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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 computationTue, 29 Nov 2011 07:42:56 -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/Nov/29/t132257061392e0gt01p11q0fh.htm/, Retrieved Tue, 23 Apr 2024 05:33:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=148285, Retrieved Tue, 23 Apr 2024 05:33:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact69
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Histogram] [Frequency Plot (C...] [2010-09-25 09:09:15] [b98453cac15ba1066b407e146608df68]
- RMPD    [Central Tendency] [Paper: Central te...] [2011-11-29 12:42:56] [e889f2ef2eeddd5259af4a52678400a6] [Current]
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Dataseries X:
3440
2678
2981
2260
2844
2546
2456
2295
2379
2479
2057
2280
2351
2276
2548
2311
2201
2725
2408
2139
1898
2539
2070
2063
2565
2442
2194
2798
2074
2628
2289
2154
2467
2137
1850
2075
1791
1755
2232
1952
1822
2522
2074
2366
2173
2094
1833
1858
2040
2133
2921
3252
3318
3554
2308
1621
1315
1501
1418
1657




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=148285&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=148285&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148285&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 Mean2290.1166666666759.619495406955938.412211492811
Geometric Mean2245.14991872567
Harmonic Mean2200.23311989768
Quadratic Mean2335.45475585948
Winsorized Mean ( 1 / 20 )2289.9333333333358.506452716056839.1398423084514
Winsorized Mean ( 2 / 20 )2288.6333333333356.524001035241840.4895848032132
Winsorized Mean ( 3 / 20 )2291.3333333333354.179220622571742.2917367028114
Winsorized Mean ( 4 / 20 )2275.6666666666748.71139883690346.7173335400637
Winsorized Mean ( 5 / 20 )2278.8333333333345.830806299108149.7227414778797
Winsorized Mean ( 6 / 20 )2274.7333333333343.369134710925352.4505122939493
Winsorized Mean ( 7 / 20 )2272.9833333333341.52165381346154.7421194624105
Winsorized Mean ( 8 / 20 )2264.7166666666739.237204842846257.7186034463302
Winsorized Mean ( 9 / 20 )2260.2166666666737.393155448396560.4446626545283
Winsorized Mean ( 10 / 20 )2253.2166666666735.610416266934263.2740895185456
Winsorized Mean ( 11 / 20 )224932.250922992967369.734438313298
Winsorized Mean ( 12 / 20 )2256.429.751239826038275.8422174401353
Winsorized Mean ( 13 / 20 )2275.0333333333326.583436143824785.5808602403651
Winsorized Mean ( 14 / 20 )2277.3666666666725.716094090897788.5580313486546
Winsorized Mean ( 15 / 20 )2274.6166666666724.772331609499391.8208549167989
Winsorized Mean ( 16 / 20 )2265.0166666666722.608326695487100.185064431098
Winsorized Mean ( 17 / 20 )2262.7521.9012114955258103.31620241475
Winsorized Mean ( 18 / 20 )2259.4521.3832981051359105.664242666912
Winsorized Mean ( 19 / 20 )2255.3333333333320.6515572615191109.208874893701
Winsorized Mean ( 20 / 20 )2250.3333333333318.0056749790196124.979115526379
Trimmed Mean ( 1 / 20 )2285.1379310344855.089387013928541.480547432062
Trimmed Mean ( 2 / 20 )228050.792645699381144.8883882421542
Trimmed Mean ( 3 / 20 )2275.203703703746.770410139220948.6462209104246
Trimmed Mean ( 4 / 20 )226942.880925312498952.9139701035937
Trimmed Mean ( 5 / 20 )226740.379526030514356.142313267542
Trimmed Mean ( 6 / 20 )2264.0416666666738.271959328768259.1566699582281
Trimmed Mean ( 7 / 20 )2261.7173913043536.409449097959362.1189676674102
Trimmed Mean ( 8 / 20 )2259.5227272727334.583973983431265.3343866252977
Trimmed Mean ( 9 / 20 )2258.5952380952432.903460301241368.6430915598877
Trimmed Mean ( 10 / 20 )2258.32531.229596159445572.3136152151927
Trimmed Mean ( 11 / 20 )2259.1315789473729.511243151324676.5515558718837
Trimmed Mean ( 12 / 20 )2260.6666666666728.178118269436580.2277371771383
Trimmed Mean ( 13 / 20 )2261.2941176470627.076821109127583.514017710328
Trimmed Mean ( 14 / 20 )2259.312526.420240495932385.514456249853
Trimmed Mean ( 15 / 20 )2256.7333333333325.66561872767487.9282653295246
Trimmed Mean ( 16 / 20 )2254.1785714285724.801009834547190.8905962485674
Trimmed Mean ( 17 / 20 )2252.6153846153824.194028311076393.1062556285476
Trimmed Mean ( 18 / 20 )2251.12523.411900270489896.153023632921
Trimmed Mean ( 19 / 20 )2249.8636363636422.272349585984101.015998679343
Trimmed Mean ( 20 / 20 )224920.626375552216109.035152312951
Median2268
Midrange2434.5
Midmean - Weighted Average at Xnp2250.29032258065
Midmean - Weighted Average at X(n+1)p2256.73333333333
Midmean - Empirical Distribution Function2250.29032258065
Midmean - Empirical Distribution Function - Averaging2256.73333333333
Midmean - Empirical Distribution Function - Interpolation2256.73333333333
Midmean - Closest Observation2250.29032258065
Midmean - True Basic - Statistics Graphics Toolkit2256.73333333333
Midmean - MS Excel (old versions)2259.3125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2290.11666666667 & 59.6194954069559 & 38.412211492811 \tabularnewline
Geometric Mean & 2245.14991872567 &  &  \tabularnewline
Harmonic Mean & 2200.23311989768 &  &  \tabularnewline
Quadratic Mean & 2335.45475585948 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2289.93333333333 & 58.5064527160568 & 39.1398423084514 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2288.63333333333 & 56.5240010352418 & 40.4895848032132 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2291.33333333333 & 54.1792206225717 & 42.2917367028114 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2275.66666666667 & 48.711398836903 & 46.7173335400637 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2278.83333333333 & 45.8308062991081 & 49.7227414778797 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2274.73333333333 & 43.3691347109253 & 52.4505122939493 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2272.98333333333 & 41.521653813461 & 54.7421194624105 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2264.71666666667 & 39.2372048428462 & 57.7186034463302 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2260.21666666667 & 37.3931554483965 & 60.4446626545283 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2253.21666666667 & 35.6104162669342 & 63.2740895185456 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2249 & 32.2509229929673 & 69.734438313298 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2256.4 & 29.7512398260382 & 75.8422174401353 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2275.03333333333 & 26.5834361438247 & 85.5808602403651 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2277.36666666667 & 25.7160940908977 & 88.5580313486546 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2274.61666666667 & 24.7723316094993 & 91.8208549167989 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2265.01666666667 & 22.608326695487 & 100.185064431098 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2262.75 & 21.9012114955258 & 103.31620241475 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2259.45 & 21.3832981051359 & 105.664242666912 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2255.33333333333 & 20.6515572615191 & 109.208874893701 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2250.33333333333 & 18.0056749790196 & 124.979115526379 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2285.13793103448 & 55.0893870139285 & 41.480547432062 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2280 & 50.7926456993811 & 44.8883882421542 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2275.2037037037 & 46.7704101392209 & 48.6462209104246 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2269 & 42.8809253124989 & 52.9139701035937 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2267 & 40.3795260305143 & 56.142313267542 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2264.04166666667 & 38.2719593287682 & 59.1566699582281 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2261.71739130435 & 36.4094490979593 & 62.1189676674102 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2259.52272727273 & 34.5839739834312 & 65.3343866252977 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2258.59523809524 & 32.9034603012413 & 68.6430915598877 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2258.325 & 31.2295961594455 & 72.3136152151927 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2259.13157894737 & 29.5112431513246 & 76.5515558718837 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2260.66666666667 & 28.1781182694365 & 80.2277371771383 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2261.29411764706 & 27.0768211091275 & 83.514017710328 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2259.3125 & 26.4202404959323 & 85.514456249853 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2256.73333333333 & 25.665618727674 & 87.9282653295246 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2254.17857142857 & 24.8010098345471 & 90.8905962485674 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2252.61538461538 & 24.1940283110763 & 93.1062556285476 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2251.125 & 23.4119002704898 & 96.153023632921 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2249.86363636364 & 22.272349585984 & 101.015998679343 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2249 & 20.626375552216 & 109.035152312951 \tabularnewline
Median & 2268 &  &  \tabularnewline
Midrange & 2434.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2250.29032258065 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2256.73333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2250.29032258065 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2256.73333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2256.73333333333 &  &  \tabularnewline
Midmean - Closest Observation & 2250.29032258065 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2256.73333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2259.3125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148285&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]2290.11666666667[/C][C]59.6194954069559[/C][C]38.412211492811[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2245.14991872567[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2200.23311989768[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2335.45475585948[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2289.93333333333[/C][C]58.5064527160568[/C][C]39.1398423084514[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2288.63333333333[/C][C]56.5240010352418[/C][C]40.4895848032132[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2291.33333333333[/C][C]54.1792206225717[/C][C]42.2917367028114[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2275.66666666667[/C][C]48.711398836903[/C][C]46.7173335400637[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2278.83333333333[/C][C]45.8308062991081[/C][C]49.7227414778797[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2274.73333333333[/C][C]43.3691347109253[/C][C]52.4505122939493[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2272.98333333333[/C][C]41.521653813461[/C][C]54.7421194624105[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2264.71666666667[/C][C]39.2372048428462[/C][C]57.7186034463302[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2260.21666666667[/C][C]37.3931554483965[/C][C]60.4446626545283[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2253.21666666667[/C][C]35.6104162669342[/C][C]63.2740895185456[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2249[/C][C]32.2509229929673[/C][C]69.734438313298[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2256.4[/C][C]29.7512398260382[/C][C]75.8422174401353[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2275.03333333333[/C][C]26.5834361438247[/C][C]85.5808602403651[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2277.36666666667[/C][C]25.7160940908977[/C][C]88.5580313486546[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2274.61666666667[/C][C]24.7723316094993[/C][C]91.8208549167989[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2265.01666666667[/C][C]22.608326695487[/C][C]100.185064431098[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2262.75[/C][C]21.9012114955258[/C][C]103.31620241475[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2259.45[/C][C]21.3832981051359[/C][C]105.664242666912[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2255.33333333333[/C][C]20.6515572615191[/C][C]109.208874893701[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2250.33333333333[/C][C]18.0056749790196[/C][C]124.979115526379[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2285.13793103448[/C][C]55.0893870139285[/C][C]41.480547432062[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2280[/C][C]50.7926456993811[/C][C]44.8883882421542[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2275.2037037037[/C][C]46.7704101392209[/C][C]48.6462209104246[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2269[/C][C]42.8809253124989[/C][C]52.9139701035937[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2267[/C][C]40.3795260305143[/C][C]56.142313267542[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2264.04166666667[/C][C]38.2719593287682[/C][C]59.1566699582281[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2261.71739130435[/C][C]36.4094490979593[/C][C]62.1189676674102[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2259.52272727273[/C][C]34.5839739834312[/C][C]65.3343866252977[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2258.59523809524[/C][C]32.9034603012413[/C][C]68.6430915598877[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2258.325[/C][C]31.2295961594455[/C][C]72.3136152151927[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2259.13157894737[/C][C]29.5112431513246[/C][C]76.5515558718837[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2260.66666666667[/C][C]28.1781182694365[/C][C]80.2277371771383[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2261.29411764706[/C][C]27.0768211091275[/C][C]83.514017710328[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2259.3125[/C][C]26.4202404959323[/C][C]85.514456249853[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2256.73333333333[/C][C]25.665618727674[/C][C]87.9282653295246[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2254.17857142857[/C][C]24.8010098345471[/C][C]90.8905962485674[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2252.61538461538[/C][C]24.1940283110763[/C][C]93.1062556285476[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2251.125[/C][C]23.4119002704898[/C][C]96.153023632921[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2249.86363636364[/C][C]22.272349585984[/C][C]101.015998679343[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2249[/C][C]20.626375552216[/C][C]109.035152312951[/C][/ROW]
[ROW][C]Median[/C][C]2268[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2434.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2250.29032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2256.73333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2250.29032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2256.73333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2256.73333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2250.29032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2256.73333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2259.3125[/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=148285&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148285&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 Mean2290.1166666666759.619495406955938.412211492811
Geometric Mean2245.14991872567
Harmonic Mean2200.23311989768
Quadratic Mean2335.45475585948
Winsorized Mean ( 1 / 20 )2289.9333333333358.506452716056839.1398423084514
Winsorized Mean ( 2 / 20 )2288.6333333333356.524001035241840.4895848032132
Winsorized Mean ( 3 / 20 )2291.3333333333354.179220622571742.2917367028114
Winsorized Mean ( 4 / 20 )2275.6666666666748.71139883690346.7173335400637
Winsorized Mean ( 5 / 20 )2278.8333333333345.830806299108149.7227414778797
Winsorized Mean ( 6 / 20 )2274.7333333333343.369134710925352.4505122939493
Winsorized Mean ( 7 / 20 )2272.9833333333341.52165381346154.7421194624105
Winsorized Mean ( 8 / 20 )2264.7166666666739.237204842846257.7186034463302
Winsorized Mean ( 9 / 20 )2260.2166666666737.393155448396560.4446626545283
Winsorized Mean ( 10 / 20 )2253.2166666666735.610416266934263.2740895185456
Winsorized Mean ( 11 / 20 )224932.250922992967369.734438313298
Winsorized Mean ( 12 / 20 )2256.429.751239826038275.8422174401353
Winsorized Mean ( 13 / 20 )2275.0333333333326.583436143824785.5808602403651
Winsorized Mean ( 14 / 20 )2277.3666666666725.716094090897788.5580313486546
Winsorized Mean ( 15 / 20 )2274.6166666666724.772331609499391.8208549167989
Winsorized Mean ( 16 / 20 )2265.0166666666722.608326695487100.185064431098
Winsorized Mean ( 17 / 20 )2262.7521.9012114955258103.31620241475
Winsorized Mean ( 18 / 20 )2259.4521.3832981051359105.664242666912
Winsorized Mean ( 19 / 20 )2255.3333333333320.6515572615191109.208874893701
Winsorized Mean ( 20 / 20 )2250.3333333333318.0056749790196124.979115526379
Trimmed Mean ( 1 / 20 )2285.1379310344855.089387013928541.480547432062
Trimmed Mean ( 2 / 20 )228050.792645699381144.8883882421542
Trimmed Mean ( 3 / 20 )2275.203703703746.770410139220948.6462209104246
Trimmed Mean ( 4 / 20 )226942.880925312498952.9139701035937
Trimmed Mean ( 5 / 20 )226740.379526030514356.142313267542
Trimmed Mean ( 6 / 20 )2264.0416666666738.271959328768259.1566699582281
Trimmed Mean ( 7 / 20 )2261.7173913043536.409449097959362.1189676674102
Trimmed Mean ( 8 / 20 )2259.5227272727334.583973983431265.3343866252977
Trimmed Mean ( 9 / 20 )2258.5952380952432.903460301241368.6430915598877
Trimmed Mean ( 10 / 20 )2258.32531.229596159445572.3136152151927
Trimmed Mean ( 11 / 20 )2259.1315789473729.511243151324676.5515558718837
Trimmed Mean ( 12 / 20 )2260.6666666666728.178118269436580.2277371771383
Trimmed Mean ( 13 / 20 )2261.2941176470627.076821109127583.514017710328
Trimmed Mean ( 14 / 20 )2259.312526.420240495932385.514456249853
Trimmed Mean ( 15 / 20 )2256.7333333333325.66561872767487.9282653295246
Trimmed Mean ( 16 / 20 )2254.1785714285724.801009834547190.8905962485674
Trimmed Mean ( 17 / 20 )2252.6153846153824.194028311076393.1062556285476
Trimmed Mean ( 18 / 20 )2251.12523.411900270489896.153023632921
Trimmed Mean ( 19 / 20 )2249.8636363636422.272349585984101.015998679343
Trimmed Mean ( 20 / 20 )224920.626375552216109.035152312951
Median2268
Midrange2434.5
Midmean - Weighted Average at Xnp2250.29032258065
Midmean - Weighted Average at X(n+1)p2256.73333333333
Midmean - Empirical Distribution Function2250.29032258065
Midmean - Empirical Distribution Function - Averaging2256.73333333333
Midmean - Empirical Distribution Function - Interpolation2256.73333333333
Midmean - Closest Observation2250.29032258065
Midmean - True Basic - Statistics Graphics Toolkit2256.73333333333
Midmean - MS Excel (old versions)2259.3125
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')