Free Statistics

of Irreproducible Research!

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, 22 Oct 2009 09:01:51 -0600
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/Oct/22/t1256223749iutajm2wzu06hq6.htm/, Retrieved Fri, 03 May 2024 15:18:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49749, Retrieved Fri, 03 May 2024 15:18:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact134
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [WS3] [2009-10-22 15:01:51] [78d370e6d5f4594e9982a5085e7604c6] [Current]
Feedback Forum

Post a new message
Dataseries X:
0.3213
0.2965
0.2735
0.2723
0.3096
0.3655
0.3247
0.2988
0.3337
0.3694
0.3659
0.3718
0.2906
0.3024
0.3400
0.3094
0.2800
0.1988
0.2306
0.2576
0.2174
0.1905
0.2012
0.1525
0.1513
0.1863
0.2050
0.2101
0.2269
0.2333
0.2253
0.1580
0.1613
0.1803
0.1534
0.2157
0.3294
0.4200
0.4352
0.4806
0.5127
0.6362
0.6194
0.7776
0.8788
0.8565
0.7384
0.7280
0.6466
0.4423
0.3812
0.3268
0.2573
0.0805
0.0769
-0.0474
-0.1429
-0.2182
-0.1000
-0.1506




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49749&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]3 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=49749&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49749&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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.3024366666666670.029168113633195810.3687427466159
Geometric MeanNaN
Harmonic Mean0.367727043999901
Quadratic Mean0.376382637307656
Winsorized Mean ( 1 / 20 )0.3031916666666670.028723767722154910.5554281596844
Winsorized Mean ( 2 / 20 )0.3008183333333330.027843003410838610.8040906684741
Winsorized Mean ( 3 / 20 )0.3010033333333330.026723638995608511.2635608265325
Winsorized Mean ( 4 / 20 )0.3038166666666670.025677224972678611.8321456851329
Winsorized Mean ( 5 / 20 )0.3073916666666670.021666190210971614.1876196817937
Winsorized Mean ( 6 / 20 )0.3067116666666670.021327211218792714.3812364176524
Winsorized Mean ( 7 / 20 )0.3130116666666670.019478619901991316.0694991863703
Winsorized Mean ( 8 / 20 )0.2989450.015910965451856518.7886147389705
Winsorized Mean ( 9 / 20 )0.2942650.014827339770202119.8461089150579
Winsorized Mean ( 10 / 20 )0.2886483333333330.013399178972163221.5422403068875
Winsorized Mean ( 11 / 20 )0.2879516666666670.013048413002117322.0679454750507
Winsorized Mean ( 12 / 20 )0.2887116666666670.011864640314119424.3337900705753
Winsorized Mean ( 13 / 20 )0.2816050.01016776295608227.6958659654387
Winsorized Mean ( 14 / 20 )0.2803916666666670.0096543606527794529.0430072742252
Winsorized Mean ( 15 / 20 )0.2818666666666670.0092360206373094530.5181936826830
Winsorized Mean ( 16 / 20 )0.2815733333333330.0089895761564543831.3222034535152
Winsorized Mean ( 17 / 20 )0.2825366666666670.0088096252466729432.0713604444604
Winsorized Mean ( 18 / 20 )0.2764166666666670.0074079466289926637.3135337645182
Winsorized Mean ( 19 / 20 )0.2761950.0068535925772319840.2993024297265
Winsorized Mean ( 20 / 20 )0.2753283333333330.0065668647300136741.9269079923259
Trimmed Mean ( 1 / 20 )0.3014758620689660.026990881289406911.1695449598856
Trimmed Mean ( 2 / 20 )0.29963750.02480987923285212.0773461727792
Trimmed Mean ( 3 / 20 )0.2989814814814810.022675065510500313.1854737682249
Trimmed Mean ( 4 / 20 )0.2982038461538460.020543295699610814.5158717721955
Trimmed Mean ( 5 / 20 )0.296520.018237739297782416.2585940701573
Trimmed Mean ( 6 / 20 )0.2938020833333330.016892488964575117.3924685669151
Trimmed Mean ( 7 / 20 )0.2909956521739130.015238318391673219.0963100188879
Trimmed Mean ( 8 / 20 )0.2867068181818180.013649445077634121.0050164348157
Trimmed Mean ( 9 / 20 )0.2845214285714290.012824386311663522.1859683307156
Trimmed Mean ( 10 / 20 )0.28289750.012075176108234323.4280227024670
Trimmed Mean ( 11 / 20 )0.2819894736842110.011514834756974324.4892332053151
Trimmed Mean ( 12 / 20 )0.2810861111111110.010850892109310725.9044241044405
Trimmed Mean ( 13 / 20 )0.2799647058823530.010292386714672527.2011452390576
Trimmed Mean ( 14 / 20 )0.2797281250.010031885892693027.883902188695
Trimmed Mean ( 15 / 20 )0.2796333333333330.0097905928733790428.5614300328702
Trimmed Mean ( 16 / 20 )0.2793142857142860.009539637046612629.2793409591476
Trimmed Mean ( 17 / 20 )0.2789884615384620.0092151920167365730.2748397463411
Trimmed Mean ( 18 / 20 )0.2784666666666670.0087469221639954731.8359602893124
Trimmed Mean ( 19 / 20 )0.2787772727272730.0085496131195682532.6070044139437
Trimmed Mean ( 20 / 20 )0.2791850.0083935635584968533.2617961434723
Median0.2853
Midrange0.3303
Midmean - Weighted Average at Xnp0.276758064516129
Midmean - Weighted Average at X(n+1)p0.279633333333333
Midmean - Empirical Distribution Function0.276758064516129
Midmean - Empirical Distribution Function - Averaging0.279633333333333
Midmean - Empirical Distribution Function - Interpolation0.279633333333333
Midmean - Closest Observation0.276758064516129
Midmean - True Basic - Statistics Graphics Toolkit0.279633333333333
Midmean - MS Excel (old versions)0.279728125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.302436666666667 & 0.0291681136331958 & 10.3687427466159 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0.367727043999901 &  &  \tabularnewline
Quadratic Mean & 0.376382637307656 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 0.303191666666667 & 0.0287237677221549 & 10.5554281596844 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 0.300818333333333 & 0.0278430034108386 & 10.8040906684741 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 0.301003333333333 & 0.0267236389956085 & 11.2635608265325 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 0.303816666666667 & 0.0256772249726786 & 11.8321456851329 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 0.307391666666667 & 0.0216661902109716 & 14.1876196817937 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 0.306711666666667 & 0.0213272112187927 & 14.3812364176524 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 0.313011666666667 & 0.0194786199019913 & 16.0694991863703 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.298945 & 0.0159109654518565 & 18.7886147389705 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 0.294265 & 0.0148273397702021 & 19.8461089150579 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.288648333333333 & 0.0133991789721632 & 21.5422403068875 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.287951666666667 & 0.0130484130021173 & 22.0679454750507 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.288711666666667 & 0.0118646403141194 & 24.3337900705753 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.281605 & 0.010167762956082 & 27.6958659654387 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.280391666666667 & 0.00965436065277945 & 29.0430072742252 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.281866666666667 & 0.00923602063730945 & 30.5181936826830 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.281573333333333 & 0.00898957615645438 & 31.3222034535152 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.282536666666667 & 0.00880962524667294 & 32.0713604444604 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.276416666666667 & 0.00740794662899266 & 37.3135337645182 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.276195 & 0.00685359257723198 & 40.2993024297265 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 0.275328333333333 & 0.00656686473001367 & 41.9269079923259 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 0.301475862068966 & 0.0269908812894069 & 11.1695449598856 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 0.2996375 & 0.024809879232852 & 12.0773461727792 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 0.298981481481481 & 0.0226750655105003 & 13.1854737682249 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 0.298203846153846 & 0.0205432956996108 & 14.5158717721955 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 0.29652 & 0.0182377392977824 & 16.2585940701573 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 0.293802083333333 & 0.0168924889645751 & 17.3924685669151 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.290995652173913 & 0.0152383183916732 & 19.0963100188879 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.286706818181818 & 0.0136494450776341 & 21.0050164348157 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.284521428571429 & 0.0128243863116635 & 22.1859683307156 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.2828975 & 0.0120751761082343 & 23.4280227024670 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.281989473684211 & 0.0115148347569743 & 24.4892332053151 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.281086111111111 & 0.0108508921093107 & 25.9044241044405 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.279964705882353 & 0.0102923867146725 & 27.2011452390576 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.279728125 & 0.0100318858926930 & 27.883902188695 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.279633333333333 & 0.00979059287337904 & 28.5614300328702 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.279314285714286 & 0.0095396370466126 & 29.2793409591476 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 0.278988461538462 & 0.00921519201673657 & 30.2748397463411 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 0.278466666666667 & 0.00874692216399547 & 31.8359602893124 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 0.278777272727273 & 0.00854961311956825 & 32.6070044139437 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 0.279185 & 0.00839356355849685 & 33.2617961434723 \tabularnewline
Median & 0.2853 &  &  \tabularnewline
Midrange & 0.3303 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.276758064516129 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.279633333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.276758064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.279633333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.279633333333333 &  &  \tabularnewline
Midmean - Closest Observation & 0.276758064516129 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.279633333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.279728125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49749&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]0.302436666666667[/C][C]0.0291681136331958[/C][C]10.3687427466159[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.367727043999901[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.376382637307656[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]0.303191666666667[/C][C]0.0287237677221549[/C][C]10.5554281596844[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]0.300818333333333[/C][C]0.0278430034108386[/C][C]10.8040906684741[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]0.301003333333333[/C][C]0.0267236389956085[/C][C]11.2635608265325[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]0.303816666666667[/C][C]0.0256772249726786[/C][C]11.8321456851329[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]0.307391666666667[/C][C]0.0216661902109716[/C][C]14.1876196817937[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]0.306711666666667[/C][C]0.0213272112187927[/C][C]14.3812364176524[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]0.313011666666667[/C][C]0.0194786199019913[/C][C]16.0694991863703[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.298945[/C][C]0.0159109654518565[/C][C]18.7886147389705[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]0.294265[/C][C]0.0148273397702021[/C][C]19.8461089150579[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.288648333333333[/C][C]0.0133991789721632[/C][C]21.5422403068875[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.287951666666667[/C][C]0.0130484130021173[/C][C]22.0679454750507[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.288711666666667[/C][C]0.0118646403141194[/C][C]24.3337900705753[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.281605[/C][C]0.010167762956082[/C][C]27.6958659654387[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.280391666666667[/C][C]0.00965436065277945[/C][C]29.0430072742252[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.281866666666667[/C][C]0.00923602063730945[/C][C]30.5181936826830[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.281573333333333[/C][C]0.00898957615645438[/C][C]31.3222034535152[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.282536666666667[/C][C]0.00880962524667294[/C][C]32.0713604444604[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.276416666666667[/C][C]0.00740794662899266[/C][C]37.3135337645182[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.276195[/C][C]0.00685359257723198[/C][C]40.2993024297265[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]0.275328333333333[/C][C]0.00656686473001367[/C][C]41.9269079923259[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]0.301475862068966[/C][C]0.0269908812894069[/C][C]11.1695449598856[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]0.2996375[/C][C]0.024809879232852[/C][C]12.0773461727792[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]0.298981481481481[/C][C]0.0226750655105003[/C][C]13.1854737682249[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]0.298203846153846[/C][C]0.0205432956996108[/C][C]14.5158717721955[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]0.29652[/C][C]0.0182377392977824[/C][C]16.2585940701573[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]0.293802083333333[/C][C]0.0168924889645751[/C][C]17.3924685669151[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.290995652173913[/C][C]0.0152383183916732[/C][C]19.0963100188879[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.286706818181818[/C][C]0.0136494450776341[/C][C]21.0050164348157[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.284521428571429[/C][C]0.0128243863116635[/C][C]22.1859683307156[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.2828975[/C][C]0.0120751761082343[/C][C]23.4280227024670[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.281989473684211[/C][C]0.0115148347569743[/C][C]24.4892332053151[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.281086111111111[/C][C]0.0108508921093107[/C][C]25.9044241044405[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.279964705882353[/C][C]0.0102923867146725[/C][C]27.2011452390576[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.279728125[/C][C]0.0100318858926930[/C][C]27.883902188695[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.279633333333333[/C][C]0.00979059287337904[/C][C]28.5614300328702[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.279314285714286[/C][C]0.0095396370466126[/C][C]29.2793409591476[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]0.278988461538462[/C][C]0.00921519201673657[/C][C]30.2748397463411[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]0.278466666666667[/C][C]0.00874692216399547[/C][C]31.8359602893124[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]0.278777272727273[/C][C]0.00854961311956825[/C][C]32.6070044139437[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]0.279185[/C][C]0.00839356355849685[/C][C]33.2617961434723[/C][/ROW]
[ROW][C]Median[/C][C]0.2853[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.3303[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.276758064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.279633333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.276758064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.279633333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.279633333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.276758064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.279633333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.279728125[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49749&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49749&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 Mean0.3024366666666670.029168113633195810.3687427466159
Geometric MeanNaN
Harmonic Mean0.367727043999901
Quadratic Mean0.376382637307656
Winsorized Mean ( 1 / 20 )0.3031916666666670.028723767722154910.5554281596844
Winsorized Mean ( 2 / 20 )0.3008183333333330.027843003410838610.8040906684741
Winsorized Mean ( 3 / 20 )0.3010033333333330.026723638995608511.2635608265325
Winsorized Mean ( 4 / 20 )0.3038166666666670.025677224972678611.8321456851329
Winsorized Mean ( 5 / 20 )0.3073916666666670.021666190210971614.1876196817937
Winsorized Mean ( 6 / 20 )0.3067116666666670.021327211218792714.3812364176524
Winsorized Mean ( 7 / 20 )0.3130116666666670.019478619901991316.0694991863703
Winsorized Mean ( 8 / 20 )0.2989450.015910965451856518.7886147389705
Winsorized Mean ( 9 / 20 )0.2942650.014827339770202119.8461089150579
Winsorized Mean ( 10 / 20 )0.2886483333333330.013399178972163221.5422403068875
Winsorized Mean ( 11 / 20 )0.2879516666666670.013048413002117322.0679454750507
Winsorized Mean ( 12 / 20 )0.2887116666666670.011864640314119424.3337900705753
Winsorized Mean ( 13 / 20 )0.2816050.01016776295608227.6958659654387
Winsorized Mean ( 14 / 20 )0.2803916666666670.0096543606527794529.0430072742252
Winsorized Mean ( 15 / 20 )0.2818666666666670.0092360206373094530.5181936826830
Winsorized Mean ( 16 / 20 )0.2815733333333330.0089895761564543831.3222034535152
Winsorized Mean ( 17 / 20 )0.2825366666666670.0088096252466729432.0713604444604
Winsorized Mean ( 18 / 20 )0.2764166666666670.0074079466289926637.3135337645182
Winsorized Mean ( 19 / 20 )0.2761950.0068535925772319840.2993024297265
Winsorized Mean ( 20 / 20 )0.2753283333333330.0065668647300136741.9269079923259
Trimmed Mean ( 1 / 20 )0.3014758620689660.026990881289406911.1695449598856
Trimmed Mean ( 2 / 20 )0.29963750.02480987923285212.0773461727792
Trimmed Mean ( 3 / 20 )0.2989814814814810.022675065510500313.1854737682249
Trimmed Mean ( 4 / 20 )0.2982038461538460.020543295699610814.5158717721955
Trimmed Mean ( 5 / 20 )0.296520.018237739297782416.2585940701573
Trimmed Mean ( 6 / 20 )0.2938020833333330.016892488964575117.3924685669151
Trimmed Mean ( 7 / 20 )0.2909956521739130.015238318391673219.0963100188879
Trimmed Mean ( 8 / 20 )0.2867068181818180.013649445077634121.0050164348157
Trimmed Mean ( 9 / 20 )0.2845214285714290.012824386311663522.1859683307156
Trimmed Mean ( 10 / 20 )0.28289750.012075176108234323.4280227024670
Trimmed Mean ( 11 / 20 )0.2819894736842110.011514834756974324.4892332053151
Trimmed Mean ( 12 / 20 )0.2810861111111110.010850892109310725.9044241044405
Trimmed Mean ( 13 / 20 )0.2799647058823530.010292386714672527.2011452390576
Trimmed Mean ( 14 / 20 )0.2797281250.010031885892693027.883902188695
Trimmed Mean ( 15 / 20 )0.2796333333333330.0097905928733790428.5614300328702
Trimmed Mean ( 16 / 20 )0.2793142857142860.009539637046612629.2793409591476
Trimmed Mean ( 17 / 20 )0.2789884615384620.0092151920167365730.2748397463411
Trimmed Mean ( 18 / 20 )0.2784666666666670.0087469221639954731.8359602893124
Trimmed Mean ( 19 / 20 )0.2787772727272730.0085496131195682532.6070044139437
Trimmed Mean ( 20 / 20 )0.2791850.0083935635584968533.2617961434723
Median0.2853
Midrange0.3303
Midmean - Weighted Average at Xnp0.276758064516129
Midmean - Weighted Average at X(n+1)p0.279633333333333
Midmean - Empirical Distribution Function0.276758064516129
Midmean - Empirical Distribution Function - Averaging0.279633333333333
Midmean - Empirical Distribution Function - Interpolation0.279633333333333
Midmean - Closest Observation0.276758064516129
Midmean - True Basic - Statistics Graphics Toolkit0.279633333333333
Midmean - MS Excel (old versions)0.279728125
Number of observations60



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')