852795055
Trimmed Mean ( 4 / 24 )7.953846153846150.068957795170618115.3436842661
Trimmed Mean ( 5 / 24 )7.958730158730160.0673784931916473118.119740910395
Trimmed Mean ( 6 / 24 )7.96393442622950.0662431679902453120.222728891865
Trimmed Mean ( 7 / 24 )7.969491525423730.0648359994313096122.917693801682
Trimmed Mean ( 8 / 24 )7.973684210526320.0635975715058193125.377180633331
Trimmed Mean ( 9 / 24 )7.978181818181820.0620465182873996128.583876072254
Trimmed Mean ( 10 / 24 )7.983018867924530.0601000525887081132.828816682673
Trimmed Mean ( 11 / 24 )7.988235294117650.0587214801079375136.036000445395
Trimmed Mean ( 12 / 24 )7.991836734693880.0575755001731295138.806205949795
Trimmed Mean ( 13 / 24 )7.995744680851060.0560788930538682142.580287260138
Trimmed Mean ( 14 / 24 )80.0541229427257326147.811622892346
Trimmed Mean ( 15 / 24 )8.00465116279070.0529269004628409151.239749405137
Trimmed Mean ( 16 / 24 )8.009756097560980.0513007485858923156.133318096720
Trimmed Mean ( 17 / 24 )8.015384615384620.0490859035945468163.293003253893
Trimmed Mean ( 18 / 24 )8.018918918918920.0471146193333077170.200227283805
Trimmed Mean ( 19 / 24 )8.022857142857140.0443601975970840180.857110144715
Trimmed Mean ( 20 / 24 )8.027272727272730.0427006687001271187.989391539642
Trimmed Mean ( 21 / 24 )8.032258064516130.0402644742622708199.487469082457
Trimmed Mean ( 22 / 24 )8.037931034482760.0366093049571354219.559782516879
Trimmed Mean ( 23 / 24 )8.037037037037040.0346525892473085231.931789560611
Trimmed Mean ( 24 / 24 )8.040.0331662479035540242.415121040522
Median8
Midrange7.7
Midmean - Weighted Average at Xnp7.98918918918919
Midmean - Weighted Average at X(n+1)p8.05
Midmean - Empirical Distribution Function8.05
Midmean - Empirical Distribution Function - Averaging8.05
Midmean - Empirical Distribution Function - Interpolation8.05
Midmean - Closest Observation8.05
Midmean - True Basic - Statistics Graphics Toolkit8.05
Midmean - MS Excel (old versions)8.05
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.93013698630137 & 0.0813388007067143 & 97.4951304592663 \tabularnewline
Geometric Mean & 7.89898377115985 &  &  \tabularnewline
Harmonic Mean & 7.86666382992008 &  &  \tabularnewline
Quadratic Mean & 7.96011461334158 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 7.93424657534247 & 0.0801496692145301 & 98.9928798596225 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 7.92602739726027 & 0.0771699629773262 & 102.708710636405 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 7.92602739726027 & 0.0754496262965982 & 105.050585222284 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 7.93698630136986 & 0.0729229605715515 & 108.840703108620 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 7.93698630136986 & 0.0704007567424181 & 112.740070826364 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 7.93698630136986 & 0.0704007567424181 & 112.740070826364 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 7.94657534246575 & 0.068498858209685 & 116.010332875041 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 7.94657534246575 & 0.068498858209685 & 116.010332875041 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 7.94657534246575 & 0.068498858209685 & 116.010332875041 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 7.94657534246575 & 0.0639004348181 & 124.358705305944 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 7.96164383561644 & 0.0612102117213603 & 130.070516205029 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 7.96164383561644 & 0.0612102117213603 & 130.070516205029 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 7.96164383561644 & 0.0612102117213603 & 130.070516205029 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 7.96164383561644 & 0.0552643480197526 & 144.064738315031 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 7.96164383561644 & 0.0552643480197526 & 144.064738315031 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 7.96164383561644 & 0.0552643480197526 & 144.064738315031 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 7.98493150684932 & 0.0514874352155087 & 155.085050817294 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 7.98493150684931 & 0.0514874352155087 & 155.085050817294 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 7.98493150684931 & 0.0439086862459055 & 181.853118130901 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 7.98493150684931 & 0.0439086862459055 & 181.853118130901 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 7.98493150684931 & 0.0439086862459055 & 181.853118130901 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 8.04520547945205 & 0.0351145708984906 & 229.113022702432 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 8.01369863013699 & 0.0308624796521335 & 259.658288007426 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 8.01369863013699 & 0.0308624796521335 & 259.658288007426 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 7.93661971830986 & 0.0771013975196022 & 102.937430106790 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 7.93913043478261 & 0.073466632453048 & 108.064439184094 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 7.94626865671642 & 0.0710561393221155 & 111.830852795055 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 7.95384615384615 & 0.068957795170618 & 115.3436842661 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 7.95873015873016 & 0.0673784931916473 & 118.119740910395 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 7.9639344262295 & 0.0662431679902453 & 120.222728891865 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 7.96949152542373 & 0.0648359994313096 & 122.917693801682 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 7.97368421052632 & 0.0635975715058193 & 125.377180633331 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 7.97818181818182 & 0.0620465182873996 & 128.583876072254 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 7.98301886792453 & 0.0601000525887081 & 132.828816682673 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 7.98823529411765 & 0.0587214801079375 & 136.036000445395 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 7.99183673469388 & 0.0575755001731295 & 138.806205949795 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 7.99574468085106 & 0.0560788930538682 & 142.580287260138 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 8 & 0.0541229427257326 & 147.811622892346 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 8.0046511627907 & 0.0529269004628409 & 151.239749405137 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 8.00975609756098 & 0.0513007485858923 & 156.133318096720 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 8.01538461538462 & 0.0490859035945468 & 163.293003253893 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 8.01891891891892 & 0.0471146193333077 & 170.200227283805 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 8.02285714285714 & 0.0443601975970840 & 180.857110144715 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 8.02727272727273 & 0.0427006687001271 & 187.989391539642 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 8.03225806451613 & 0.0402644742622708 & 199.487469082457 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 8.03793103448276 & 0.0366093049571354 & 219.559782516879 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 8.03703703703704 & 0.0346525892473085 & 231.931789560611 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 8.04 & 0.0331662479035540 & 242.415121040522 \tabularnewline
Median & 8 &  &  \tabularnewline
Midrange & 7.7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.98918918918919 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.05 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.05 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.05 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.05 &  &  \tabularnewline
Midmean - Closest Observation & 8.05 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.05 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.05 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64408&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]7.93013698630137[/C][C]0.0813388007067143[/C][C]97.4951304592663[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.89898377115985[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.86666382992008[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.96011461334158[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]7.93424657534247[/C][C]0.0801496692145301[/C][C]98.9928798596225[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]7.92602739726027[/C][C]0.0771699629773262[/C][C]102.708710636405[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]7.92602739726027[/C][C]0.0754496262965982[/C][C]105.050585222284[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]7.93698630136986[/C][C]0.0729229605715515[/C][C]108.840703108620[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]7.93698630136986[/C][C]0.0704007567424181[/C][C]112.740070826364[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]7.93698630136986[/C][C]0.0704007567424181[/C][C]112.740070826364[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]7.94657534246575[/C][C]0.068498858209685[/C][C]116.010332875041[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]7.94657534246575[/C][C]0.068498858209685[/C][C]116.010332875041[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]7.94657534246575[/C][C]0.068498858209685[/C][C]116.010332875041[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]7.94657534246575[/C][C]0.0639004348181[/C][C]124.358705305944[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]7.96164383561644[/C][C]0.0612102117213603[/C][C]130.070516205029[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]7.96164383561644[/C][C]0.0612102117213603[/C][C]130.070516205029[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]7.96164383561644[/C][C]0.0612102117213603[/C][C]130.070516205029[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]7.96164383561644[/C][C]0.0552643480197526[/C][C]144.064738315031[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]7.96164383561644[/C][C]0.0552643480197526[/C][C]144.064738315031[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]7.96164383561644[/C][C]0.0552643480197526[/C][C]144.064738315031[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]7.98493150684932[/C][C]0.0514874352155087[/C][C]155.085050817294[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]7.98493150684931[/C][C]0.0514874352155087[/C][C]155.085050817294[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]7.98493150684931[/C][C]0.0439086862459055[/C][C]181.853118130901[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]7.98493150684931[/C][C]0.0439086862459055[/C][C]181.853118130901[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]7.98493150684931[/C][C]0.0439086862459055[/C][C]181.853118130901[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]8.04520547945205[/C][C]0.0351145708984906[/C][C]229.113022702432[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]8.01369863013699[/C][C]0.0308624796521335[/C][C]259.658288007426[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]8.01369863013699[/C][C]0.0308624796521335[/C][C]259.658288007426[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]7.93661971830986[/C][C]0.0771013975196022[/C][C]102.937430106790[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]7.93913043478261[/C][C]0.073466632453048[/C][C]108.064439184094[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]7.94626865671642[/C][C]0.0710561393221155[/C][C]111.830852795055[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]7.95384615384615[/C][C]0.068957795170618[/C][C]115.3436842661[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]7.95873015873016[/C][C]0.0673784931916473[/C][C]118.119740910395[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]7.9639344262295[/C][C]0.0662431679902453[/C][C]120.222728891865[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]7.96949152542373[/C][C]0.0648359994313096[/C][C]122.917693801682[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]7.97368421052632[/C][C]0.0635975715058193[/C][C]125.377180633331[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]7.97818181818182[/C][C]0.0620465182873996[/C][C]128.583876072254[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]7.98301886792453[/C][C]0.0601000525887081[/C][C]132.828816682673[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]7.98823529411765[/C][C]0.0587214801079375[/C][C]136.036000445395[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]7.99183673469388[/C][C]0.0575755001731295[/C][C]138.806205949795[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]7.99574468085106[/C][C]0.0560788930538682[/C][C]142.580287260138[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]8[/C][C]0.0541229427257326[/C][C]147.811622892346[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]8.0046511627907[/C][C]0.0529269004628409[/C][C]151.239749405137[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]8.00975609756098[/C][C]0.0513007485858923[/C][C]156.133318096720[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]8.01538461538462[/C][C]0.0490859035945468[/C][C]163.293003253893[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]8.01891891891892[/C][C]0.0471146193333077[/C][C]170.200227283805[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]8.02285714285714[/C][C]0.0443601975970840[/C][C]180.857110144715[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]8.02727272727273[/C][C]0.0427006687001271[/C][C]187.989391539642[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]8.03225806451613[/C][C]0.0402644742622708[/C][C]199.487469082457[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]8.03793103448276[/C][C]0.0366093049571354[/C][C]219.559782516879[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]8.03703703703704[/C][C]0.0346525892473085[/C][C]231.931789560611[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]8.04[/C][C]0.0331662479035540[/C][C]242.415121040522[/C][/ROW]
[ROW][C]Median[/C][C]8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.98918918918919[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64408&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64408&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 Mean7.930136986301370.081338800706714397.4951304592663
Geometric Mean7.89898377115985
Harmonic Mean7.86666382992008
Quadratic Mean7.96011461334158
Winsorized Mean ( 1 / 24 )7.934246575342470.080149669214530198.9928798596225
Winsorized Mean ( 2 / 24 )7.926027397260270.0771699629773262102.708710636405
Winsorized Mean ( 3 / 24 )7.926027397260270.0754496262965982105.050585222284
Winsorized Mean ( 4 / 24 )7.936986301369860.0729229605715515108.840703108620
Winsorized Mean ( 5 / 24 )7.936986301369860.0704007567424181112.740070826364
Winsorized Mean ( 6 / 24 )7.936986301369860.0704007567424181112.740070826364
Winsorized Mean ( 7 / 24 )7.946575342465750.068498858209685116.010332875041
Winsorized Mean ( 8 / 24 )7.946575342465750.068498858209685116.010332875041
Winsorized Mean ( 9 / 24 )7.946575342465750.068498858209685116.010332875041
Winsorized Mean ( 10 / 24 )7.946575342465750.0639004348181124.358705305944
Winsorized Mean ( 11 / 24 )7.961643835616440.0612102117213603130.070516205029
Winsorized Mean ( 12 / 24 )7.961643835616440.0612102117213603130.070516205029
Winsorized Mean ( 13 / 24 )7.961643835616440.0612102117213603130.070516205029
Winsorized Mean ( 14 / 24 )7.961643835616440.0552643480197526144.064738315031
Winsorized Mean ( 15 / 24 )7.961643835616440.0552643480197526144.064738315031
Winsorized Mean ( 16 / 24 )7.961643835616440.0552643480197526144.064738315031
Winsorized Mean ( 17 / 24 )7.984931506849320.0514874352155087155.085050817294
Winsorized Mean ( 18 / 24 )7.984931506849310.0514874352155087155.085050817294
Winsorized Mean ( 19 / 24 )7.984931506849310.0439086862459055181.853118130901
Winsorized Mean ( 20 / 24 )7.984931506849310.0439086862459055181.853118130901
Winsorized Mean ( 21 / 24 )7.984931506849310.0439086862459055181.853118130901
Winsorized Mean ( 22 / 24 )8.045205479452050.0351145708984906229.113022702432
Winsorized Mean ( 23 / 24 )8.013698630136990.0308624796521335259.658288007426
Winsorized Mean ( 24 / 24 )8.013698630136990.0308624796521335259.658288007426
Trimmed Mean ( 1 / 24 )7.936619718309860.0771013975196022102.937430106790
Trimmed Mean ( 2 / 24 )7.939130434782610.073466632453048108.064439184094
Trimmed Mean ( 3 / 24 )7.946268656716420.0710561393221155111.830852795055
Trimmed Mean ( 4 / 24 )7.953846153846150.068957795170618115.3436842661
Trimmed Mean ( 5 / 24 )7.958730158730160.0673784931916473118.119740910395
Trimmed Mean ( 6 / 24 )7.96393442622950.0662431679902453120.222728891865
Trimmed Mean ( 7 / 24 )7.969491525423730.0648359994313096122.917693801682
Trimmed Mean ( 8 / 24 )7.973684210526320.0635975715058193125.377180633331
Trimmed Mean ( 9 / 24 )7.978181818181820.0620465182873996128.583876072254
Trimmed Mean ( 10 / 24 )7.983018867924530.0601000525887081132.828816682673
Trimmed Mean ( 11 / 24 )7.988235294117650.0587214801079375136.036000445395
Trimmed Mean ( 12 / 24 )7.991836734693880.0575755001731295138.806205949795
Trimmed Mean ( 13 / 24 )7.995744680851060.0560788930538682142.580287260138
Trimmed Mean ( 14 / 24 )80.0541229427257326147.811622892346
Trimmed Mean ( 15 / 24 )8.00465116279070.0529269004628409151.239749405137
Trimmed Mean ( 16 / 24 )8.009756097560980.0513007485858923156.133318096720
Trimmed Mean ( 17 / 24 )8.015384615384620.0490859035945468163.293003253893
Trimmed Mean ( 18 / 24 )8.018918918918920.0471146193333077170.200227283805
Trimmed Mean ( 19 / 24 )8.022857142857140.0443601975970840180.857110144715
Trimmed Mean ( 20 / 24 )8.027272727272730.0427006687001271187.989391539642
Trimmed Mean ( 21 / 24 )8.032258064516130.0402644742622708199.487469082457
Trimmed Mean ( 22 / 24 )8.037931034482760.0366093049571354219.559782516879
Trimmed Mean ( 23 / 24 )8.037037037037040.0346525892473085231.931789560611
Trimmed Mean ( 24 / 24 )8.040.0331662479035540242.415121040522
Median8
Midrange7.7
Midmean - Weighted Average at Xnp7.98918918918919
Midmean - Weighted Average at X(n+1)p8.05
Midmean - Empirical Distribution Function8.05
Midmean - Empirical Distribution Function - Averaging8.05
Midmean - Empirical Distribution Function - Interpolation8.05
Midmean - Closest Observation8.05
Midmean - True Basic - Statistics Graphics Toolkit8.05
Midmean - MS Excel (old versions)8.05
Number of observations73



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')