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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 computationThu, 17 Dec 2009 06:29:44 -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/17/t12610567625yr4t21o743hzzz.htm/, Retrieved Tue, 30 Apr 2024 01:14:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=68867, Retrieved Tue, 30 Apr 2024 01:14:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
- RMPD  [Bivariate Explorative Data Analysis] [WS 4 - Deel 1 - V...] [2009-10-26 08:28:42] [b103a1dc147def8132c7f643ad8c8f84]
-  M D    [Bivariate Explorative Data Analysis] [Paper: Bivariate EDA] [2009-12-17 09:40:23] [b103a1dc147def8132c7f643ad8c8f84]
-    D      [Bivariate Explorative Data Analysis] [Paper Bivariate E...] [2009-12-17 13:23:43] [4395c69e961f9a13a0559fd2f0a72538]
- RMPD          [Central Tendency] [Paper Robustness ...] [2009-12-17 13:29:44] [d1081bd6cdf1fed9ed45c42dbd523bf1] [Current]
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Dataseries X:
7.6
8.3
8.4
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




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=68867&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=68867&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68867&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 Mean7.926027397260270.081603679867769997.1283085530403
Geometric Mean7.89469802992062
Harmonic Mean7.86224238139754
Quadratic Mean7.9562158004301
Winsorized Mean ( 1 / 24 )7.930136986301370.080421381944869498.6073205225154
Winsorized Mean ( 2 / 24 )7.921917808219180.0774460723491367102.289471472564
Winsorized Mean ( 3 / 24 )7.921917808219180.0757320080592225104.604618459664
Winsorized Mean ( 4 / 24 )7.932876712328770.0732236309626662108.337658321989
Winsorized Mean ( 5 / 24 )7.932876712328770.0707121524403112112.185479278473
Winsorized Mean ( 6 / 24 )7.932876712328770.0707121524403112112.185479278473
Winsorized Mean ( 7 / 24 )7.942465753424660.0688268128585198115.397843130571
Winsorized Mean ( 8 / 24 )7.942465753424660.0688268128585198115.397843130571
Winsorized Mean ( 9 / 24 )7.942465753424660.0688268128585198115.397843130571
Winsorized Mean ( 10 / 24 )7.942465753424660.0642518650482103123.614555740369
Winsorized Mean ( 11 / 24 )7.957534246575340.0615909632886585129.199704334559
Winsorized Mean ( 12 / 24 )7.957534246575340.0615909632886585129.199704334559
Winsorized Mean ( 13 / 24 )7.957534246575340.0615909632886585129.199704334559
Winsorized Mean ( 14 / 24 )7.957534246575340.0556857692943131142.900679067893
Winsorized Mean ( 15 / 24 )7.957534246575340.0556857692943131142.900679067893
Winsorized Mean ( 16 / 24 )7.957534246575340.0556857692943131142.900679067893
Winsorized Mean ( 17 / 24 )7.980821917808220.0519650953514032153.580434401969
Winsorized Mean ( 18 / 24 )7.980821917808220.0519650953514032153.580434401969
Winsorized Mean ( 19 / 24 )7.980821917808220.0444678296935053179.474059625038
Winsorized Mean ( 20 / 24 )7.980821917808220.0444678296935053179.474059625038
Winsorized Mean ( 21 / 24 )7.980821917808220.0444678296935053179.474059625038
Winsorized Mean ( 22 / 24 )8.010958904109590.0400514150077541200.016875872142
Winsorized Mean ( 23 / 24 )8.042465753424660.0356990319705538225.285261517972
Winsorized Mean ( 24 / 24 )8.009589041095890.0312818716352576256.045710259495
Trimmed Mean ( 1 / 24 )7.932394366197180.0774018401636135102.483278813908
Trimmed Mean ( 2 / 24 )7.934782608695650.0738026355570039107.513539981468
Trimmed Mean ( 3 / 24 )7.941791044776120.0714313583696378111.180736668614
Trimmed Mean ( 4 / 24 )7.949230769230770.0693764492891956114.581112908999
Trimmed Mean ( 5 / 24 )7.953968253968250.0678401103898203117.245803526313
Trimmed Mean ( 6 / 24 )7.959016393442620.0667503729622755119.235534428260
Trimmed Mean ( 7 / 24 )7.964406779661020.0653973473790065121.784859766617
Trimmed Mean ( 8 / 24 )7.968421052631580.0642167916742779124.08625290795
Trimmed Mean ( 9 / 24 )7.972727272727270.0627353237403917127.085137963416
Trimmed Mean ( 10 / 24 )7.977358490566040.0608742255076878131.046570597577
Trimmed Mean ( 11 / 24 )7.982352941176470.0595871997277571133.960867059475
Trimmed Mean ( 12 / 24 )7.985714285714290.0585394802530678136.415872692956
Trimmed Mean ( 13 / 24 )7.989361702127660.0571634495820068139.76346355141
Trimmed Mean ( 14 / 24 )7.993333333333330.0553592491336946144.390205041061
Trimmed Mean ( 15 / 24 )7.997674418604650.0543244398308434147.22055935612
Trimmed Mean ( 16 / 24 )8.002439024390240.0529020960530438151.268846065501
Trimmed Mean ( 17 / 24 )8.007692307692310.050953739886581157.156124859859
Trimmed Mean ( 18 / 24 )8.010810810810810.049286772492216162.534700605035
Trimmed Mean ( 19 / 24 )8.014285714285710.0469476477861571170.706863755777
Trimmed Mean ( 20 / 24 )8.018181818181820.045737754085223175.307729435983
Trimmed Mean ( 21 / 24 )8.022580645161290.0439231189080396182.650523109662
Trimmed Mean ( 22 / 24 )8.027586206896550.0411941670879794194.871914505562
Trimmed Mean ( 23 / 24 )8.029629629629630.0387904057567029207.000403140720
Trimmed Mean ( 24 / 24 )8.0280.0367514172062339218.440555773677
Median8
Midrange7.7
Midmean - Weighted Average at Xnp7.98108108108108
Midmean - Weighted Average at X(n+1)p8.04285714285714
Midmean - Empirical Distribution Function8.04285714285714
Midmean - Empirical Distribution Function - Averaging8.04285714285714
Midmean - Empirical Distribution Function - Interpolation8.04285714285714
Midmean - Closest Observation8.04285714285714
Midmean - True Basic - Statistics Graphics Toolkit8.04285714285714
Midmean - MS Excel (old versions)8.04285714285714
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.92602739726027 & 0.0816036798677699 & 97.1283085530403 \tabularnewline
Geometric Mean & 7.89469802992062 &  &  \tabularnewline
Harmonic Mean & 7.86224238139754 &  &  \tabularnewline
Quadratic Mean & 7.9562158004301 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 7.93013698630137 & 0.0804213819448694 & 98.6073205225154 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 7.92191780821918 & 0.0774460723491367 & 102.289471472564 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 7.92191780821918 & 0.0757320080592225 & 104.604618459664 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 7.93287671232877 & 0.0732236309626662 & 108.337658321989 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 7.93287671232877 & 0.0707121524403112 & 112.185479278473 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 7.93287671232877 & 0.0707121524403112 & 112.185479278473 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 7.94246575342466 & 0.0688268128585198 & 115.397843130571 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 7.94246575342466 & 0.0688268128585198 & 115.397843130571 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 7.94246575342466 & 0.0688268128585198 & 115.397843130571 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 7.94246575342466 & 0.0642518650482103 & 123.614555740369 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 7.95753424657534 & 0.0615909632886585 & 129.199704334559 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 7.95753424657534 & 0.0615909632886585 & 129.199704334559 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 7.95753424657534 & 0.0615909632886585 & 129.199704334559 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 7.95753424657534 & 0.0556857692943131 & 142.900679067893 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 7.95753424657534 & 0.0556857692943131 & 142.900679067893 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 7.95753424657534 & 0.0556857692943131 & 142.900679067893 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 7.98082191780822 & 0.0519650953514032 & 153.580434401969 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 7.98082191780822 & 0.0519650953514032 & 153.580434401969 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 7.98082191780822 & 0.0444678296935053 & 179.474059625038 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 7.98082191780822 & 0.0444678296935053 & 179.474059625038 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 7.98082191780822 & 0.0444678296935053 & 179.474059625038 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 8.01095890410959 & 0.0400514150077541 & 200.016875872142 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 8.04246575342466 & 0.0356990319705538 & 225.285261517972 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 8.00958904109589 & 0.0312818716352576 & 256.045710259495 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 7.93239436619718 & 0.0774018401636135 & 102.483278813908 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 7.93478260869565 & 0.0738026355570039 & 107.513539981468 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 7.94179104477612 & 0.0714313583696378 & 111.180736668614 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 7.94923076923077 & 0.0693764492891956 & 114.581112908999 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 7.95396825396825 & 0.0678401103898203 & 117.245803526313 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 7.95901639344262 & 0.0667503729622755 & 119.235534428260 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 7.96440677966102 & 0.0653973473790065 & 121.784859766617 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 7.96842105263158 & 0.0642167916742779 & 124.08625290795 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 7.97272727272727 & 0.0627353237403917 & 127.085137963416 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 7.97735849056604 & 0.0608742255076878 & 131.046570597577 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 7.98235294117647 & 0.0595871997277571 & 133.960867059475 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 7.98571428571429 & 0.0585394802530678 & 136.415872692956 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 7.98936170212766 & 0.0571634495820068 & 139.76346355141 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 7.99333333333333 & 0.0553592491336946 & 144.390205041061 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 7.99767441860465 & 0.0543244398308434 & 147.22055935612 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 8.00243902439024 & 0.0529020960530438 & 151.268846065501 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 8.00769230769231 & 0.050953739886581 & 157.156124859859 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 8.01081081081081 & 0.049286772492216 & 162.534700605035 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 8.01428571428571 & 0.0469476477861571 & 170.706863755777 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 8.01818181818182 & 0.045737754085223 & 175.307729435983 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 8.02258064516129 & 0.0439231189080396 & 182.650523109662 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 8.02758620689655 & 0.0411941670879794 & 194.871914505562 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 8.02962962962963 & 0.0387904057567029 & 207.000403140720 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 8.028 & 0.0367514172062339 & 218.440555773677 \tabularnewline
Median & 8 &  &  \tabularnewline
Midrange & 7.7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.98108108108108 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.04285714285714 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.04285714285714 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.04285714285714 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.04285714285714 &  &  \tabularnewline
Midmean - Closest Observation & 8.04285714285714 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.04285714285714 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.04285714285714 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68867&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]7.92602739726027[/C][C]0.0816036798677699[/C][C]97.1283085530403[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.89469802992062[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.86224238139754[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.9562158004301[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]7.93013698630137[/C][C]0.0804213819448694[/C][C]98.6073205225154[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]7.92191780821918[/C][C]0.0774460723491367[/C][C]102.289471472564[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]7.92191780821918[/C][C]0.0757320080592225[/C][C]104.604618459664[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]7.93287671232877[/C][C]0.0732236309626662[/C][C]108.337658321989[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]7.93287671232877[/C][C]0.0707121524403112[/C][C]112.185479278473[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]7.93287671232877[/C][C]0.0707121524403112[/C][C]112.185479278473[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]7.94246575342466[/C][C]0.0688268128585198[/C][C]115.397843130571[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]7.94246575342466[/C][C]0.0688268128585198[/C][C]115.397843130571[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]7.94246575342466[/C][C]0.0688268128585198[/C][C]115.397843130571[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]7.94246575342466[/C][C]0.0642518650482103[/C][C]123.614555740369[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]7.95753424657534[/C][C]0.0615909632886585[/C][C]129.199704334559[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]7.95753424657534[/C][C]0.0615909632886585[/C][C]129.199704334559[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]7.95753424657534[/C][C]0.0615909632886585[/C][C]129.199704334559[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]7.95753424657534[/C][C]0.0556857692943131[/C][C]142.900679067893[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]7.95753424657534[/C][C]0.0556857692943131[/C][C]142.900679067893[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]7.95753424657534[/C][C]0.0556857692943131[/C][C]142.900679067893[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]7.98082191780822[/C][C]0.0519650953514032[/C][C]153.580434401969[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]7.98082191780822[/C][C]0.0519650953514032[/C][C]153.580434401969[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]7.98082191780822[/C][C]0.0444678296935053[/C][C]179.474059625038[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]7.98082191780822[/C][C]0.0444678296935053[/C][C]179.474059625038[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]7.98082191780822[/C][C]0.0444678296935053[/C][C]179.474059625038[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]8.01095890410959[/C][C]0.0400514150077541[/C][C]200.016875872142[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]8.04246575342466[/C][C]0.0356990319705538[/C][C]225.285261517972[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]8.00958904109589[/C][C]0.0312818716352576[/C][C]256.045710259495[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]7.93239436619718[/C][C]0.0774018401636135[/C][C]102.483278813908[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]7.93478260869565[/C][C]0.0738026355570039[/C][C]107.513539981468[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]7.94179104477612[/C][C]0.0714313583696378[/C][C]111.180736668614[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]7.94923076923077[/C][C]0.0693764492891956[/C][C]114.581112908999[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]7.95396825396825[/C][C]0.0678401103898203[/C][C]117.245803526313[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]7.95901639344262[/C][C]0.0667503729622755[/C][C]119.235534428260[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]7.96440677966102[/C][C]0.0653973473790065[/C][C]121.784859766617[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]7.96842105263158[/C][C]0.0642167916742779[/C][C]124.08625290795[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]7.97272727272727[/C][C]0.0627353237403917[/C][C]127.085137963416[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]7.97735849056604[/C][C]0.0608742255076878[/C][C]131.046570597577[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]7.98235294117647[/C][C]0.0595871997277571[/C][C]133.960867059475[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]7.98571428571429[/C][C]0.0585394802530678[/C][C]136.415872692956[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]7.98936170212766[/C][C]0.0571634495820068[/C][C]139.76346355141[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]7.99333333333333[/C][C]0.0553592491336946[/C][C]144.390205041061[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]7.99767441860465[/C][C]0.0543244398308434[/C][C]147.22055935612[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]8.00243902439024[/C][C]0.0529020960530438[/C][C]151.268846065501[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]8.00769230769231[/C][C]0.050953739886581[/C][C]157.156124859859[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]8.01081081081081[/C][C]0.049286772492216[/C][C]162.534700605035[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]8.01428571428571[/C][C]0.0469476477861571[/C][C]170.706863755777[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]8.01818181818182[/C][C]0.045737754085223[/C][C]175.307729435983[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]8.02258064516129[/C][C]0.0439231189080396[/C][C]182.650523109662[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]8.02758620689655[/C][C]0.0411941670879794[/C][C]194.871914505562[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]8.02962962962963[/C][C]0.0387904057567029[/C][C]207.000403140720[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]8.028[/C][C]0.0367514172062339[/C][C]218.440555773677[/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]7.98108108108108[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.04285714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.04285714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.04285714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.04285714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.04285714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.04285714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.04285714285714[/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=68867&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68867&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 Mean7.926027397260270.081603679867769997.1283085530403
Geometric Mean7.89469802992062
Harmonic Mean7.86224238139754
Quadratic Mean7.9562158004301
Winsorized Mean ( 1 / 24 )7.930136986301370.080421381944869498.6073205225154
Winsorized Mean ( 2 / 24 )7.921917808219180.0774460723491367102.289471472564
Winsorized Mean ( 3 / 24 )7.921917808219180.0757320080592225104.604618459664
Winsorized Mean ( 4 / 24 )7.932876712328770.0732236309626662108.337658321989
Winsorized Mean ( 5 / 24 )7.932876712328770.0707121524403112112.185479278473
Winsorized Mean ( 6 / 24 )7.932876712328770.0707121524403112112.185479278473
Winsorized Mean ( 7 / 24 )7.942465753424660.0688268128585198115.397843130571
Winsorized Mean ( 8 / 24 )7.942465753424660.0688268128585198115.397843130571
Winsorized Mean ( 9 / 24 )7.942465753424660.0688268128585198115.397843130571
Winsorized Mean ( 10 / 24 )7.942465753424660.0642518650482103123.614555740369
Winsorized Mean ( 11 / 24 )7.957534246575340.0615909632886585129.199704334559
Winsorized Mean ( 12 / 24 )7.957534246575340.0615909632886585129.199704334559
Winsorized Mean ( 13 / 24 )7.957534246575340.0615909632886585129.199704334559
Winsorized Mean ( 14 / 24 )7.957534246575340.0556857692943131142.900679067893
Winsorized Mean ( 15 / 24 )7.957534246575340.0556857692943131142.900679067893
Winsorized Mean ( 16 / 24 )7.957534246575340.0556857692943131142.900679067893
Winsorized Mean ( 17 / 24 )7.980821917808220.0519650953514032153.580434401969
Winsorized Mean ( 18 / 24 )7.980821917808220.0519650953514032153.580434401969
Winsorized Mean ( 19 / 24 )7.980821917808220.0444678296935053179.474059625038
Winsorized Mean ( 20 / 24 )7.980821917808220.0444678296935053179.474059625038
Winsorized Mean ( 21 / 24 )7.980821917808220.0444678296935053179.474059625038
Winsorized Mean ( 22 / 24 )8.010958904109590.0400514150077541200.016875872142
Winsorized Mean ( 23 / 24 )8.042465753424660.0356990319705538225.285261517972
Winsorized Mean ( 24 / 24 )8.009589041095890.0312818716352576256.045710259495
Trimmed Mean ( 1 / 24 )7.932394366197180.0774018401636135102.483278813908
Trimmed Mean ( 2 / 24 )7.934782608695650.0738026355570039107.513539981468
Trimmed Mean ( 3 / 24 )7.941791044776120.0714313583696378111.180736668614
Trimmed Mean ( 4 / 24 )7.949230769230770.0693764492891956114.581112908999
Trimmed Mean ( 5 / 24 )7.953968253968250.0678401103898203117.245803526313
Trimmed Mean ( 6 / 24 )7.959016393442620.0667503729622755119.235534428260
Trimmed Mean ( 7 / 24 )7.964406779661020.0653973473790065121.784859766617
Trimmed Mean ( 8 / 24 )7.968421052631580.0642167916742779124.08625290795
Trimmed Mean ( 9 / 24 )7.972727272727270.0627353237403917127.085137963416
Trimmed Mean ( 10 / 24 )7.977358490566040.0608742255076878131.046570597577
Trimmed Mean ( 11 / 24 )7.982352941176470.0595871997277571133.960867059475
Trimmed Mean ( 12 / 24 )7.985714285714290.0585394802530678136.415872692956
Trimmed Mean ( 13 / 24 )7.989361702127660.0571634495820068139.76346355141
Trimmed Mean ( 14 / 24 )7.993333333333330.0553592491336946144.390205041061
Trimmed Mean ( 15 / 24 )7.997674418604650.0543244398308434147.22055935612
Trimmed Mean ( 16 / 24 )8.002439024390240.0529020960530438151.268846065501
Trimmed Mean ( 17 / 24 )8.007692307692310.050953739886581157.156124859859
Trimmed Mean ( 18 / 24 )8.010810810810810.049286772492216162.534700605035
Trimmed Mean ( 19 / 24 )8.014285714285710.0469476477861571170.706863755777
Trimmed Mean ( 20 / 24 )8.018181818181820.045737754085223175.307729435983
Trimmed Mean ( 21 / 24 )8.022580645161290.0439231189080396182.650523109662
Trimmed Mean ( 22 / 24 )8.027586206896550.0411941670879794194.871914505562
Trimmed Mean ( 23 / 24 )8.029629629629630.0387904057567029207.000403140720
Trimmed Mean ( 24 / 24 )8.0280.0367514172062339218.440555773677
Median8
Midrange7.7
Midmean - Weighted Average at Xnp7.98108108108108
Midmean - Weighted Average at X(n+1)p8.04285714285714
Midmean - Empirical Distribution Function8.04285714285714
Midmean - Empirical Distribution Function - Averaging8.04285714285714
Midmean - Empirical Distribution Function - Interpolation8.04285714285714
Midmean - Closest Observation8.04285714285714
Midmean - True Basic - Statistics Graphics Toolkit8.04285714285714
Midmean - MS Excel (old versions)8.04285714285714
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')