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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 computationMon, 20 Oct 2008 10:01:01 -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/2008/Oct/20/t1224518517a88yqhje11x7itl.htm/, Retrieved Fri, 17 May 2024 07:29:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17559, Retrieved Fri, 17 May 2024 07:29:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact169
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Pearson Correlation] [Q3 Clothing produ...] [2007-10-20 14:22:11] [b731da8b544846036771bbf9bf2f34ce]
- RMPD  [Harrell-Davis Quantiles] [Compute the 95% C...] [2008-10-19 19:58:52] [988ab43f527fc78aae41c84649095267]
- RMPD      [Central Tendency] [Nederland.Uitvoer] [2008-10-20 16:01:01] [5d823194959040fa9b19b8c8302177e6] [Current]
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Dataseries X:
2236
2084.9
2409.5
2199.3
2203.5
2254.1
1975.8
1742.2
2520.6
2438.1
2126.3
2267.5
2201.1
2128.5
2596
2458.2
2210.5
2621.2
2231.4
2103.6
2685.8
2539.3
2462.4
2693.3
2307.7
2385.9
2737.6
2653.9
2545.4
2848.8
2359.5
2488.3
2861.1
2717.9
2844
2749
2652.9
2660.2
3187.1
2774.1
3158.2
3244.6
2665.5
2820.8
2983.4
3077.4
3024.8
2731.8
3046.2
2834.8
3292.8
2946.1
3196.9
3284.2
3003
2979
3137.4
3647.7
3283
2947.3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17559&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17559&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17559&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2657.7951.209093786559851.9007426899157
Geometric Mean2628.27279566731
Harmonic Mean2598.33176585493
Quadratic Mean2686.73921138617
Winsorized Mean ( 1 / 20 )2655.7683333333348.517776839468354.7380466776235
Winsorized Mean ( 2 / 20 )2659.1183333333347.650144651025555.8050422051784
Winsorized Mean ( 3 / 20 )2659.9933333333347.448390092926756.0607710424693
Winsorized Mean ( 4 / 20 )2658.9466666666746.593697014795857.0666600210393
Winsorized Mean ( 5 / 20 )2655.15545.735379215719358.054727992447
Winsorized Mean ( 6 / 20 )2661.25544.219439855771560.1829197448021
Winsorized Mean ( 7 / 20 )2658.0933333333343.5138837423561.0860972344406
Winsorized Mean ( 8 / 20 )2655.6442.92288323359461.8700282911456
Winsorized Mean ( 9 / 20 )2647.6941.07930195551764.4531399989968
Winsorized Mean ( 10 / 20 )2645.9733333333339.548380074009966.9047209615595
Winsorized Mean ( 11 / 20 )2642.8933333333338.734001097932268.2318701507555
Winsorized Mean ( 12 / 20 )2642.1533333333337.371913716585770.6989038177284
Winsorized Mean ( 13 / 20 )2640.8136.174057462957373.0028696035612
Winsorized Mean ( 14 / 20 )2649.1633333333334.398031983406477.014968025243
Winsorized Mean ( 15 / 20 )2654.1883333333330.982559892091685.6671734865531
Winsorized Mean ( 16 / 20 )2660.9083333333329.812834351052889.2537858695534
Winsorized Mean ( 17 / 20 )2643.5116666666725.0177005238479105.665653170113
Winsorized Mean ( 18 / 20 )2648.4016666666723.1328718459236114.486505796009
Winsorized Mean ( 19 / 20 )2653.2466666666721.9390771075597120.937022722456
Winsorized Mean ( 20 / 20 )2651.5821.27833873767124.614051533346
Trimmed Mean ( 1 / 20 )2656.5086206896647.518176436603255.9051045284505
Trimmed Mean ( 2 / 20 )2657.3017857142946.279101373816657.4190445974759
Trimmed Mean ( 3 / 20 )2656.2925925925945.310890968225258.6237113380831
Trimmed Mean ( 4 / 20 )2654.8692307692344.185136398687360.0851201819104
Trimmed Mean ( 5 / 20 )2653.64643.096127314056761.5750454945045
Trimmed Mean ( 6 / 20 )2653.2687541.999116648538463.1743941712721
Trimmed Mean ( 7 / 20 )2651.5326086956541.050308013030964.5922707292221
Trimmed Mean ( 8 / 20 )2650.2545454545540.008860468776166.2416903256435
Trimmed Mean ( 9 / 20 )2649.2928571428638.794270412962668.2908282316254
Trimmed Mean ( 10 / 20 )2649.5637.687857290903270.3027497570027
Trimmed Mean ( 11 / 20 )2650.1263157894736.601649156428472.404560364571
Trimmed Mean ( 12 / 20 )2651.2222222222235.317908607820175.0673617643142
Trimmed Mean ( 13 / 20 )2652.5558823529433.909714767835378.2240694300678
Trimmed Mean ( 14 / 20 )2654.2532.259267235643282.2786822965192
Trimmed Mean ( 15 / 20 )2654.9766666666730.451765773060287.1862960740179
Trimmed Mean ( 16 / 20 )2655.0892857142928.959011052608991.6843907718696
Trimmed Mean ( 17 / 20 )2654.2527.084811667739697.9977277509168
Trimmed Mean ( 18 / 20 )2655.8291666666726.0323874917483102.020191867093
Trimmed Mean ( 19 / 20 )2656.9545454545525.0285825588183106.156812484710
Trimmed Mean ( 20 / 20 )2657.5423.7815943868141111.747764122724
Median2662.85
Midrange2694.95
Midmean - Weighted Average at Xnp2643.77419354839
Midmean - Weighted Average at X(n+1)p2654.97666666667
Midmean - Empirical Distribution Function2643.77419354839
Midmean - Empirical Distribution Function - Averaging2654.97666666667
Midmean - Empirical Distribution Function - Interpolation2654.97666666667
Midmean - Closest Observation2643.77419354839
Midmean - True Basic - Statistics Graphics Toolkit2654.97666666667
Midmean - MS Excel (old versions)2654.25
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2657.79 & 51.2090937865598 & 51.9007426899157 \tabularnewline
Geometric Mean & 2628.27279566731 &  &  \tabularnewline
Harmonic Mean & 2598.33176585493 &  &  \tabularnewline
Quadratic Mean & 2686.73921138617 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2655.76833333333 & 48.5177768394683 & 54.7380466776235 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2659.11833333333 & 47.6501446510255 & 55.8050422051784 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2659.99333333333 & 47.4483900929267 & 56.0607710424693 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2658.94666666667 & 46.5936970147958 & 57.0666600210393 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2655.155 & 45.7353792157193 & 58.054727992447 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2661.255 & 44.2194398557715 & 60.1829197448021 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2658.09333333333 & 43.51388374235 & 61.0860972344406 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2655.64 & 42.922883233594 & 61.8700282911456 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2647.69 & 41.079301955517 & 64.4531399989968 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2645.97333333333 & 39.5483800740099 & 66.9047209615595 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2642.89333333333 & 38.7340010979322 & 68.2318701507555 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2642.15333333333 & 37.3719137165857 & 70.6989038177284 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2640.81 & 36.1740574629573 & 73.0028696035612 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2649.16333333333 & 34.3980319834064 & 77.014968025243 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2654.18833333333 & 30.9825598920916 & 85.6671734865531 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2660.90833333333 & 29.8128343510528 & 89.2537858695534 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2643.51166666667 & 25.0177005238479 & 105.665653170113 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2648.40166666667 & 23.1328718459236 & 114.486505796009 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2653.24666666667 & 21.9390771075597 & 120.937022722456 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2651.58 & 21.27833873767 & 124.614051533346 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2656.50862068966 & 47.5181764366032 & 55.9051045284505 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2657.30178571429 & 46.2791013738166 & 57.4190445974759 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2656.29259259259 & 45.3108909682252 & 58.6237113380831 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2654.86923076923 & 44.1851363986873 & 60.0851201819104 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2653.646 & 43.0961273140567 & 61.5750454945045 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2653.26875 & 41.9991166485384 & 63.1743941712721 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2651.53260869565 & 41.0503080130309 & 64.5922707292221 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2650.25454545455 & 40.0088604687761 & 66.2416903256435 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2649.29285714286 & 38.7942704129626 & 68.2908282316254 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2649.56 & 37.6878572909032 & 70.3027497570027 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2650.12631578947 & 36.6016491564284 & 72.404560364571 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2651.22222222222 & 35.3179086078201 & 75.0673617643142 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2652.55588235294 & 33.9097147678353 & 78.2240694300678 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2654.25 & 32.2592672356432 & 82.2786822965192 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2654.97666666667 & 30.4517657730602 & 87.1862960740179 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2655.08928571429 & 28.9590110526089 & 91.6843907718696 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2654.25 & 27.0848116677396 & 97.9977277509168 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2655.82916666667 & 26.0323874917483 & 102.020191867093 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2656.95454545455 & 25.0285825588183 & 106.156812484710 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2657.54 & 23.7815943868141 & 111.747764122724 \tabularnewline
Median & 2662.85 &  &  \tabularnewline
Midrange & 2694.95 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2643.77419354839 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2654.97666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2643.77419354839 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2654.97666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2654.97666666667 &  &  \tabularnewline
Midmean - Closest Observation & 2643.77419354839 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2654.97666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2654.25 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17559&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]2657.79[/C][C]51.2090937865598[/C][C]51.9007426899157[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2628.27279566731[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2598.33176585493[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2686.73921138617[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2655.76833333333[/C][C]48.5177768394683[/C][C]54.7380466776235[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2659.11833333333[/C][C]47.6501446510255[/C][C]55.8050422051784[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2659.99333333333[/C][C]47.4483900929267[/C][C]56.0607710424693[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2658.94666666667[/C][C]46.5936970147958[/C][C]57.0666600210393[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2655.155[/C][C]45.7353792157193[/C][C]58.054727992447[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2661.255[/C][C]44.2194398557715[/C][C]60.1829197448021[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2658.09333333333[/C][C]43.51388374235[/C][C]61.0860972344406[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2655.64[/C][C]42.922883233594[/C][C]61.8700282911456[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2647.69[/C][C]41.079301955517[/C][C]64.4531399989968[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2645.97333333333[/C][C]39.5483800740099[/C][C]66.9047209615595[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2642.89333333333[/C][C]38.7340010979322[/C][C]68.2318701507555[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2642.15333333333[/C][C]37.3719137165857[/C][C]70.6989038177284[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2640.81[/C][C]36.1740574629573[/C][C]73.0028696035612[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2649.16333333333[/C][C]34.3980319834064[/C][C]77.014968025243[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2654.18833333333[/C][C]30.9825598920916[/C][C]85.6671734865531[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2660.90833333333[/C][C]29.8128343510528[/C][C]89.2537858695534[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2643.51166666667[/C][C]25.0177005238479[/C][C]105.665653170113[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2648.40166666667[/C][C]23.1328718459236[/C][C]114.486505796009[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2653.24666666667[/C][C]21.9390771075597[/C][C]120.937022722456[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2651.58[/C][C]21.27833873767[/C][C]124.614051533346[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2656.50862068966[/C][C]47.5181764366032[/C][C]55.9051045284505[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2657.30178571429[/C][C]46.2791013738166[/C][C]57.4190445974759[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2656.29259259259[/C][C]45.3108909682252[/C][C]58.6237113380831[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2654.86923076923[/C][C]44.1851363986873[/C][C]60.0851201819104[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2653.646[/C][C]43.0961273140567[/C][C]61.5750454945045[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2653.26875[/C][C]41.9991166485384[/C][C]63.1743941712721[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2651.53260869565[/C][C]41.0503080130309[/C][C]64.5922707292221[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2650.25454545455[/C][C]40.0088604687761[/C][C]66.2416903256435[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2649.29285714286[/C][C]38.7942704129626[/C][C]68.2908282316254[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2649.56[/C][C]37.6878572909032[/C][C]70.3027497570027[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2650.12631578947[/C][C]36.6016491564284[/C][C]72.404560364571[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2651.22222222222[/C][C]35.3179086078201[/C][C]75.0673617643142[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2652.55588235294[/C][C]33.9097147678353[/C][C]78.2240694300678[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2654.25[/C][C]32.2592672356432[/C][C]82.2786822965192[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2654.97666666667[/C][C]30.4517657730602[/C][C]87.1862960740179[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2655.08928571429[/C][C]28.9590110526089[/C][C]91.6843907718696[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2654.25[/C][C]27.0848116677396[/C][C]97.9977277509168[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2655.82916666667[/C][C]26.0323874917483[/C][C]102.020191867093[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2656.95454545455[/C][C]25.0285825588183[/C][C]106.156812484710[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2657.54[/C][C]23.7815943868141[/C][C]111.747764122724[/C][/ROW]
[ROW][C]Median[/C][C]2662.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2694.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2643.77419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2654.97666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2643.77419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2654.97666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2654.97666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2643.77419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2654.97666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2654.25[/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=17559&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17559&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 Mean2657.7951.209093786559851.9007426899157
Geometric Mean2628.27279566731
Harmonic Mean2598.33176585493
Quadratic Mean2686.73921138617
Winsorized Mean ( 1 / 20 )2655.7683333333348.517776839468354.7380466776235
Winsorized Mean ( 2 / 20 )2659.1183333333347.650144651025555.8050422051784
Winsorized Mean ( 3 / 20 )2659.9933333333347.448390092926756.0607710424693
Winsorized Mean ( 4 / 20 )2658.9466666666746.593697014795857.0666600210393
Winsorized Mean ( 5 / 20 )2655.15545.735379215719358.054727992447
Winsorized Mean ( 6 / 20 )2661.25544.219439855771560.1829197448021
Winsorized Mean ( 7 / 20 )2658.0933333333343.5138837423561.0860972344406
Winsorized Mean ( 8 / 20 )2655.6442.92288323359461.8700282911456
Winsorized Mean ( 9 / 20 )2647.6941.07930195551764.4531399989968
Winsorized Mean ( 10 / 20 )2645.9733333333339.548380074009966.9047209615595
Winsorized Mean ( 11 / 20 )2642.8933333333338.734001097932268.2318701507555
Winsorized Mean ( 12 / 20 )2642.1533333333337.371913716585770.6989038177284
Winsorized Mean ( 13 / 20 )2640.8136.174057462957373.0028696035612
Winsorized Mean ( 14 / 20 )2649.1633333333334.398031983406477.014968025243
Winsorized Mean ( 15 / 20 )2654.1883333333330.982559892091685.6671734865531
Winsorized Mean ( 16 / 20 )2660.9083333333329.812834351052889.2537858695534
Winsorized Mean ( 17 / 20 )2643.5116666666725.0177005238479105.665653170113
Winsorized Mean ( 18 / 20 )2648.4016666666723.1328718459236114.486505796009
Winsorized Mean ( 19 / 20 )2653.2466666666721.9390771075597120.937022722456
Winsorized Mean ( 20 / 20 )2651.5821.27833873767124.614051533346
Trimmed Mean ( 1 / 20 )2656.5086206896647.518176436603255.9051045284505
Trimmed Mean ( 2 / 20 )2657.3017857142946.279101373816657.4190445974759
Trimmed Mean ( 3 / 20 )2656.2925925925945.310890968225258.6237113380831
Trimmed Mean ( 4 / 20 )2654.8692307692344.185136398687360.0851201819104
Trimmed Mean ( 5 / 20 )2653.64643.096127314056761.5750454945045
Trimmed Mean ( 6 / 20 )2653.2687541.999116648538463.1743941712721
Trimmed Mean ( 7 / 20 )2651.5326086956541.050308013030964.5922707292221
Trimmed Mean ( 8 / 20 )2650.2545454545540.008860468776166.2416903256435
Trimmed Mean ( 9 / 20 )2649.2928571428638.794270412962668.2908282316254
Trimmed Mean ( 10 / 20 )2649.5637.687857290903270.3027497570027
Trimmed Mean ( 11 / 20 )2650.1263157894736.601649156428472.404560364571
Trimmed Mean ( 12 / 20 )2651.2222222222235.317908607820175.0673617643142
Trimmed Mean ( 13 / 20 )2652.5558823529433.909714767835378.2240694300678
Trimmed Mean ( 14 / 20 )2654.2532.259267235643282.2786822965192
Trimmed Mean ( 15 / 20 )2654.9766666666730.451765773060287.1862960740179
Trimmed Mean ( 16 / 20 )2655.0892857142928.959011052608991.6843907718696
Trimmed Mean ( 17 / 20 )2654.2527.084811667739697.9977277509168
Trimmed Mean ( 18 / 20 )2655.8291666666726.0323874917483102.020191867093
Trimmed Mean ( 19 / 20 )2656.9545454545525.0285825588183106.156812484710
Trimmed Mean ( 20 / 20 )2657.5423.7815943868141111.747764122724
Median2662.85
Midrange2694.95
Midmean - Weighted Average at Xnp2643.77419354839
Midmean - Weighted Average at X(n+1)p2654.97666666667
Midmean - Empirical Distribution Function2643.77419354839
Midmean - Empirical Distribution Function - Averaging2654.97666666667
Midmean - Empirical Distribution Function - Interpolation2654.97666666667
Midmean - Closest Observation2643.77419354839
Midmean - True Basic - Statistics Graphics Toolkit2654.97666666667
Midmean - MS Excel (old versions)2654.25
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')