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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 18 Dec 2011 09:50:26 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/18/t1324219849hhkqxf4w028fp0f.htm/, Retrieved Sun, 05 May 2024 10:52:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=156933, Retrieved Sun, 05 May 2024 10:52:31 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact63
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [paper5] [2011-12-18 14:50:26] [47995d3a8fac585eeb070a274b466f8c] [Current]
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Dataseries X:
1200
916
878
841
824
819
823
825
773
836
862
886
1010
846
911
856
881
830
830
827
773
797
826
947
1110
896
917
873
845
807
841
829
781
861
831
969
991
891
945
911
847
823
838
862
822
864
862
1044
1035
858
889
832
810
792
812
783
773
840
820
945




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156933&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156933&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156933&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean871.110.570765036000482.4065237504888
Geometric Mean867.658751357354
Harmonic Mean864.516404002466
Quadratic Mean874.87595311183
Winsorized Mean ( 1 / 20 )869.69.8624208302408488.1730778850536
Winsorized Mean ( 2 / 20 )867.49.039811507459495.9533281511728
Winsorized Mean ( 3 / 20 )867.358.8242355345016598.2918006448004
Winsorized Mean ( 4 / 20 )865.8166666666678.2870974407489104.47767422274
Winsorized Mean ( 5 / 20 )864.9833333333337.71001592568964112.189565063183
Winsorized Mean ( 6 / 20 )863.2833333333337.04437475088351122.549319685904
Winsorized Mean ( 7 / 20 )861.8833333333336.2390284113707138.143838512186
Winsorized Mean ( 8 / 20 )862.0166666666676.11890151447786140.877682804186
Winsorized Mean ( 9 / 20 )862.3166666666676.07623376449825141.916308701772
Winsorized Mean ( 10 / 20 )858.8166666666674.89860418645127175.318648737126
Winsorized Mean ( 11 / 20 )858.8166666666674.83668255282077177.563165927812
Winsorized Mean ( 12 / 20 )858.2166666666674.58486158393898187.184858464004
Winsorized Mean ( 13 / 20 )858.4333333333334.55607663181305188.415033965688
Winsorized Mean ( 14 / 20 )854.9333333333333.89914279052994219.261868380341
Winsorized Mean ( 15 / 20 )853.9333333333333.6449691873386234.27724335767
Winsorized Mean ( 16 / 20 )853.6666666666673.51660039565907242.753389813765
Winsorized Mean ( 17 / 20 )853.13.33401405478653255.877745558761
Winsorized Mean ( 18 / 20 )851.93.04548382878853279.725668528301
Winsorized Mean ( 19 / 20 )851.5833333333332.80559284717249303.530618917698
Winsorized Mean ( 20 / 20 )850.252.4980924926221340.359695452085
Trimmed Mean ( 1 / 20 )867.1206896551729.1509845812312994.7570921967939
Trimmed Mean ( 2 / 20 )864.4642857142868.22969616005521105.042065818926
Trimmed Mean ( 3 / 20 )862.8333333333337.6584017979753112.664934028591
Trimmed Mean ( 4 / 20 )861.0961538461547.038048908608122.34870274814
Trimmed Mean ( 5 / 20 )859.686.48366487444267132.591677183793
Trimmed Mean ( 6 / 20 )858.3541666666675.99508439178776143.176327566375
Trimmed Mean ( 7 / 20 )857.2826086956525.60466188316625152.958845076903
Trimmed Mean ( 8 / 20 )856.3863636363645.36266317720072159.694229404016
Trimmed Mean ( 9 / 20 )855.3809523809525.07572762226413168.523809006007
Trimmed Mean ( 10 / 20 )854.2254.69567278978401181.91748834341
Trimmed Mean ( 11 / 20 )853.54.55685593239683187.300193963137
Trimmed Mean ( 12 / 20 )852.6944444444444.37739856145004194.794792494743
Trimmed Mean ( 13 / 20 )851.8823529411764.19866813316817202.893471434804
Trimmed Mean ( 14 / 20 )850.93753.94287267860343215.816631517861
Trimmed Mean ( 15 / 20 )850.3666666666673.80576795559067223.441543622616
Trimmed Mean ( 16 / 20 )849.8571428571433.68168435605999230.833787111134
Trimmed Mean ( 17 / 20 )849.3076923076923.52781005540013240.746434465096
Trimmed Mean ( 18 / 20 )848.753.34937264296603253.405664425679
Trimmed Mean ( 19 / 20 )848.2727272727273.1808285412105266.682946371548
Trimmed Mean ( 20 / 20 )847.752.9972575183956282.841896232457
Median845.5
Midrange986.5
Midmean - Weighted Average at Xnp848.65625
Midmean - Weighted Average at X(n+1)p850.366666666667
Midmean - Empirical Distribution Function848.65625
Midmean - Empirical Distribution Function - Averaging850.366666666667
Midmean - Empirical Distribution Function - Interpolation850.366666666667
Midmean - Closest Observation848.65625
Midmean - True Basic - Statistics Graphics Toolkit850.366666666667
Midmean - MS Excel (old versions)850.090909090909
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 871.1 & 10.5707650360004 & 82.4065237504888 \tabularnewline
Geometric Mean & 867.658751357354 &  &  \tabularnewline
Harmonic Mean & 864.516404002466 &  &  \tabularnewline
Quadratic Mean & 874.87595311183 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 869.6 & 9.86242083024084 & 88.1730778850536 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 867.4 & 9.0398115074594 & 95.9533281511728 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 867.35 & 8.82423553450165 & 98.2918006448004 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 865.816666666667 & 8.2870974407489 & 104.47767422274 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 864.983333333333 & 7.71001592568964 & 112.189565063183 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 863.283333333333 & 7.04437475088351 & 122.549319685904 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 861.883333333333 & 6.2390284113707 & 138.143838512186 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 862.016666666667 & 6.11890151447786 & 140.877682804186 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 862.316666666667 & 6.07623376449825 & 141.916308701772 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 858.816666666667 & 4.89860418645127 & 175.318648737126 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 858.816666666667 & 4.83668255282077 & 177.563165927812 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 858.216666666667 & 4.58486158393898 & 187.184858464004 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 858.433333333333 & 4.55607663181305 & 188.415033965688 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 854.933333333333 & 3.89914279052994 & 219.261868380341 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 853.933333333333 & 3.6449691873386 & 234.27724335767 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 853.666666666667 & 3.51660039565907 & 242.753389813765 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 853.1 & 3.33401405478653 & 255.877745558761 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 851.9 & 3.04548382878853 & 279.725668528301 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 851.583333333333 & 2.80559284717249 & 303.530618917698 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 850.25 & 2.4980924926221 & 340.359695452085 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 867.120689655172 & 9.15098458123129 & 94.7570921967939 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 864.464285714286 & 8.22969616005521 & 105.042065818926 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 862.833333333333 & 7.6584017979753 & 112.664934028591 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 861.096153846154 & 7.038048908608 & 122.34870274814 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 859.68 & 6.48366487444267 & 132.591677183793 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 858.354166666667 & 5.99508439178776 & 143.176327566375 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 857.282608695652 & 5.60466188316625 & 152.958845076903 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 856.386363636364 & 5.36266317720072 & 159.694229404016 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 855.380952380952 & 5.07572762226413 & 168.523809006007 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 854.225 & 4.69567278978401 & 181.91748834341 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 853.5 & 4.55685593239683 & 187.300193963137 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 852.694444444444 & 4.37739856145004 & 194.794792494743 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 851.882352941176 & 4.19866813316817 & 202.893471434804 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 850.9375 & 3.94287267860343 & 215.816631517861 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 850.366666666667 & 3.80576795559067 & 223.441543622616 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 849.857142857143 & 3.68168435605999 & 230.833787111134 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 849.307692307692 & 3.52781005540013 & 240.746434465096 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 848.75 & 3.34937264296603 & 253.405664425679 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 848.272727272727 & 3.1808285412105 & 266.682946371548 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 847.75 & 2.9972575183956 & 282.841896232457 \tabularnewline
Median & 845.5 &  &  \tabularnewline
Midrange & 986.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 848.65625 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 850.366666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 848.65625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 850.366666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 850.366666666667 &  &  \tabularnewline
Midmean - Closest Observation & 848.65625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 850.366666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 850.090909090909 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156933&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]871.1[/C][C]10.5707650360004[/C][C]82.4065237504888[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]867.658751357354[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]864.516404002466[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]874.87595311183[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]869.6[/C][C]9.86242083024084[/C][C]88.1730778850536[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]867.4[/C][C]9.0398115074594[/C][C]95.9533281511728[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]867.35[/C][C]8.82423553450165[/C][C]98.2918006448004[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]865.816666666667[/C][C]8.2870974407489[/C][C]104.47767422274[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]864.983333333333[/C][C]7.71001592568964[/C][C]112.189565063183[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]863.283333333333[/C][C]7.04437475088351[/C][C]122.549319685904[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]861.883333333333[/C][C]6.2390284113707[/C][C]138.143838512186[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]862.016666666667[/C][C]6.11890151447786[/C][C]140.877682804186[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]862.316666666667[/C][C]6.07623376449825[/C][C]141.916308701772[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]858.816666666667[/C][C]4.89860418645127[/C][C]175.318648737126[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]858.816666666667[/C][C]4.83668255282077[/C][C]177.563165927812[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]858.216666666667[/C][C]4.58486158393898[/C][C]187.184858464004[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]858.433333333333[/C][C]4.55607663181305[/C][C]188.415033965688[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]854.933333333333[/C][C]3.89914279052994[/C][C]219.261868380341[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]853.933333333333[/C][C]3.6449691873386[/C][C]234.27724335767[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]853.666666666667[/C][C]3.51660039565907[/C][C]242.753389813765[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]853.1[/C][C]3.33401405478653[/C][C]255.877745558761[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]851.9[/C][C]3.04548382878853[/C][C]279.725668528301[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]851.583333333333[/C][C]2.80559284717249[/C][C]303.530618917698[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]850.25[/C][C]2.4980924926221[/C][C]340.359695452085[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]867.120689655172[/C][C]9.15098458123129[/C][C]94.7570921967939[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]864.464285714286[/C][C]8.22969616005521[/C][C]105.042065818926[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]862.833333333333[/C][C]7.6584017979753[/C][C]112.664934028591[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]861.096153846154[/C][C]7.038048908608[/C][C]122.34870274814[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]859.68[/C][C]6.48366487444267[/C][C]132.591677183793[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]858.354166666667[/C][C]5.99508439178776[/C][C]143.176327566375[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]857.282608695652[/C][C]5.60466188316625[/C][C]152.958845076903[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]856.386363636364[/C][C]5.36266317720072[/C][C]159.694229404016[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]855.380952380952[/C][C]5.07572762226413[/C][C]168.523809006007[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]854.225[/C][C]4.69567278978401[/C][C]181.91748834341[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]853.5[/C][C]4.55685593239683[/C][C]187.300193963137[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]852.694444444444[/C][C]4.37739856145004[/C][C]194.794792494743[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]851.882352941176[/C][C]4.19866813316817[/C][C]202.893471434804[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]850.9375[/C][C]3.94287267860343[/C][C]215.816631517861[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]850.366666666667[/C][C]3.80576795559067[/C][C]223.441543622616[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]849.857142857143[/C][C]3.68168435605999[/C][C]230.833787111134[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]849.307692307692[/C][C]3.52781005540013[/C][C]240.746434465096[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]848.75[/C][C]3.34937264296603[/C][C]253.405664425679[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]848.272727272727[/C][C]3.1808285412105[/C][C]266.682946371548[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]847.75[/C][C]2.9972575183956[/C][C]282.841896232457[/C][/ROW]
[ROW][C]Median[/C][C]845.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]986.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]848.65625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]850.366666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]848.65625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]850.366666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]850.366666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]848.65625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]850.366666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]850.090909090909[/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=156933&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156933&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 Mean871.110.570765036000482.4065237504888
Geometric Mean867.658751357354
Harmonic Mean864.516404002466
Quadratic Mean874.87595311183
Winsorized Mean ( 1 / 20 )869.69.8624208302408488.1730778850536
Winsorized Mean ( 2 / 20 )867.49.039811507459495.9533281511728
Winsorized Mean ( 3 / 20 )867.358.8242355345016598.2918006448004
Winsorized Mean ( 4 / 20 )865.8166666666678.2870974407489104.47767422274
Winsorized Mean ( 5 / 20 )864.9833333333337.71001592568964112.189565063183
Winsorized Mean ( 6 / 20 )863.2833333333337.04437475088351122.549319685904
Winsorized Mean ( 7 / 20 )861.8833333333336.2390284113707138.143838512186
Winsorized Mean ( 8 / 20 )862.0166666666676.11890151447786140.877682804186
Winsorized Mean ( 9 / 20 )862.3166666666676.07623376449825141.916308701772
Winsorized Mean ( 10 / 20 )858.8166666666674.89860418645127175.318648737126
Winsorized Mean ( 11 / 20 )858.8166666666674.83668255282077177.563165927812
Winsorized Mean ( 12 / 20 )858.2166666666674.58486158393898187.184858464004
Winsorized Mean ( 13 / 20 )858.4333333333334.55607663181305188.415033965688
Winsorized Mean ( 14 / 20 )854.9333333333333.89914279052994219.261868380341
Winsorized Mean ( 15 / 20 )853.9333333333333.6449691873386234.27724335767
Winsorized Mean ( 16 / 20 )853.6666666666673.51660039565907242.753389813765
Winsorized Mean ( 17 / 20 )853.13.33401405478653255.877745558761
Winsorized Mean ( 18 / 20 )851.93.04548382878853279.725668528301
Winsorized Mean ( 19 / 20 )851.5833333333332.80559284717249303.530618917698
Winsorized Mean ( 20 / 20 )850.252.4980924926221340.359695452085
Trimmed Mean ( 1 / 20 )867.1206896551729.1509845812312994.7570921967939
Trimmed Mean ( 2 / 20 )864.4642857142868.22969616005521105.042065818926
Trimmed Mean ( 3 / 20 )862.8333333333337.6584017979753112.664934028591
Trimmed Mean ( 4 / 20 )861.0961538461547.038048908608122.34870274814
Trimmed Mean ( 5 / 20 )859.686.48366487444267132.591677183793
Trimmed Mean ( 6 / 20 )858.3541666666675.99508439178776143.176327566375
Trimmed Mean ( 7 / 20 )857.2826086956525.60466188316625152.958845076903
Trimmed Mean ( 8 / 20 )856.3863636363645.36266317720072159.694229404016
Trimmed Mean ( 9 / 20 )855.3809523809525.07572762226413168.523809006007
Trimmed Mean ( 10 / 20 )854.2254.69567278978401181.91748834341
Trimmed Mean ( 11 / 20 )853.54.55685593239683187.300193963137
Trimmed Mean ( 12 / 20 )852.6944444444444.37739856145004194.794792494743
Trimmed Mean ( 13 / 20 )851.8823529411764.19866813316817202.893471434804
Trimmed Mean ( 14 / 20 )850.93753.94287267860343215.816631517861
Trimmed Mean ( 15 / 20 )850.3666666666673.80576795559067223.441543622616
Trimmed Mean ( 16 / 20 )849.8571428571433.68168435605999230.833787111134
Trimmed Mean ( 17 / 20 )849.3076923076923.52781005540013240.746434465096
Trimmed Mean ( 18 / 20 )848.753.34937264296603253.405664425679
Trimmed Mean ( 19 / 20 )848.2727272727273.1808285412105266.682946371548
Trimmed Mean ( 20 / 20 )847.752.9972575183956282.841896232457
Median845.5
Midrange986.5
Midmean - Weighted Average at Xnp848.65625
Midmean - Weighted Average at X(n+1)p850.366666666667
Midmean - Empirical Distribution Function848.65625
Midmean - Empirical Distribution Function - Averaging850.366666666667
Midmean - Empirical Distribution Function - Interpolation850.366666666667
Midmean - Closest Observation848.65625
Midmean - True Basic - Statistics Graphics Toolkit850.366666666667
Midmean - MS Excel (old versions)850.090909090909
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')