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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 13 Oct 2014 20:20:23 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/13/t1413228057nfqxvauxiyjh980.htm/, Retrieved Fri, 10 May 2024 08:01:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240833, Retrieved Fri, 10 May 2024 08:01:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-13 19:20:23] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
129,62
127,96
130,1
131,7
136,34
140,73
141,51
134,66
133,94
123,66
109,88
102,36
101,41
105,33
106,58
109,72
113,47
120,35
117,55
122,55
118,82
114,87
119,98
119,48
121,81
121,08
126,63
130,04
131,21
128,48
127,4
126,35
126,28
126
127,34
132,96
135,19
134,55
140,03
144,6
146,27
141,74
140,72
141,45
144,04
141,19
140,13
139,51
144,67
147,05
153,2
157,97
150,44
147,31
146,61
152,62
157,08
152,62
144,63
144,34
144,09
148,21
146,81
146,46
142,8
143,66
144,31
146,07
147,21
139,5
137,44
139,94




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240833&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240833&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240833&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' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean134.0640277777781.5987559553729583.8552171313127
Geometric Mean133.35318757226
Harmonic Mean132.607068900035
Quadratic Mean134.739159144417
Winsorized Mean ( 1 / 24 )134.0648611111111.5924482262874184.1878931434185
Winsorized Mean ( 2 / 24 )134.0395833333331.549731947611786.4921082254917
Winsorized Mean ( 3 / 24 )134.06751.5321906431831287.5005343470022
Winsorized Mean ( 4 / 24 )134.2419444444441.4899069883963790.1008891762653
Winsorized Mean ( 5 / 24 )134.1016666666671.4622486542173991.7092084714137
Winsorized Mean ( 6 / 24 )134.2151.3672254096577498.1659637481419
Winsorized Mean ( 7 / 24 )134.2636111111111.32628489543085101.2328584708
Winsorized Mean ( 8 / 24 )134.5502777777781.26584787862064106.292612287974
Winsorized Mean ( 9 / 24 )134.6890277777781.23362465090961109.181530766644
Winsorized Mean ( 10 / 24 )134.7473611111111.21250308540749111.131561422647
Winsorized Mean ( 11 / 24 )134.7931944444441.19479006979954112.817471329553
Winsorized Mean ( 12 / 24 )134.8298611111111.18060366732029114.204169310388
Winsorized Mean ( 13 / 24 )134.9273611111111.15331608363609116.990791185121
Winsorized Mean ( 14 / 24 )135.0304166666671.12417266461647120.115370989504
Winsorized Mean ( 15 / 24 )134.8929166666671.05959542574318127.306057943819
Winsorized Mean ( 16 / 24 )135.1306944444441.01862476574816132.659934244965
Winsorized Mean ( 17 / 24 )135.6761111111110.933381235263785145.359801531437
Winsorized Mean ( 18 / 24 )135.6811111111110.914491712459925148.367786457176
Winsorized Mean ( 19 / 24 )135.6916666666670.910764674679886148.986527957246
Winsorized Mean ( 20 / 24 )135.7083333333330.891449185886226152.23339196661
Winsorized Mean ( 21 / 24 )135.9008333333330.86013994089254157.998514976892
Winsorized Mean ( 22 / 24 )135.8030555555560.842200003913498161.247987324284
Winsorized Mean ( 23 / 24 )135.7072222222220.781513824867737173.646604710018
Winsorized Mean ( 24 / 24 )135.5272222222220.713043143944366190.068754427006
Trimmed Mean ( 1 / 24 )134.1891.538162103393187.2398297318508
Trimmed Mean ( 2 / 24 )134.3204411764711.4732949913114391.1700928657253
Trimmed Mean ( 3 / 24 )134.4736363636361.4233167154775394.4790677305576
Trimmed Mean ( 4 / 24 )134.62593751.3712957629127498.174253243548
Trimmed Mean ( 5 / 24 )134.7374193548391.32473520767907101.708944228106
Trimmed Mean ( 6 / 24 )134.891.2768319065226105.644289832456
Trimmed Mean ( 7 / 24 )135.0296551724141.24615451964961108.357072131296
Trimmed Mean ( 8 / 24 )135.1703571428571.21884070329906110.900757397573
Trimmed Mean ( 9 / 24 )135.2737037037041.19974913800789112.751657340898
Trimmed Mean ( 10 / 24 )135.3636538461541.18272680148107114.450483134943
Trimmed Mean ( 11 / 24 )135.45241.16514476844235116.253708267585
Trimmed Mean ( 12 / 24 )135.5422916666671.14578951842406118.29597800222
Trimmed Mean ( 13 / 24 )135.6352173913041.12317556794907120.760477045432
Trimmed Mean ( 14 / 24 )135.7243181818181.09921437434859123.473929516479
Trimmed Mean ( 15 / 24 )135.8092857142861.07368115317472126.489400799034
Trimmed Mean ( 16 / 24 )135.919251.05317038991433129.057226923229
Trimmed Mean ( 17 / 24 )136.0126315789471.03419629422774131.515295827386
Trimmed Mean ( 18 / 24 )136.0522222222221.02730655005963132.435855893575
Trimmed Mean ( 19 / 24 )136.0958823529411.01920227776582133.531768248473
Trimmed Mean ( 20 / 24 )136.143751.00551721464708135.396737138692
Trimmed Mean ( 21 / 24 )136.1960.987996998459771137.850621218811
Trimmed Mean ( 22 / 24 )136.2321428571430.968584899861055140.650698639516
Trimmed Mean ( 23 / 24 )136.2861538461540.941349943419731144.777353840437
Trimmed Mean ( 24 / 24 )136.3616666666670.916929079699225148.715609184733
Median136.89
Midrange129.69
Midmean - Weighted Average at Xnp135.780540540541
Midmean - Weighted Average at X(n+1)p136.052222222222
Midmean - Empirical Distribution Function135.780540540541
Midmean - Empirical Distribution Function - Averaging136.052222222222
Midmean - Empirical Distribution Function - Interpolation136.052222222222
Midmean - Closest Observation135.780540540541
Midmean - True Basic - Statistics Graphics Toolkit136.052222222222
Midmean - MS Excel (old versions)136.012631578947
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 134.064027777778 & 1.59875595537295 & 83.8552171313127 \tabularnewline
Geometric Mean & 133.35318757226 &  &  \tabularnewline
Harmonic Mean & 132.607068900035 &  &  \tabularnewline
Quadratic Mean & 134.739159144417 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 134.064861111111 & 1.59244822628741 & 84.1878931434185 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 134.039583333333 & 1.5497319476117 & 86.4921082254917 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 134.0675 & 1.53219064318312 & 87.5005343470022 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 134.241944444444 & 1.48990698839637 & 90.1008891762653 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 134.101666666667 & 1.46224865421739 & 91.7092084714137 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 134.215 & 1.36722540965774 & 98.1659637481419 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 134.263611111111 & 1.32628489543085 & 101.2328584708 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 134.550277777778 & 1.26584787862064 & 106.292612287974 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 134.689027777778 & 1.23362465090961 & 109.181530766644 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 134.747361111111 & 1.21250308540749 & 111.131561422647 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 134.793194444444 & 1.19479006979954 & 112.817471329553 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 134.829861111111 & 1.18060366732029 & 114.204169310388 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 134.927361111111 & 1.15331608363609 & 116.990791185121 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 135.030416666667 & 1.12417266461647 & 120.115370989504 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 134.892916666667 & 1.05959542574318 & 127.306057943819 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 135.130694444444 & 1.01862476574816 & 132.659934244965 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 135.676111111111 & 0.933381235263785 & 145.359801531437 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 135.681111111111 & 0.914491712459925 & 148.367786457176 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 135.691666666667 & 0.910764674679886 & 148.986527957246 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 135.708333333333 & 0.891449185886226 & 152.23339196661 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 135.900833333333 & 0.86013994089254 & 157.998514976892 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 135.803055555556 & 0.842200003913498 & 161.247987324284 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 135.707222222222 & 0.781513824867737 & 173.646604710018 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 135.527222222222 & 0.713043143944366 & 190.068754427006 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 134.189 & 1.5381621033931 & 87.2398297318508 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 134.320441176471 & 1.47329499131143 & 91.1700928657253 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 134.473636363636 & 1.42331671547753 & 94.4790677305576 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 134.6259375 & 1.37129576291274 & 98.174253243548 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 134.737419354839 & 1.32473520767907 & 101.708944228106 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 134.89 & 1.2768319065226 & 105.644289832456 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 135.029655172414 & 1.24615451964961 & 108.357072131296 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 135.170357142857 & 1.21884070329906 & 110.900757397573 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 135.273703703704 & 1.19974913800789 & 112.751657340898 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 135.363653846154 & 1.18272680148107 & 114.450483134943 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 135.4524 & 1.16514476844235 & 116.253708267585 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 135.542291666667 & 1.14578951842406 & 118.29597800222 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 135.635217391304 & 1.12317556794907 & 120.760477045432 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 135.724318181818 & 1.09921437434859 & 123.473929516479 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 135.809285714286 & 1.07368115317472 & 126.489400799034 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 135.91925 & 1.05317038991433 & 129.057226923229 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 136.012631578947 & 1.03419629422774 & 131.515295827386 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 136.052222222222 & 1.02730655005963 & 132.435855893575 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 136.095882352941 & 1.01920227776582 & 133.531768248473 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 136.14375 & 1.00551721464708 & 135.396737138692 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 136.196 & 0.987996998459771 & 137.850621218811 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 136.232142857143 & 0.968584899861055 & 140.650698639516 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 136.286153846154 & 0.941349943419731 & 144.777353840437 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 136.361666666667 & 0.916929079699225 & 148.715609184733 \tabularnewline
Median & 136.89 &  &  \tabularnewline
Midrange & 129.69 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 135.780540540541 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 136.052222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 135.780540540541 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 136.052222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 136.052222222222 &  &  \tabularnewline
Midmean - Closest Observation & 135.780540540541 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 136.052222222222 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 136.012631578947 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240833&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]134.064027777778[/C][C]1.59875595537295[/C][C]83.8552171313127[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]133.35318757226[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]132.607068900035[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]134.739159144417[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]134.064861111111[/C][C]1.59244822628741[/C][C]84.1878931434185[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]134.039583333333[/C][C]1.5497319476117[/C][C]86.4921082254917[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]134.0675[/C][C]1.53219064318312[/C][C]87.5005343470022[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]134.241944444444[/C][C]1.48990698839637[/C][C]90.1008891762653[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]134.101666666667[/C][C]1.46224865421739[/C][C]91.7092084714137[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]134.215[/C][C]1.36722540965774[/C][C]98.1659637481419[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]134.263611111111[/C][C]1.32628489543085[/C][C]101.2328584708[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]134.550277777778[/C][C]1.26584787862064[/C][C]106.292612287974[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]134.689027777778[/C][C]1.23362465090961[/C][C]109.181530766644[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]134.747361111111[/C][C]1.21250308540749[/C][C]111.131561422647[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]134.793194444444[/C][C]1.19479006979954[/C][C]112.817471329553[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]134.829861111111[/C][C]1.18060366732029[/C][C]114.204169310388[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]134.927361111111[/C][C]1.15331608363609[/C][C]116.990791185121[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]135.030416666667[/C][C]1.12417266461647[/C][C]120.115370989504[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]134.892916666667[/C][C]1.05959542574318[/C][C]127.306057943819[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]135.130694444444[/C][C]1.01862476574816[/C][C]132.659934244965[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]135.676111111111[/C][C]0.933381235263785[/C][C]145.359801531437[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]135.681111111111[/C][C]0.914491712459925[/C][C]148.367786457176[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]135.691666666667[/C][C]0.910764674679886[/C][C]148.986527957246[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]135.708333333333[/C][C]0.891449185886226[/C][C]152.23339196661[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]135.900833333333[/C][C]0.86013994089254[/C][C]157.998514976892[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]135.803055555556[/C][C]0.842200003913498[/C][C]161.247987324284[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]135.707222222222[/C][C]0.781513824867737[/C][C]173.646604710018[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]135.527222222222[/C][C]0.713043143944366[/C][C]190.068754427006[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]134.189[/C][C]1.5381621033931[/C][C]87.2398297318508[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]134.320441176471[/C][C]1.47329499131143[/C][C]91.1700928657253[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]134.473636363636[/C][C]1.42331671547753[/C][C]94.4790677305576[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]134.6259375[/C][C]1.37129576291274[/C][C]98.174253243548[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]134.737419354839[/C][C]1.32473520767907[/C][C]101.708944228106[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]134.89[/C][C]1.2768319065226[/C][C]105.644289832456[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]135.029655172414[/C][C]1.24615451964961[/C][C]108.357072131296[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]135.170357142857[/C][C]1.21884070329906[/C][C]110.900757397573[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]135.273703703704[/C][C]1.19974913800789[/C][C]112.751657340898[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]135.363653846154[/C][C]1.18272680148107[/C][C]114.450483134943[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]135.4524[/C][C]1.16514476844235[/C][C]116.253708267585[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]135.542291666667[/C][C]1.14578951842406[/C][C]118.29597800222[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]135.635217391304[/C][C]1.12317556794907[/C][C]120.760477045432[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]135.724318181818[/C][C]1.09921437434859[/C][C]123.473929516479[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]135.809285714286[/C][C]1.07368115317472[/C][C]126.489400799034[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]135.91925[/C][C]1.05317038991433[/C][C]129.057226923229[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]136.012631578947[/C][C]1.03419629422774[/C][C]131.515295827386[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]136.052222222222[/C][C]1.02730655005963[/C][C]132.435855893575[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]136.095882352941[/C][C]1.01920227776582[/C][C]133.531768248473[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]136.14375[/C][C]1.00551721464708[/C][C]135.396737138692[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]136.196[/C][C]0.987996998459771[/C][C]137.850621218811[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]136.232142857143[/C][C]0.968584899861055[/C][C]140.650698639516[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]136.286153846154[/C][C]0.941349943419731[/C][C]144.777353840437[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]136.361666666667[/C][C]0.916929079699225[/C][C]148.715609184733[/C][/ROW]
[ROW][C]Median[/C][C]136.89[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]129.69[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]135.780540540541[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]136.052222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]135.780540540541[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]136.052222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]136.052222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]135.780540540541[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]136.052222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]136.012631578947[/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=240833&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240833&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 Mean134.0640277777781.5987559553729583.8552171313127
Geometric Mean133.35318757226
Harmonic Mean132.607068900035
Quadratic Mean134.739159144417
Winsorized Mean ( 1 / 24 )134.0648611111111.5924482262874184.1878931434185
Winsorized Mean ( 2 / 24 )134.0395833333331.549731947611786.4921082254917
Winsorized Mean ( 3 / 24 )134.06751.5321906431831287.5005343470022
Winsorized Mean ( 4 / 24 )134.2419444444441.4899069883963790.1008891762653
Winsorized Mean ( 5 / 24 )134.1016666666671.4622486542173991.7092084714137
Winsorized Mean ( 6 / 24 )134.2151.3672254096577498.1659637481419
Winsorized Mean ( 7 / 24 )134.2636111111111.32628489543085101.2328584708
Winsorized Mean ( 8 / 24 )134.5502777777781.26584787862064106.292612287974
Winsorized Mean ( 9 / 24 )134.6890277777781.23362465090961109.181530766644
Winsorized Mean ( 10 / 24 )134.7473611111111.21250308540749111.131561422647
Winsorized Mean ( 11 / 24 )134.7931944444441.19479006979954112.817471329553
Winsorized Mean ( 12 / 24 )134.8298611111111.18060366732029114.204169310388
Winsorized Mean ( 13 / 24 )134.9273611111111.15331608363609116.990791185121
Winsorized Mean ( 14 / 24 )135.0304166666671.12417266461647120.115370989504
Winsorized Mean ( 15 / 24 )134.8929166666671.05959542574318127.306057943819
Winsorized Mean ( 16 / 24 )135.1306944444441.01862476574816132.659934244965
Winsorized Mean ( 17 / 24 )135.6761111111110.933381235263785145.359801531437
Winsorized Mean ( 18 / 24 )135.6811111111110.914491712459925148.367786457176
Winsorized Mean ( 19 / 24 )135.6916666666670.910764674679886148.986527957246
Winsorized Mean ( 20 / 24 )135.7083333333330.891449185886226152.23339196661
Winsorized Mean ( 21 / 24 )135.9008333333330.86013994089254157.998514976892
Winsorized Mean ( 22 / 24 )135.8030555555560.842200003913498161.247987324284
Winsorized Mean ( 23 / 24 )135.7072222222220.781513824867737173.646604710018
Winsorized Mean ( 24 / 24 )135.5272222222220.713043143944366190.068754427006
Trimmed Mean ( 1 / 24 )134.1891.538162103393187.2398297318508
Trimmed Mean ( 2 / 24 )134.3204411764711.4732949913114391.1700928657253
Trimmed Mean ( 3 / 24 )134.4736363636361.4233167154775394.4790677305576
Trimmed Mean ( 4 / 24 )134.62593751.3712957629127498.174253243548
Trimmed Mean ( 5 / 24 )134.7374193548391.32473520767907101.708944228106
Trimmed Mean ( 6 / 24 )134.891.2768319065226105.644289832456
Trimmed Mean ( 7 / 24 )135.0296551724141.24615451964961108.357072131296
Trimmed Mean ( 8 / 24 )135.1703571428571.21884070329906110.900757397573
Trimmed Mean ( 9 / 24 )135.2737037037041.19974913800789112.751657340898
Trimmed Mean ( 10 / 24 )135.3636538461541.18272680148107114.450483134943
Trimmed Mean ( 11 / 24 )135.45241.16514476844235116.253708267585
Trimmed Mean ( 12 / 24 )135.5422916666671.14578951842406118.29597800222
Trimmed Mean ( 13 / 24 )135.6352173913041.12317556794907120.760477045432
Trimmed Mean ( 14 / 24 )135.7243181818181.09921437434859123.473929516479
Trimmed Mean ( 15 / 24 )135.8092857142861.07368115317472126.489400799034
Trimmed Mean ( 16 / 24 )135.919251.05317038991433129.057226923229
Trimmed Mean ( 17 / 24 )136.0126315789471.03419629422774131.515295827386
Trimmed Mean ( 18 / 24 )136.0522222222221.02730655005963132.435855893575
Trimmed Mean ( 19 / 24 )136.0958823529411.01920227776582133.531768248473
Trimmed Mean ( 20 / 24 )136.143751.00551721464708135.396737138692
Trimmed Mean ( 21 / 24 )136.1960.987996998459771137.850621218811
Trimmed Mean ( 22 / 24 )136.2321428571430.968584899861055140.650698639516
Trimmed Mean ( 23 / 24 )136.2861538461540.941349943419731144.777353840437
Trimmed Mean ( 24 / 24 )136.3616666666670.916929079699225148.715609184733
Median136.89
Midrange129.69
Midmean - Weighted Average at Xnp135.780540540541
Midmean - Weighted Average at X(n+1)p136.052222222222
Midmean - Empirical Distribution Function135.780540540541
Midmean - Empirical Distribution Function - Averaging136.052222222222
Midmean - Empirical Distribution Function - Interpolation136.052222222222
Midmean - Closest Observation135.780540540541
Midmean - True Basic - Statistics Graphics Toolkit136.052222222222
Midmean - MS Excel (old versions)136.012631578947
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')