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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 26 Dec 2012 19:12:00 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/26/t1356567141ebwakwwode0v9l7.htm/, Retrieved Thu, 25 Apr 2024 22:09:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204750, Retrieved Thu, 25 Apr 2024 22:09:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Harrell-Davis Quantiles] [] [2012-12-26 18:07:12] [529459d2862caba1018e23a9e1de2fb7]
- RMP     [Central Tendency] [] [2012-12-27 00:12:00] [712f2f4436a9b7aba1a90edc9e618eb7] [Current]
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Dataseries X:
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
8,1
7,9
7,9
8,3
8,6
8,7
8,5
8,3
8
8
8,8
8,7
8,5
8,1
7,8
7,7
7,5
7,2
6,9
6,6
6,5
6,6
7,7
8
7,7
7,2
7
7
7,3
7,3
7,1
6,9
6,7
6,8
7,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204750&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204750&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204750&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' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.62531645569620.073301792096365104.026330565994
Geometric Mean7.59737955015988
Harmonic Mean7.569012037433
Quadratic Mean7.65274832736745
Winsorized Mean ( 1 / 26 )7.627848101265820.0721294030995594105.752269857789
Winsorized Mean ( 2 / 26 )7.630379746835440.071596856098888106.57422912951
Winsorized Mean ( 3 / 26 )7.630379746835440.071596856098888106.57422912951
Winsorized Mean ( 4 / 26 )7.635443037974680.0706081978731393108.138194543545
Winsorized Mean ( 5 / 26 )7.629113924050630.0694287886849604109.88401308092
Winsorized Mean ( 6 / 26 )7.629113924050630.0694287886849604109.88401308092
Winsorized Mean ( 7 / 26 )7.629113924050630.0662471031188998115.161472198384
Winsorized Mean ( 8 / 26 )7.639240506329110.0644910597810869118.454256020296
Winsorized Mean ( 9 / 26 )7.639240506329110.0644910597810869118.454256020296
Winsorized Mean ( 10 / 26 )7.626582278481010.0583698506951181130.659616011642
Winsorized Mean ( 11 / 26 )7.626582278481010.0583698506951181130.659616011642
Winsorized Mean ( 12 / 26 )7.626582278481010.0583698506951181130.659616011642
Winsorized Mean ( 13 / 26 )7.626582278481010.0583698506951181130.659616011642
Winsorized Mean ( 14 / 26 )7.626582278481010.0530690321241335143.710596806094
Winsorized Mean ( 15 / 26 )7.607594936708860.0505655182782649150.450251391548
Winsorized Mean ( 16 / 26 )7.607594936708860.0505655182782649150.450251391548
Winsorized Mean ( 17 / 26 )7.607594936708860.0505655182782649150.450251391548
Winsorized Mean ( 18 / 26 )7.607594936708860.0505655182782649150.450251391548
Winsorized Mean ( 19 / 26 )7.631645569620250.0469637793611633162.500669099286
Winsorized Mean ( 20 / 26 )7.606329113924050.043884041091106173.327909755003
Winsorized Mean ( 21 / 26 )7.632911392405060.0400714032847025190.482757446106
Winsorized Mean ( 22 / 26 )7.632911392405060.0400714032847025190.482757446106
Winsorized Mean ( 23 / 26 )7.632911392405060.0400714032847025190.482757446106
Winsorized Mean ( 24 / 26 )7.632911392405060.0400714032847025190.482757446106
Winsorized Mean ( 25 / 26 )7.664556962025320.0358074648147661214.049137565993
Winsorized Mean ( 26 / 26 )7.664556962025320.0358074648147661214.049137565993
Trimmed Mean ( 1 / 26 )7.629870129870130.0708812060374716107.643063040386
Trimmed Mean ( 2 / 26 )7.6320.0694160975177559109.94567935842
Trimmed Mean ( 3 / 26 )7.632876712328770.0680242702938645112.208138056532
Trimmed Mean ( 4 / 26 )7.633802816901410.0663793033964936115.00275577319
Trimmed Mean ( 5 / 26 )7.633333333333330.0647859175896369117.823959547566
Trimmed Mean ( 6 / 26 )7.634328358208950.0632509964491748120.698942100359
Trimmed Mean ( 7 / 26 )7.635384615384620.0614109255356726124.332674500229
Trimmed Mean ( 8 / 26 )7.636507936507940.0600094542517969127.255080582228
Trimmed Mean ( 9 / 26 )7.636065573770490.0587219430451798130.037685706268
Trimmed Mean ( 10 / 26 )7.635593220338980.0571463771994998133.614650561013
Trimmed Mean ( 11 / 26 )7.636842105263160.0565082323137001135.145655643021
Trimmed Mean ( 12 / 26 )7.638181818181820.0556861641951308137.164804374328
Trimmed Mean ( 13 / 26 )7.639622641509430.0546355933417746139.828675305484
Trimmed Mean ( 14 / 26 )7.641176470588240.0532972773161959143.368983470873
Trimmed Mean ( 15 / 26 )7.642857142857140.0526508199702285145.161217758409
Trimmed Mean ( 16 / 26 )7.64680851063830.0522262090208899146.417070164516
Trimmed Mean ( 17 / 26 )7.651111111111110.0516028170695883148.269252447852
Trimmed Mean ( 18 / 26 )7.655813953488370.0507204272959863150.941432508283
Trimmed Mean ( 19 / 26 )7.66097560975610.0494947704530597154.783536515675
Trimmed Mean ( 20 / 26 )7.664102564102560.048664648732568157.488089685388
Trimmed Mean ( 21 / 26 )7.664102564102560.0480654060237631159.451530697847
Trimmed Mean ( 22 / 26 )7.674285714285710.0480445971293894159.732543778399
Trimmed Mean ( 23 / 26 )7.678787878787880.0478233760669292160.565575045169
Trimmed Mean ( 24 / 26 )7.683870967741940.0473142716866444162.400702659677
Trimmed Mean ( 25 / 26 )7.689655172413790.0463826522867958165.787310412235
Trimmed Mean ( 26 / 26 )7.692592592592590.0462021835444105166.498463978403
Median7.7
Midrange7.45
Midmean - Weighted Average at Xnp7.65
Midmean - Weighted Average at X(n+1)p7.7
Midmean - Empirical Distribution Function7.7
Midmean - Empirical Distribution Function - Averaging7.7
Midmean - Empirical Distribution Function - Interpolation7.65
Midmean - Closest Observation7.65
Midmean - True Basic - Statistics Graphics Toolkit7.7
Midmean - MS Excel (old versions)7.7
Number of observations79

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.6253164556962 & 0.073301792096365 & 104.026330565994 \tabularnewline
Geometric Mean & 7.59737955015988 &  &  \tabularnewline
Harmonic Mean & 7.569012037433 &  &  \tabularnewline
Quadratic Mean & 7.65274832736745 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 7.62784810126582 & 0.0721294030995594 & 105.752269857789 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 7.63037974683544 & 0.071596856098888 & 106.57422912951 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 7.63037974683544 & 0.071596856098888 & 106.57422912951 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 7.63544303797468 & 0.0706081978731393 & 108.138194543545 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 7.62911392405063 & 0.0694287886849604 & 109.88401308092 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 7.62911392405063 & 0.0694287886849604 & 109.88401308092 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 7.62911392405063 & 0.0662471031188998 & 115.161472198384 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 7.63924050632911 & 0.0644910597810869 & 118.454256020296 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 7.63924050632911 & 0.0644910597810869 & 118.454256020296 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 7.62658227848101 & 0.0583698506951181 & 130.659616011642 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 7.62658227848101 & 0.0583698506951181 & 130.659616011642 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 7.62658227848101 & 0.0583698506951181 & 130.659616011642 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 7.62658227848101 & 0.0583698506951181 & 130.659616011642 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 7.62658227848101 & 0.0530690321241335 & 143.710596806094 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 7.60759493670886 & 0.0505655182782649 & 150.450251391548 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 7.60759493670886 & 0.0505655182782649 & 150.450251391548 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 7.60759493670886 & 0.0505655182782649 & 150.450251391548 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 7.60759493670886 & 0.0505655182782649 & 150.450251391548 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 7.63164556962025 & 0.0469637793611633 & 162.500669099286 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 7.60632911392405 & 0.043884041091106 & 173.327909755003 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 7.63291139240506 & 0.0400714032847025 & 190.482757446106 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 7.63291139240506 & 0.0400714032847025 & 190.482757446106 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 7.63291139240506 & 0.0400714032847025 & 190.482757446106 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 7.63291139240506 & 0.0400714032847025 & 190.482757446106 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 7.66455696202532 & 0.0358074648147661 & 214.049137565993 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 7.66455696202532 & 0.0358074648147661 & 214.049137565993 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 7.62987012987013 & 0.0708812060374716 & 107.643063040386 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 7.632 & 0.0694160975177559 & 109.94567935842 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 7.63287671232877 & 0.0680242702938645 & 112.208138056532 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 7.63380281690141 & 0.0663793033964936 & 115.00275577319 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 7.63333333333333 & 0.0647859175896369 & 117.823959547566 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 7.63432835820895 & 0.0632509964491748 & 120.698942100359 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 7.63538461538462 & 0.0614109255356726 & 124.332674500229 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 7.63650793650794 & 0.0600094542517969 & 127.255080582228 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 7.63606557377049 & 0.0587219430451798 & 130.037685706268 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 7.63559322033898 & 0.0571463771994998 & 133.614650561013 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 7.63684210526316 & 0.0565082323137001 & 135.145655643021 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 7.63818181818182 & 0.0556861641951308 & 137.164804374328 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 7.63962264150943 & 0.0546355933417746 & 139.828675305484 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 7.64117647058824 & 0.0532972773161959 & 143.368983470873 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 7.64285714285714 & 0.0526508199702285 & 145.161217758409 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 7.6468085106383 & 0.0522262090208899 & 146.417070164516 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 7.65111111111111 & 0.0516028170695883 & 148.269252447852 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 7.65581395348837 & 0.0507204272959863 & 150.941432508283 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 7.6609756097561 & 0.0494947704530597 & 154.783536515675 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 7.66410256410256 & 0.048664648732568 & 157.488089685388 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 7.66410256410256 & 0.0480654060237631 & 159.451530697847 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 7.67428571428571 & 0.0480445971293894 & 159.732543778399 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 7.67878787878788 & 0.0478233760669292 & 160.565575045169 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 7.68387096774194 & 0.0473142716866444 & 162.400702659677 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 7.68965517241379 & 0.0463826522867958 & 165.787310412235 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 7.69259259259259 & 0.0462021835444105 & 166.498463978403 \tabularnewline
Median & 7.7 &  &  \tabularnewline
Midrange & 7.45 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.65 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.7 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.7 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.7 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.65 &  &  \tabularnewline
Midmean - Closest Observation & 7.65 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.7 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.7 &  &  \tabularnewline
Number of observations & 79 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204750&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]7.6253164556962[/C][C]0.073301792096365[/C][C]104.026330565994[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.59737955015988[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.569012037433[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.65274832736745[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]7.62784810126582[/C][C]0.0721294030995594[/C][C]105.752269857789[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]7.63037974683544[/C][C]0.071596856098888[/C][C]106.57422912951[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]7.63037974683544[/C][C]0.071596856098888[/C][C]106.57422912951[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]7.63544303797468[/C][C]0.0706081978731393[/C][C]108.138194543545[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]7.62911392405063[/C][C]0.0694287886849604[/C][C]109.88401308092[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]7.62911392405063[/C][C]0.0694287886849604[/C][C]109.88401308092[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]7.62911392405063[/C][C]0.0662471031188998[/C][C]115.161472198384[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]7.63924050632911[/C][C]0.0644910597810869[/C][C]118.454256020296[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]7.63924050632911[/C][C]0.0644910597810869[/C][C]118.454256020296[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]7.62658227848101[/C][C]0.0583698506951181[/C][C]130.659616011642[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]7.62658227848101[/C][C]0.0583698506951181[/C][C]130.659616011642[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]7.62658227848101[/C][C]0.0583698506951181[/C][C]130.659616011642[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]7.62658227848101[/C][C]0.0583698506951181[/C][C]130.659616011642[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]7.62658227848101[/C][C]0.0530690321241335[/C][C]143.710596806094[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]7.60759493670886[/C][C]0.0505655182782649[/C][C]150.450251391548[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]7.60759493670886[/C][C]0.0505655182782649[/C][C]150.450251391548[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]7.60759493670886[/C][C]0.0505655182782649[/C][C]150.450251391548[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]7.60759493670886[/C][C]0.0505655182782649[/C][C]150.450251391548[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]7.63164556962025[/C][C]0.0469637793611633[/C][C]162.500669099286[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]7.60632911392405[/C][C]0.043884041091106[/C][C]173.327909755003[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]7.63291139240506[/C][C]0.0400714032847025[/C][C]190.482757446106[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]7.63291139240506[/C][C]0.0400714032847025[/C][C]190.482757446106[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]7.63291139240506[/C][C]0.0400714032847025[/C][C]190.482757446106[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]7.63291139240506[/C][C]0.0400714032847025[/C][C]190.482757446106[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]7.66455696202532[/C][C]0.0358074648147661[/C][C]214.049137565993[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]7.66455696202532[/C][C]0.0358074648147661[/C][C]214.049137565993[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]7.62987012987013[/C][C]0.0708812060374716[/C][C]107.643063040386[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]7.632[/C][C]0.0694160975177559[/C][C]109.94567935842[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]7.63287671232877[/C][C]0.0680242702938645[/C][C]112.208138056532[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]7.63380281690141[/C][C]0.0663793033964936[/C][C]115.00275577319[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]7.63333333333333[/C][C]0.0647859175896369[/C][C]117.823959547566[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]7.63432835820895[/C][C]0.0632509964491748[/C][C]120.698942100359[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]7.63538461538462[/C][C]0.0614109255356726[/C][C]124.332674500229[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]7.63650793650794[/C][C]0.0600094542517969[/C][C]127.255080582228[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]7.63606557377049[/C][C]0.0587219430451798[/C][C]130.037685706268[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]7.63559322033898[/C][C]0.0571463771994998[/C][C]133.614650561013[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]7.63684210526316[/C][C]0.0565082323137001[/C][C]135.145655643021[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]7.63818181818182[/C][C]0.0556861641951308[/C][C]137.164804374328[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]7.63962264150943[/C][C]0.0546355933417746[/C][C]139.828675305484[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]7.64117647058824[/C][C]0.0532972773161959[/C][C]143.368983470873[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]7.64285714285714[/C][C]0.0526508199702285[/C][C]145.161217758409[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]7.6468085106383[/C][C]0.0522262090208899[/C][C]146.417070164516[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]7.65111111111111[/C][C]0.0516028170695883[/C][C]148.269252447852[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]7.65581395348837[/C][C]0.0507204272959863[/C][C]150.941432508283[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]7.6609756097561[/C][C]0.0494947704530597[/C][C]154.783536515675[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]7.66410256410256[/C][C]0.048664648732568[/C][C]157.488089685388[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]7.66410256410256[/C][C]0.0480654060237631[/C][C]159.451530697847[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]7.67428571428571[/C][C]0.0480445971293894[/C][C]159.732543778399[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]7.67878787878788[/C][C]0.0478233760669292[/C][C]160.565575045169[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]7.68387096774194[/C][C]0.0473142716866444[/C][C]162.400702659677[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]7.68965517241379[/C][C]0.0463826522867958[/C][C]165.787310412235[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]7.69259259259259[/C][C]0.0462021835444105[/C][C]166.498463978403[/C][/ROW]
[ROW][C]Median[/C][C]7.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]79[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204750&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204750&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 Mean7.62531645569620.073301792096365104.026330565994
Geometric Mean7.59737955015988
Harmonic Mean7.569012037433
Quadratic Mean7.65274832736745
Winsorized Mean ( 1 / 26 )7.627848101265820.0721294030995594105.752269857789
Winsorized Mean ( 2 / 26 )7.630379746835440.071596856098888106.57422912951
Winsorized Mean ( 3 / 26 )7.630379746835440.071596856098888106.57422912951
Winsorized Mean ( 4 / 26 )7.635443037974680.0706081978731393108.138194543545
Winsorized Mean ( 5 / 26 )7.629113924050630.0694287886849604109.88401308092
Winsorized Mean ( 6 / 26 )7.629113924050630.0694287886849604109.88401308092
Winsorized Mean ( 7 / 26 )7.629113924050630.0662471031188998115.161472198384
Winsorized Mean ( 8 / 26 )7.639240506329110.0644910597810869118.454256020296
Winsorized Mean ( 9 / 26 )7.639240506329110.0644910597810869118.454256020296
Winsorized Mean ( 10 / 26 )7.626582278481010.0583698506951181130.659616011642
Winsorized Mean ( 11 / 26 )7.626582278481010.0583698506951181130.659616011642
Winsorized Mean ( 12 / 26 )7.626582278481010.0583698506951181130.659616011642
Winsorized Mean ( 13 / 26 )7.626582278481010.0583698506951181130.659616011642
Winsorized Mean ( 14 / 26 )7.626582278481010.0530690321241335143.710596806094
Winsorized Mean ( 15 / 26 )7.607594936708860.0505655182782649150.450251391548
Winsorized Mean ( 16 / 26 )7.607594936708860.0505655182782649150.450251391548
Winsorized Mean ( 17 / 26 )7.607594936708860.0505655182782649150.450251391548
Winsorized Mean ( 18 / 26 )7.607594936708860.0505655182782649150.450251391548
Winsorized Mean ( 19 / 26 )7.631645569620250.0469637793611633162.500669099286
Winsorized Mean ( 20 / 26 )7.606329113924050.043884041091106173.327909755003
Winsorized Mean ( 21 / 26 )7.632911392405060.0400714032847025190.482757446106
Winsorized Mean ( 22 / 26 )7.632911392405060.0400714032847025190.482757446106
Winsorized Mean ( 23 / 26 )7.632911392405060.0400714032847025190.482757446106
Winsorized Mean ( 24 / 26 )7.632911392405060.0400714032847025190.482757446106
Winsorized Mean ( 25 / 26 )7.664556962025320.0358074648147661214.049137565993
Winsorized Mean ( 26 / 26 )7.664556962025320.0358074648147661214.049137565993
Trimmed Mean ( 1 / 26 )7.629870129870130.0708812060374716107.643063040386
Trimmed Mean ( 2 / 26 )7.6320.0694160975177559109.94567935842
Trimmed Mean ( 3 / 26 )7.632876712328770.0680242702938645112.208138056532
Trimmed Mean ( 4 / 26 )7.633802816901410.0663793033964936115.00275577319
Trimmed Mean ( 5 / 26 )7.633333333333330.0647859175896369117.823959547566
Trimmed Mean ( 6 / 26 )7.634328358208950.0632509964491748120.698942100359
Trimmed Mean ( 7 / 26 )7.635384615384620.0614109255356726124.332674500229
Trimmed Mean ( 8 / 26 )7.636507936507940.0600094542517969127.255080582228
Trimmed Mean ( 9 / 26 )7.636065573770490.0587219430451798130.037685706268
Trimmed Mean ( 10 / 26 )7.635593220338980.0571463771994998133.614650561013
Trimmed Mean ( 11 / 26 )7.636842105263160.0565082323137001135.145655643021
Trimmed Mean ( 12 / 26 )7.638181818181820.0556861641951308137.164804374328
Trimmed Mean ( 13 / 26 )7.639622641509430.0546355933417746139.828675305484
Trimmed Mean ( 14 / 26 )7.641176470588240.0532972773161959143.368983470873
Trimmed Mean ( 15 / 26 )7.642857142857140.0526508199702285145.161217758409
Trimmed Mean ( 16 / 26 )7.64680851063830.0522262090208899146.417070164516
Trimmed Mean ( 17 / 26 )7.651111111111110.0516028170695883148.269252447852
Trimmed Mean ( 18 / 26 )7.655813953488370.0507204272959863150.941432508283
Trimmed Mean ( 19 / 26 )7.66097560975610.0494947704530597154.783536515675
Trimmed Mean ( 20 / 26 )7.664102564102560.048664648732568157.488089685388
Trimmed Mean ( 21 / 26 )7.664102564102560.0480654060237631159.451530697847
Trimmed Mean ( 22 / 26 )7.674285714285710.0480445971293894159.732543778399
Trimmed Mean ( 23 / 26 )7.678787878787880.0478233760669292160.565575045169
Trimmed Mean ( 24 / 26 )7.683870967741940.0473142716866444162.400702659677
Trimmed Mean ( 25 / 26 )7.689655172413790.0463826522867958165.787310412235
Trimmed Mean ( 26 / 26 )7.692592592592590.0462021835444105166.498463978403
Median7.7
Midrange7.45
Midmean - Weighted Average at Xnp7.65
Midmean - Weighted Average at X(n+1)p7.7
Midmean - Empirical Distribution Function7.7
Midmean - Empirical Distribution Function - Averaging7.7
Midmean - Empirical Distribution Function - Interpolation7.65
Midmean - Closest Observation7.65
Midmean - True Basic - Statistics Graphics Toolkit7.7
Midmean - MS Excel (old versions)7.7
Number of observations79



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')