Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 14 Mar 2017 18:39:04 +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/2017/Mar/14/t14895171293arzur3bi8of8f7.htm/, Retrieved Tue, 14 May 2024 14:57:38 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 14:57:38 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
94,72
95,76
96,14
97,11
97,19
97,43
97,43
97,56
97,66
97,75
97,82
97,82
97,82
98,35
98,19
98,19
98,21
98,22
98,26
98,23
98,26
98,5
98,51
98,51
98,51
98,89
99,55
99,9
100,12
100,09
100,09
100,09
100,46
100,71
100,79
100,79
100,93
101,15
101,53
101,91
102,18
102,24
102,2
102,32
102,43
102,45
102,84
102,96
102,96
103,1
103,4
103,74
103,97
104,29
104,33
104,46
104,9
105,31
105,63
105,68
105,87
106,34
106,6
107,1
107,06
107,4
107,4
107,43
107,75
107,84
107,97
108,04






Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean101.4908333333330.42441259000779239.132475621118
Geometric Mean101.428233444092
Harmonic Mean101.366060516976
Quadratic Mean101.553819229018
Winsorized Mean ( 1 / 24 )101.5043055555560.421190829253739240.993626892113
Winsorized Mean ( 2 / 24 )101.511250.418447646199075242.590084857847
Winsorized Mean ( 3 / 24 )101.5479166666670.410916945633689247.125161777074
Winsorized Mean ( 4 / 24 )101.5345833333330.406538882481717249.753683370986
Winsorized Mean ( 5 / 24 )101.5491666666670.403661244405184251.570266093552
Winsorized Mean ( 6 / 24 )101.5491666666670.403661244405184251.570266093552
Winsorized Mean ( 7 / 24 )101.5326388888890.395994172564236256.399325857299
Winsorized Mean ( 8 / 24 )101.5393055555560.39355877632458258.002899856089
Winsorized Mean ( 9 / 24 )101.4930555555560.380885614439208266.465972218425
Winsorized Mean ( 10 / 24 )101.4666666666670.372808148372535272.168586200735
Winsorized Mean ( 11 / 24 )101.3948611111110.359904677491288281.726988984647
Winsorized Mean ( 12 / 24 )101.3631944444440.354415133853532286.001315300307
Winsorized Mean ( 13 / 24 )101.4209722222220.343732513268251295.057838020324
Winsorized Mean ( 14 / 24 )101.358750.333167560745136304.227547763981
Winsorized Mean ( 15 / 24 )101.27750.318626794286919317.856193565444
Winsorized Mean ( 16 / 24 )101.1819444444440.303036642222189333.893431838705
Winsorized Mean ( 17 / 24 )101.1536111111110.298068987820955339.363084534888
Winsorized Mean ( 18 / 24 )101.1511111111110.295535809228936342.263468427119
Winsorized Mean ( 19 / 24 )101.0666666666670.283116666673576356.978866183082
Winsorized Mean ( 20 / 24 )101.0277777777780.270500985842986373.483954089616
Winsorized Mean ( 21 / 24 )100.9723611111110.250635927737643402.864673163719
Winsorized Mean ( 22 / 24 )100.883750.237937344422627423.992922358624
Winsorized Mean ( 23 / 24 )100.8390277777780.23212540790908434.416157568046
Winsorized Mean ( 24 / 24 )100.8390277777780.23212540790908434.416157568046
Trimmed Mean ( 1 / 24 )101.4940.415055156104217244.53135567003
Trimmed Mean ( 2 / 24 )101.4830882352940.407685831704788248.924736508331
Trimmed Mean ( 3 / 24 )101.4677272727270.400543907330411253.324855067702
Trimmed Mean ( 4 / 24 )101.437656250.395207320905618256.669476713021
Trimmed Mean ( 5 / 24 )101.4095161290320.390173280968022259.908920153206
Trimmed Mean ( 6 / 24 )101.3760.384723703043646263.503390090054
Trimmed Mean ( 7 / 24 )101.3401724137930.377862015883775268.193594894079
Trimmed Mean ( 8 / 24 )101.3048214285710.371245008805613272.878608535355
Trimmed Mean ( 9 / 24 )101.2657407407410.363424353595481278.643243742155
Trimmed Mean ( 10 / 24 )101.2307692307690.356541312970516283.924374394
Trimmed Mean ( 11 / 24 )101.19680.349537004551765289.516699754784
Trimmed Mean ( 12 / 24 )101.1697916666670.343412486088318294.601378124172
Trimmed Mean ( 13 / 24 )101.1445652173910.336551523791457300.532186210113
Trimmed Mean ( 14 / 24 )101.1097727272730.329616903751182306.749355317036
Trimmed Mean ( 15 / 24 )101.0792857142860.322730329539661313.200453946997
Trimmed Mean ( 16 / 24 )101.05550.316735542442198319.053236718584
Trimmed Mean ( 17 / 24 )101.0405263157890.311996039696667323.851951499207
Trimmed Mean ( 18 / 24 )101.0272222222220.306200632201329329.937993582574
Trimmed Mean ( 19 / 24 )101.0126470588240.29828036818304338.650001252637
Trimmed Mean ( 20 / 24 )101.006250.290128847210805348.14273372344
Trimmed Mean ( 21 / 24 )101.0036666666670.28156397502282358.72368494045
Trimmed Mean ( 22 / 24 )101.00750.274490689985815367.981515166215
Trimmed Mean ( 23 / 24 )101.0230769230770.267002027783005378.360710448159
Trimmed Mean ( 24 / 24 )101.0470833333330.25628864442906394.270622322883
Median100.86
Midrange101.38
Midmean - Weighted Average at Xnp100.951621621622
Midmean - Weighted Average at X(n+1)p101.027222222222
Midmean - Empirical Distribution Function100.951621621622
Midmean - Empirical Distribution Function - Averaging101.027222222222
Midmean - Empirical Distribution Function - Interpolation101.027222222222
Midmean - Closest Observation100.951621621622
Midmean - True Basic - Statistics Graphics Toolkit101.027222222222
Midmean - MS Excel (old versions)101.040526315789
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 101.490833333333 & 0.42441259000779 & 239.132475621118 \tabularnewline
Geometric Mean & 101.428233444092 &  &  \tabularnewline
Harmonic Mean & 101.366060516976 &  &  \tabularnewline
Quadratic Mean & 101.553819229018 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 101.504305555556 & 0.421190829253739 & 240.993626892113 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 101.51125 & 0.418447646199075 & 242.590084857847 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 101.547916666667 & 0.410916945633689 & 247.125161777074 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 101.534583333333 & 0.406538882481717 & 249.753683370986 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 101.549166666667 & 0.403661244405184 & 251.570266093552 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 101.549166666667 & 0.403661244405184 & 251.570266093552 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 101.532638888889 & 0.395994172564236 & 256.399325857299 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 101.539305555556 & 0.39355877632458 & 258.002899856089 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 101.493055555556 & 0.380885614439208 & 266.465972218425 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 101.466666666667 & 0.372808148372535 & 272.168586200735 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 101.394861111111 & 0.359904677491288 & 281.726988984647 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 101.363194444444 & 0.354415133853532 & 286.001315300307 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 101.420972222222 & 0.343732513268251 & 295.057838020324 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 101.35875 & 0.333167560745136 & 304.227547763981 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 101.2775 & 0.318626794286919 & 317.856193565444 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 101.181944444444 & 0.303036642222189 & 333.893431838705 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 101.153611111111 & 0.298068987820955 & 339.363084534888 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 101.151111111111 & 0.295535809228936 & 342.263468427119 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 101.066666666667 & 0.283116666673576 & 356.978866183082 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 101.027777777778 & 0.270500985842986 & 373.483954089616 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 100.972361111111 & 0.250635927737643 & 402.864673163719 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 100.88375 & 0.237937344422627 & 423.992922358624 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 100.839027777778 & 0.23212540790908 & 434.416157568046 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 100.839027777778 & 0.23212540790908 & 434.416157568046 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 101.494 & 0.415055156104217 & 244.53135567003 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 101.483088235294 & 0.407685831704788 & 248.924736508331 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 101.467727272727 & 0.400543907330411 & 253.324855067702 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 101.43765625 & 0.395207320905618 & 256.669476713021 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 101.409516129032 & 0.390173280968022 & 259.908920153206 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 101.376 & 0.384723703043646 & 263.503390090054 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 101.340172413793 & 0.377862015883775 & 268.193594894079 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 101.304821428571 & 0.371245008805613 & 272.878608535355 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 101.265740740741 & 0.363424353595481 & 278.643243742155 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 101.230769230769 & 0.356541312970516 & 283.924374394 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 101.1968 & 0.349537004551765 & 289.516699754784 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 101.169791666667 & 0.343412486088318 & 294.601378124172 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 101.144565217391 & 0.336551523791457 & 300.532186210113 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 101.109772727273 & 0.329616903751182 & 306.749355317036 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 101.079285714286 & 0.322730329539661 & 313.200453946997 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 101.0555 & 0.316735542442198 & 319.053236718584 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 101.040526315789 & 0.311996039696667 & 323.851951499207 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 101.027222222222 & 0.306200632201329 & 329.937993582574 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 101.012647058824 & 0.29828036818304 & 338.650001252637 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 101.00625 & 0.290128847210805 & 348.14273372344 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 101.003666666667 & 0.28156397502282 & 358.72368494045 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 101.0075 & 0.274490689985815 & 367.981515166215 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 101.023076923077 & 0.267002027783005 & 378.360710448159 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 101.047083333333 & 0.25628864442906 & 394.270622322883 \tabularnewline
Median & 100.86 &  &  \tabularnewline
Midrange & 101.38 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 100.951621621622 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 101.027222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 100.951621621622 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 101.027222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 101.027222222222 &  &  \tabularnewline
Midmean - Closest Observation & 100.951621621622 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 101.027222222222 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 101.040526315789 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]101.490833333333[/C][C]0.42441259000779[/C][C]239.132475621118[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]101.428233444092[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]101.366060516976[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]101.553819229018[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]101.504305555556[/C][C]0.421190829253739[/C][C]240.993626892113[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]101.51125[/C][C]0.418447646199075[/C][C]242.590084857847[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]101.547916666667[/C][C]0.410916945633689[/C][C]247.125161777074[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]101.534583333333[/C][C]0.406538882481717[/C][C]249.753683370986[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]101.549166666667[/C][C]0.403661244405184[/C][C]251.570266093552[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]101.549166666667[/C][C]0.403661244405184[/C][C]251.570266093552[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]101.532638888889[/C][C]0.395994172564236[/C][C]256.399325857299[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]101.539305555556[/C][C]0.39355877632458[/C][C]258.002899856089[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]101.493055555556[/C][C]0.380885614439208[/C][C]266.465972218425[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]101.466666666667[/C][C]0.372808148372535[/C][C]272.168586200735[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]101.394861111111[/C][C]0.359904677491288[/C][C]281.726988984647[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]101.363194444444[/C][C]0.354415133853532[/C][C]286.001315300307[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]101.420972222222[/C][C]0.343732513268251[/C][C]295.057838020324[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]101.35875[/C][C]0.333167560745136[/C][C]304.227547763981[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]101.2775[/C][C]0.318626794286919[/C][C]317.856193565444[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]101.181944444444[/C][C]0.303036642222189[/C][C]333.893431838705[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]101.153611111111[/C][C]0.298068987820955[/C][C]339.363084534888[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]101.151111111111[/C][C]0.295535809228936[/C][C]342.263468427119[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]101.066666666667[/C][C]0.283116666673576[/C][C]356.978866183082[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]101.027777777778[/C][C]0.270500985842986[/C][C]373.483954089616[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]100.972361111111[/C][C]0.250635927737643[/C][C]402.864673163719[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]100.88375[/C][C]0.237937344422627[/C][C]423.992922358624[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]100.839027777778[/C][C]0.23212540790908[/C][C]434.416157568046[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]100.839027777778[/C][C]0.23212540790908[/C][C]434.416157568046[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]101.494[/C][C]0.415055156104217[/C][C]244.53135567003[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]101.483088235294[/C][C]0.407685831704788[/C][C]248.924736508331[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]101.467727272727[/C][C]0.400543907330411[/C][C]253.324855067702[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]101.43765625[/C][C]0.395207320905618[/C][C]256.669476713021[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]101.409516129032[/C][C]0.390173280968022[/C][C]259.908920153206[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]101.376[/C][C]0.384723703043646[/C][C]263.503390090054[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]101.340172413793[/C][C]0.377862015883775[/C][C]268.193594894079[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]101.304821428571[/C][C]0.371245008805613[/C][C]272.878608535355[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]101.265740740741[/C][C]0.363424353595481[/C][C]278.643243742155[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]101.230769230769[/C][C]0.356541312970516[/C][C]283.924374394[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]101.1968[/C][C]0.349537004551765[/C][C]289.516699754784[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]101.169791666667[/C][C]0.343412486088318[/C][C]294.601378124172[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]101.144565217391[/C][C]0.336551523791457[/C][C]300.532186210113[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]101.109772727273[/C][C]0.329616903751182[/C][C]306.749355317036[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]101.079285714286[/C][C]0.322730329539661[/C][C]313.200453946997[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]101.0555[/C][C]0.316735542442198[/C][C]319.053236718584[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]101.040526315789[/C][C]0.311996039696667[/C][C]323.851951499207[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]101.027222222222[/C][C]0.306200632201329[/C][C]329.937993582574[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]101.012647058824[/C][C]0.29828036818304[/C][C]338.650001252637[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]101.00625[/C][C]0.290128847210805[/C][C]348.14273372344[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]101.003666666667[/C][C]0.28156397502282[/C][C]358.72368494045[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]101.0075[/C][C]0.274490689985815[/C][C]367.981515166215[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]101.023076923077[/C][C]0.267002027783005[/C][C]378.360710448159[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]101.047083333333[/C][C]0.25628864442906[/C][C]394.270622322883[/C][/ROW]
[ROW][C]Median[/C][C]100.86[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]101.38[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]100.951621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]101.027222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]100.951621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]101.027222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]101.027222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]100.951621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]101.027222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]101.040526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean101.4908333333330.42441259000779239.132475621118
Geometric Mean101.428233444092
Harmonic Mean101.366060516976
Quadratic Mean101.553819229018
Winsorized Mean ( 1 / 24 )101.5043055555560.421190829253739240.993626892113
Winsorized Mean ( 2 / 24 )101.511250.418447646199075242.590084857847
Winsorized Mean ( 3 / 24 )101.5479166666670.410916945633689247.125161777074
Winsorized Mean ( 4 / 24 )101.5345833333330.406538882481717249.753683370986
Winsorized Mean ( 5 / 24 )101.5491666666670.403661244405184251.570266093552
Winsorized Mean ( 6 / 24 )101.5491666666670.403661244405184251.570266093552
Winsorized Mean ( 7 / 24 )101.5326388888890.395994172564236256.399325857299
Winsorized Mean ( 8 / 24 )101.5393055555560.39355877632458258.002899856089
Winsorized Mean ( 9 / 24 )101.4930555555560.380885614439208266.465972218425
Winsorized Mean ( 10 / 24 )101.4666666666670.372808148372535272.168586200735
Winsorized Mean ( 11 / 24 )101.3948611111110.359904677491288281.726988984647
Winsorized Mean ( 12 / 24 )101.3631944444440.354415133853532286.001315300307
Winsorized Mean ( 13 / 24 )101.4209722222220.343732513268251295.057838020324
Winsorized Mean ( 14 / 24 )101.358750.333167560745136304.227547763981
Winsorized Mean ( 15 / 24 )101.27750.318626794286919317.856193565444
Winsorized Mean ( 16 / 24 )101.1819444444440.303036642222189333.893431838705
Winsorized Mean ( 17 / 24 )101.1536111111110.298068987820955339.363084534888
Winsorized Mean ( 18 / 24 )101.1511111111110.295535809228936342.263468427119
Winsorized Mean ( 19 / 24 )101.0666666666670.283116666673576356.978866183082
Winsorized Mean ( 20 / 24 )101.0277777777780.270500985842986373.483954089616
Winsorized Mean ( 21 / 24 )100.9723611111110.250635927737643402.864673163719
Winsorized Mean ( 22 / 24 )100.883750.237937344422627423.992922358624
Winsorized Mean ( 23 / 24 )100.8390277777780.23212540790908434.416157568046
Winsorized Mean ( 24 / 24 )100.8390277777780.23212540790908434.416157568046
Trimmed Mean ( 1 / 24 )101.4940.415055156104217244.53135567003
Trimmed Mean ( 2 / 24 )101.4830882352940.407685831704788248.924736508331
Trimmed Mean ( 3 / 24 )101.4677272727270.400543907330411253.324855067702
Trimmed Mean ( 4 / 24 )101.437656250.395207320905618256.669476713021
Trimmed Mean ( 5 / 24 )101.4095161290320.390173280968022259.908920153206
Trimmed Mean ( 6 / 24 )101.3760.384723703043646263.503390090054
Trimmed Mean ( 7 / 24 )101.3401724137930.377862015883775268.193594894079
Trimmed Mean ( 8 / 24 )101.3048214285710.371245008805613272.878608535355
Trimmed Mean ( 9 / 24 )101.2657407407410.363424353595481278.643243742155
Trimmed Mean ( 10 / 24 )101.2307692307690.356541312970516283.924374394
Trimmed Mean ( 11 / 24 )101.19680.349537004551765289.516699754784
Trimmed Mean ( 12 / 24 )101.1697916666670.343412486088318294.601378124172
Trimmed Mean ( 13 / 24 )101.1445652173910.336551523791457300.532186210113
Trimmed Mean ( 14 / 24 )101.1097727272730.329616903751182306.749355317036
Trimmed Mean ( 15 / 24 )101.0792857142860.322730329539661313.200453946997
Trimmed Mean ( 16 / 24 )101.05550.316735542442198319.053236718584
Trimmed Mean ( 17 / 24 )101.0405263157890.311996039696667323.851951499207
Trimmed Mean ( 18 / 24 )101.0272222222220.306200632201329329.937993582574
Trimmed Mean ( 19 / 24 )101.0126470588240.29828036818304338.650001252637
Trimmed Mean ( 20 / 24 )101.006250.290128847210805348.14273372344
Trimmed Mean ( 21 / 24 )101.0036666666670.28156397502282358.72368494045
Trimmed Mean ( 22 / 24 )101.00750.274490689985815367.981515166215
Trimmed Mean ( 23 / 24 )101.0230769230770.267002027783005378.360710448159
Trimmed Mean ( 24 / 24 )101.0470833333330.25628864442906394.270622322883
Median100.86
Midrange101.38
Midmean - Weighted Average at Xnp100.951621621622
Midmean - Weighted Average at X(n+1)p101.027222222222
Midmean - Empirical Distribution Function100.951621621622
Midmean - Empirical Distribution Function - Averaging101.027222222222
Midmean - Empirical Distribution Function - Interpolation101.027222222222
Midmean - Closest Observation100.951621621622
Midmean - True Basic - Statistics Graphics Toolkit101.027222222222
Midmean - MS Excel (old versions)101.040526315789
Number of observations72



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')