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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 computationSat, 28 Nov 2015 10:19:09 +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/2015/Nov/28/t1448706091apzhv9w2kgwup4d.htm/, Retrieved Tue, 14 May 2024 16:45:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284342, Retrieved Tue, 14 May 2024 16:45:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [multiple regression] [2015-11-27 09:58:54] [7f0b4e0465c416ccc680332e4c4dca5e]
- RMPD  [] [central tendency] [-0001-11-30 00:00:00] [74be16979710d4c4e7c6647856088456]
- RM D      [Central Tendency] [central tendency] [2015-11-28 10:19:09] [002d4648fc88037d8570a4a28cacbbc2] [Current]
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Dataseries X:
6.5
6.8
6.8
6.5
6.2
6.2
6.6
6.7
6.5
6.4
6.5
6.8
7.1
7.2
7.1
7
6.9
6.9
7.4
7.3
7
6.8
6.5
6.4
6.3
6
5.9
5.7
5.7
5.7
6.2
6.4
6.2
6.2
6.1
6.1
6.2
6.1
6.1
6.2
6.2
6.2
6.4
6.4
6.4
6.7
6.9
7.1
7.3
7.2
7.1
6.9
6.8
6.7
7.2
7.2
7.1
7.1
7
7.1
7.3
7.2
7.1
7
6.9
7
7.5
7.6
7.5
7.3
7.3
7.4
7.7
7.8
7.7
7.5
7.3
7.3
7.6
7.6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284342&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284342&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284342&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean6.79750.0593470537163398114.538120670487
Geometric Mean6.77673913736271
Harmonic Mean6.75570631629483
Quadratic Mean6.81793590465619
Winsorized Mean ( 1 / 26 )6.796250.0590923903837526115.010578449516
Winsorized Mean ( 2 / 26 )6.796250.0590923903837526115.010578449516
Winsorized Mean ( 3 / 26 )6.80.0567584265756352119.805999042952
Winsorized Mean ( 4 / 26 )6.8050.0557997096312939121.954039635066
Winsorized Mean ( 5 / 26 )6.811250.0547142678612712124.487638530959
Winsorized Mean ( 6 / 26 )6.803750.0534103931359498127.386255755165
Winsorized Mean ( 7 / 26 )6.803750.0534103931359498127.386255755165
Winsorized Mean ( 8 / 26 )6.803750.0534103931359498127.386255755165
Winsorized Mean ( 9 / 26 )6.803750.0498238590474458136.556062297804
Winsorized Mean ( 10 / 26 )6.803750.0498238590474458136.556062297804
Winsorized Mean ( 11 / 26 )6.790.0478526218479355141.89400157795
Winsorized Mean ( 12 / 26 )6.790.0478526218479355141.89400157795
Winsorized Mean ( 13 / 26 )6.790.0478526218479355141.89400157795
Winsorized Mean ( 14 / 26 )6.790.0478526218479355141.89400157795
Winsorized Mean ( 15 / 26 )6.790.0478526218479355141.89400157795
Winsorized Mean ( 16 / 26 )6.790.0478526218479355141.89400157795
Winsorized Mean ( 17 / 26 )6.790.0478526218479355141.89400157795
Winsorized Mean ( 18 / 26 )6.790.0414759347641131163.709390484311
Winsorized Mean ( 19 / 26 )6.813750.038059902402477179.026996126941
Winsorized Mean ( 20 / 26 )6.813750.038059902402477179.026996126941
Winsorized Mean ( 21 / 26 )6.813750.038059902402477179.026996126941
Winsorized Mean ( 22 / 26 )6.813750.038059902402477179.026996126941
Winsorized Mean ( 23 / 26 )6.7850.0345449624457712196.410692605358
Winsorized Mean ( 24 / 26 )6.7850.0345449624457712196.410692605358
Winsorized Mean ( 25 / 26 )6.816250.0302648514646481225.220005059729
Winsorized Mean ( 26 / 26 )6.816250.0302648514646481225.220005059729
Trimmed Mean ( 1 / 26 )6.798717948717950.0577780840124795117.669494669458
Trimmed Mean ( 2 / 26 )6.801315789473680.0562417532684658120.930010076466
Trimmed Mean ( 3 / 26 )6.804054054054050.054437964693401124.987296868556
Trimmed Mean ( 4 / 26 )6.805555555555560.053364460139512127.529736790434
Trimmed Mean ( 5 / 26 )6.805714285714290.0524309943533874129.803265599799
Trimmed Mean ( 6 / 26 )6.804411764705880.0516383819590572131.770429408515
Trimmed Mean ( 7 / 26 )6.804545454545450.0510236390291341133.360645850056
Trimmed Mean ( 8 / 26 )6.80468750.0502686082332733135.366538664102
Trimmed Mean ( 9 / 26 )6.804838709677420.0493440537360424137.905952074362
Trimmed Mean ( 10 / 26 )6.8050.0489681667609908138.967832576102
Trimmed Mean ( 11 / 26 )6.80517241379310.0484747652522626140.385876618051
Trimmed Mean ( 12 / 26 )6.807142857142860.0482052661116038141.21160209723
Trimmed Mean ( 13 / 26 )6.809259259259260.0478225024822562142.386092442271
Trimmed Mean ( 14 / 26 )6.811538461538460.0472991383945268144.009778882709
Trimmed Mean ( 15 / 26 )6.8140.0465994657059674146.224852512148
Trimmed Mean ( 16 / 26 )6.816666666666670.0456759062972553149.239877634925
Trimmed Mean ( 17 / 26 )6.81956521739130.0444634752366448153.37454351231
Trimmed Mean ( 18 / 26 )6.822727272727270.0428705259025236159.147272609633
Trimmed Mean ( 19 / 26 )6.826190476190480.0421627183393635161.901099953925
Trimmed Mean ( 20 / 26 )6.82750.0419076365356005162.917801250854
Trimmed Mean ( 21 / 26 )6.828947368421050.0414714926744776164.666061625116
Trimmed Mean ( 22 / 26 )6.830555555555560.0407897132310019167.457797922542
Trimmed Mean ( 23 / 26 )6.832352941176470.0397677276325532171.806470923011
Trimmed Mean ( 24 / 26 )6.83750.0390796333393173174.963258755064
Trimmed Mean ( 25 / 26 )6.843333333333330.037960455326331180.275322687884
Trimmed Mean ( 26 / 26 )6.846428571428570.0376147777363793182.014330096839
Median6.9
Midrange6.75
Midmean - Weighted Average at Xnp6.83488372093023
Midmean - Weighted Average at X(n+1)p6.83488372093023
Midmean - Empirical Distribution Function6.83488372093023
Midmean - Empirical Distribution Function - Averaging6.83488372093023
Midmean - Empirical Distribution Function - Interpolation6.83488372093023
Midmean - Closest Observation6.83488372093023
Midmean - True Basic - Statistics Graphics Toolkit6.83488372093023
Midmean - MS Excel (old versions)6.83488372093023
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 6.7975 & 0.0593470537163398 & 114.538120670487 \tabularnewline
Geometric Mean & 6.77673913736271 &  &  \tabularnewline
Harmonic Mean & 6.75570631629483 &  &  \tabularnewline
Quadratic Mean & 6.81793590465619 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 6.79625 & 0.0590923903837526 & 115.010578449516 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 6.79625 & 0.0590923903837526 & 115.010578449516 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 6.8 & 0.0567584265756352 & 119.805999042952 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 6.805 & 0.0557997096312939 & 121.954039635066 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 6.81125 & 0.0547142678612712 & 124.487638530959 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 6.80375 & 0.0534103931359498 & 127.386255755165 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 6.80375 & 0.0534103931359498 & 127.386255755165 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 6.80375 & 0.0534103931359498 & 127.386255755165 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 6.80375 & 0.0498238590474458 & 136.556062297804 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 6.80375 & 0.0498238590474458 & 136.556062297804 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 6.79 & 0.0478526218479355 & 141.89400157795 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 6.79 & 0.0478526218479355 & 141.89400157795 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 6.79 & 0.0478526218479355 & 141.89400157795 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 6.79 & 0.0478526218479355 & 141.89400157795 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 6.79 & 0.0478526218479355 & 141.89400157795 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 6.79 & 0.0478526218479355 & 141.89400157795 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 6.79 & 0.0478526218479355 & 141.89400157795 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 6.79 & 0.0414759347641131 & 163.709390484311 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 6.81375 & 0.038059902402477 & 179.026996126941 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 6.81375 & 0.038059902402477 & 179.026996126941 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 6.81375 & 0.038059902402477 & 179.026996126941 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 6.81375 & 0.038059902402477 & 179.026996126941 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 6.785 & 0.0345449624457712 & 196.410692605358 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 6.785 & 0.0345449624457712 & 196.410692605358 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 6.81625 & 0.0302648514646481 & 225.220005059729 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 6.81625 & 0.0302648514646481 & 225.220005059729 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 6.79871794871795 & 0.0577780840124795 & 117.669494669458 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 6.80131578947368 & 0.0562417532684658 & 120.930010076466 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 6.80405405405405 & 0.054437964693401 & 124.987296868556 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 6.80555555555556 & 0.053364460139512 & 127.529736790434 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 6.80571428571429 & 0.0524309943533874 & 129.803265599799 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 6.80441176470588 & 0.0516383819590572 & 131.770429408515 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 6.80454545454545 & 0.0510236390291341 & 133.360645850056 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 6.8046875 & 0.0502686082332733 & 135.366538664102 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 6.80483870967742 & 0.0493440537360424 & 137.905952074362 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 6.805 & 0.0489681667609908 & 138.967832576102 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 6.8051724137931 & 0.0484747652522626 & 140.385876618051 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 6.80714285714286 & 0.0482052661116038 & 141.21160209723 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 6.80925925925926 & 0.0478225024822562 & 142.386092442271 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 6.81153846153846 & 0.0472991383945268 & 144.009778882709 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 6.814 & 0.0465994657059674 & 146.224852512148 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 6.81666666666667 & 0.0456759062972553 & 149.239877634925 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 6.8195652173913 & 0.0444634752366448 & 153.37454351231 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 6.82272727272727 & 0.0428705259025236 & 159.147272609633 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 6.82619047619048 & 0.0421627183393635 & 161.901099953925 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 6.8275 & 0.0419076365356005 & 162.917801250854 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 6.82894736842105 & 0.0414714926744776 & 164.666061625116 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 6.83055555555556 & 0.0407897132310019 & 167.457797922542 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 6.83235294117647 & 0.0397677276325532 & 171.806470923011 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 6.8375 & 0.0390796333393173 & 174.963258755064 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 6.84333333333333 & 0.037960455326331 & 180.275322687884 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 6.84642857142857 & 0.0376147777363793 & 182.014330096839 \tabularnewline
Median & 6.9 &  &  \tabularnewline
Midrange & 6.75 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 6.83488372093023 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 6.83488372093023 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 6.83488372093023 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 6.83488372093023 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 6.83488372093023 &  &  \tabularnewline
Midmean - Closest Observation & 6.83488372093023 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 6.83488372093023 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 6.83488372093023 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284342&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]6.7975[/C][C]0.0593470537163398[/C][C]114.538120670487[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]6.77673913736271[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]6.75570631629483[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]6.81793590465619[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]6.79625[/C][C]0.0590923903837526[/C][C]115.010578449516[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]6.79625[/C][C]0.0590923903837526[/C][C]115.010578449516[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]6.8[/C][C]0.0567584265756352[/C][C]119.805999042952[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]6.805[/C][C]0.0557997096312939[/C][C]121.954039635066[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]6.81125[/C][C]0.0547142678612712[/C][C]124.487638530959[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]6.80375[/C][C]0.0534103931359498[/C][C]127.386255755165[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]6.80375[/C][C]0.0534103931359498[/C][C]127.386255755165[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]6.80375[/C][C]0.0534103931359498[/C][C]127.386255755165[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]6.80375[/C][C]0.0498238590474458[/C][C]136.556062297804[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]6.80375[/C][C]0.0498238590474458[/C][C]136.556062297804[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]6.79[/C][C]0.0478526218479355[/C][C]141.89400157795[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]6.79[/C][C]0.0478526218479355[/C][C]141.89400157795[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]6.79[/C][C]0.0478526218479355[/C][C]141.89400157795[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]6.79[/C][C]0.0478526218479355[/C][C]141.89400157795[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]6.79[/C][C]0.0478526218479355[/C][C]141.89400157795[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]6.79[/C][C]0.0478526218479355[/C][C]141.89400157795[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]6.79[/C][C]0.0478526218479355[/C][C]141.89400157795[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]6.79[/C][C]0.0414759347641131[/C][C]163.709390484311[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]6.81375[/C][C]0.038059902402477[/C][C]179.026996126941[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]6.81375[/C][C]0.038059902402477[/C][C]179.026996126941[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]6.81375[/C][C]0.038059902402477[/C][C]179.026996126941[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]6.81375[/C][C]0.038059902402477[/C][C]179.026996126941[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]6.785[/C][C]0.0345449624457712[/C][C]196.410692605358[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]6.785[/C][C]0.0345449624457712[/C][C]196.410692605358[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]6.81625[/C][C]0.0302648514646481[/C][C]225.220005059729[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]6.81625[/C][C]0.0302648514646481[/C][C]225.220005059729[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]6.79871794871795[/C][C]0.0577780840124795[/C][C]117.669494669458[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]6.80131578947368[/C][C]0.0562417532684658[/C][C]120.930010076466[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]6.80405405405405[/C][C]0.054437964693401[/C][C]124.987296868556[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]6.80555555555556[/C][C]0.053364460139512[/C][C]127.529736790434[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]6.80571428571429[/C][C]0.0524309943533874[/C][C]129.803265599799[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]6.80441176470588[/C][C]0.0516383819590572[/C][C]131.770429408515[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]6.80454545454545[/C][C]0.0510236390291341[/C][C]133.360645850056[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]6.8046875[/C][C]0.0502686082332733[/C][C]135.366538664102[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]6.80483870967742[/C][C]0.0493440537360424[/C][C]137.905952074362[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]6.805[/C][C]0.0489681667609908[/C][C]138.967832576102[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]6.8051724137931[/C][C]0.0484747652522626[/C][C]140.385876618051[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]6.80714285714286[/C][C]0.0482052661116038[/C][C]141.21160209723[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]6.80925925925926[/C][C]0.0478225024822562[/C][C]142.386092442271[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]6.81153846153846[/C][C]0.0472991383945268[/C][C]144.009778882709[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]6.814[/C][C]0.0465994657059674[/C][C]146.224852512148[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]6.81666666666667[/C][C]0.0456759062972553[/C][C]149.239877634925[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]6.8195652173913[/C][C]0.0444634752366448[/C][C]153.37454351231[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]6.82272727272727[/C][C]0.0428705259025236[/C][C]159.147272609633[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]6.82619047619048[/C][C]0.0421627183393635[/C][C]161.901099953925[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]6.8275[/C][C]0.0419076365356005[/C][C]162.917801250854[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]6.82894736842105[/C][C]0.0414714926744776[/C][C]164.666061625116[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]6.83055555555556[/C][C]0.0407897132310019[/C][C]167.457797922542[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]6.83235294117647[/C][C]0.0397677276325532[/C][C]171.806470923011[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]6.8375[/C][C]0.0390796333393173[/C][C]174.963258755064[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]6.84333333333333[/C][C]0.037960455326331[/C][C]180.275322687884[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]6.84642857142857[/C][C]0.0376147777363793[/C][C]182.014330096839[/C][/ROW]
[ROW][C]Median[/C][C]6.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]6.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]6.83488372093023[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]6.83488372093023[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]6.83488372093023[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]6.83488372093023[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]6.83488372093023[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]6.83488372093023[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]6.83488372093023[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]6.83488372093023[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284342&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284342&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 Mean6.79750.0593470537163398114.538120670487
Geometric Mean6.77673913736271
Harmonic Mean6.75570631629483
Quadratic Mean6.81793590465619
Winsorized Mean ( 1 / 26 )6.796250.0590923903837526115.010578449516
Winsorized Mean ( 2 / 26 )6.796250.0590923903837526115.010578449516
Winsorized Mean ( 3 / 26 )6.80.0567584265756352119.805999042952
Winsorized Mean ( 4 / 26 )6.8050.0557997096312939121.954039635066
Winsorized Mean ( 5 / 26 )6.811250.0547142678612712124.487638530959
Winsorized Mean ( 6 / 26 )6.803750.0534103931359498127.386255755165
Winsorized Mean ( 7 / 26 )6.803750.0534103931359498127.386255755165
Winsorized Mean ( 8 / 26 )6.803750.0534103931359498127.386255755165
Winsorized Mean ( 9 / 26 )6.803750.0498238590474458136.556062297804
Winsorized Mean ( 10 / 26 )6.803750.0498238590474458136.556062297804
Winsorized Mean ( 11 / 26 )6.790.0478526218479355141.89400157795
Winsorized Mean ( 12 / 26 )6.790.0478526218479355141.89400157795
Winsorized Mean ( 13 / 26 )6.790.0478526218479355141.89400157795
Winsorized Mean ( 14 / 26 )6.790.0478526218479355141.89400157795
Winsorized Mean ( 15 / 26 )6.790.0478526218479355141.89400157795
Winsorized Mean ( 16 / 26 )6.790.0478526218479355141.89400157795
Winsorized Mean ( 17 / 26 )6.790.0478526218479355141.89400157795
Winsorized Mean ( 18 / 26 )6.790.0414759347641131163.709390484311
Winsorized Mean ( 19 / 26 )6.813750.038059902402477179.026996126941
Winsorized Mean ( 20 / 26 )6.813750.038059902402477179.026996126941
Winsorized Mean ( 21 / 26 )6.813750.038059902402477179.026996126941
Winsorized Mean ( 22 / 26 )6.813750.038059902402477179.026996126941
Winsorized Mean ( 23 / 26 )6.7850.0345449624457712196.410692605358
Winsorized Mean ( 24 / 26 )6.7850.0345449624457712196.410692605358
Winsorized Mean ( 25 / 26 )6.816250.0302648514646481225.220005059729
Winsorized Mean ( 26 / 26 )6.816250.0302648514646481225.220005059729
Trimmed Mean ( 1 / 26 )6.798717948717950.0577780840124795117.669494669458
Trimmed Mean ( 2 / 26 )6.801315789473680.0562417532684658120.930010076466
Trimmed Mean ( 3 / 26 )6.804054054054050.054437964693401124.987296868556
Trimmed Mean ( 4 / 26 )6.805555555555560.053364460139512127.529736790434
Trimmed Mean ( 5 / 26 )6.805714285714290.0524309943533874129.803265599799
Trimmed Mean ( 6 / 26 )6.804411764705880.0516383819590572131.770429408515
Trimmed Mean ( 7 / 26 )6.804545454545450.0510236390291341133.360645850056
Trimmed Mean ( 8 / 26 )6.80468750.0502686082332733135.366538664102
Trimmed Mean ( 9 / 26 )6.804838709677420.0493440537360424137.905952074362
Trimmed Mean ( 10 / 26 )6.8050.0489681667609908138.967832576102
Trimmed Mean ( 11 / 26 )6.80517241379310.0484747652522626140.385876618051
Trimmed Mean ( 12 / 26 )6.807142857142860.0482052661116038141.21160209723
Trimmed Mean ( 13 / 26 )6.809259259259260.0478225024822562142.386092442271
Trimmed Mean ( 14 / 26 )6.811538461538460.0472991383945268144.009778882709
Trimmed Mean ( 15 / 26 )6.8140.0465994657059674146.224852512148
Trimmed Mean ( 16 / 26 )6.816666666666670.0456759062972553149.239877634925
Trimmed Mean ( 17 / 26 )6.81956521739130.0444634752366448153.37454351231
Trimmed Mean ( 18 / 26 )6.822727272727270.0428705259025236159.147272609633
Trimmed Mean ( 19 / 26 )6.826190476190480.0421627183393635161.901099953925
Trimmed Mean ( 20 / 26 )6.82750.0419076365356005162.917801250854
Trimmed Mean ( 21 / 26 )6.828947368421050.0414714926744776164.666061625116
Trimmed Mean ( 22 / 26 )6.830555555555560.0407897132310019167.457797922542
Trimmed Mean ( 23 / 26 )6.832352941176470.0397677276325532171.806470923011
Trimmed Mean ( 24 / 26 )6.83750.0390796333393173174.963258755064
Trimmed Mean ( 25 / 26 )6.843333333333330.037960455326331180.275322687884
Trimmed Mean ( 26 / 26 )6.846428571428570.0376147777363793182.014330096839
Median6.9
Midrange6.75
Midmean - Weighted Average at Xnp6.83488372093023
Midmean - Weighted Average at X(n+1)p6.83488372093023
Midmean - Empirical Distribution Function6.83488372093023
Midmean - Empirical Distribution Function - Averaging6.83488372093023
Midmean - Empirical Distribution Function - Interpolation6.83488372093023
Midmean - Closest Observation6.83488372093023
Midmean - True Basic - Statistics Graphics Toolkit6.83488372093023
Midmean - MS Excel (old versions)6.83488372093023
Number of observations80



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')