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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, 19 Oct 2009 13:34:38 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/19/t1255981292b9b1xs4asislvar.htm/, Retrieved Thu, 31 Oct 2024 22:50:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48166, Retrieved Thu, 31 Oct 2024 22:50:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact150
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMP       [Central Tendency] [Workshop 3 deel 1...] [2009-10-19 18:45:16] [309ee52d0058ff0a6f7eec15e07b2d9f]
-    D          [Central Tendency] [] [2009-10-19 19:34:38] [2a6f24d4847085573f343c759dfbabef] [Current]
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Post a new message
Dataseries X:
2155
2172
2150
2533
2058
2160
2260
2498
2695
2799
2946
2930
2318
2540
2570
2669
2450
2842
3440
2678
2981
2260
2844
2546
2456
2295
2379
2479
2057
2280
2351
2276
2548
2311
2201
2725
2408
2139
1898
2537
2068
2063
2520
2434
2190
2794
2070
2615
2265
2139
2428
2137
1823
2063
1806
1758
2243
1993
1932
2465




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48166&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]2 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=48166&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48166&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 time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2377.3333333333342.220029430619956.3081874975952
Geometric Mean2355.81164589092
Harmonic Mean2334.78198448044
Quadratic Mean2399.35055796355
Winsorized Mean ( 1 / 20 )2370.4833333333339.364101427158360.2194194047543
Winsorized Mean ( 2 / 20 )2369.8833333333338.928059765416260.8785371686761
Winsorized Mean ( 3 / 20 )2372.8333333333337.882550927616162.6365774012213
Winsorized Mean ( 4 / 20 )2369.3666666666736.052425470383465.7200350809426
Winsorized Mean ( 5 / 20 )2374.2833333333335.022592318288467.7929066973581
Winsorized Mean ( 6 / 20 )2376.3833333333332.949791385592272.1213468553989
Winsorized Mean ( 7 / 20 )2375.9166666666732.804215414550372.4271754907703
Winsorized Mean ( 8 / 20 )2367.3833333333330.791692067449776.8838337350068
Winsorized Mean ( 9 / 20 )2362.8833333333329.925265591396778.9594774394465
Winsorized Mean ( 10 / 20 )2360.8833333333329.256986143992380.6946867908377
Winsorized Mean ( 11 / 20 )2359.628.893425835251481.6656361019388
Winsorized Mean ( 12 / 20 )2362.224.799157084271995.253237518228
Winsorized Mean ( 13 / 20 )2352.8833333333323.1109836639069101.808013347692
Winsorized Mean ( 14 / 20 )2347.7522.3115285874725105.225869702097
Winsorized Mean ( 15 / 20 )235021.8035398566950107.780663848417
Winsorized Mean ( 16 / 20 )2349.7333333333321.3541282830026110.036490471197
Winsorized Mean ( 17 / 20 )2350.321.0076835553466111.878113253559
Winsorized Mean ( 18 / 20 )2352.720.2785865741754116.018934130061
Winsorized Mean ( 19 / 20 )2354.2833333333318.8082217216687125.173095477761
Winsorized Mean ( 20 / 20 )2350.6166666666717.1850199460501136.782888471826
Trimmed Mean ( 1 / 20 )2369.6896551724138.079804496927662.2295646334951
Trimmed Mean ( 2 / 20 )2368.8392857142936.496083910057364.9066703033719
Trimmed Mean ( 3 / 20 )2368.2592592592634.826997660254768.0006724197753
Trimmed Mean ( 4 / 20 )2366.533.264553852207771.1417928679943
Trimmed Mean ( 5 / 20 )2365.6432.056617770082173.7956829060055
Trimmed Mean ( 6 / 20 )2363.4791666666730.883000866794376.5301007133638
Trimmed Mean ( 7 / 20 )2360.6739130434830.037915723505178.5898041253315
Trimmed Mean ( 8 / 20 )2357.7045454545528.970543097846881.3828217680108
Trimmed Mean ( 9 / 20 )2355.9761904761928.165544475138483.6474577140095
Trimmed Mean ( 10 / 20 )2354.82527.330289562390386.161728898786
Trimmed Mean ( 11 / 20 )2353.8684210526326.380630288403289.227148681409
Trimmed Mean ( 12 / 20 )235325.175132603172293.4652475158567
Trimmed Mean ( 13 / 20 )2351.6470588235324.676331958334195.2997010574457
Trimmed Mean ( 14 / 20 )2351.4687524.394108902420496.394943525348
Trimmed Mean ( 15 / 20 )235224.12934494254597.474672669333
Trimmed Mean ( 16 / 20 )2352.2857142857123.796250268329298.8511083788866
Trimmed Mean ( 17 / 20 )2352.6538461538523.3347507318158100.821897486401
Trimmed Mean ( 18 / 20 )235322.6356618724922103.951013814156
Trimmed Mean ( 19 / 20 )2353.0454545454521.7058730130479108.405934796126
Trimmed Mean ( 20 / 20 )2352.8520.7244166954928113.530336441831
Median2334.5
Midrange2599
Midmean - Weighted Average at Xnp2338.6875
Midmean - Weighted Average at X(n+1)p2352
Midmean - Empirical Distribution Function2338.6875
Midmean - Empirical Distribution Function - Averaging2352
Midmean - Empirical Distribution Function - Interpolation2352
Midmean - Closest Observation2338.6875
Midmean - True Basic - Statistics Graphics Toolkit2352
Midmean - MS Excel (old versions)2345.03030303030
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2377.33333333333 & 42.2200294306199 & 56.3081874975952 \tabularnewline
Geometric Mean & 2355.81164589092 &  &  \tabularnewline
Harmonic Mean & 2334.78198448044 &  &  \tabularnewline
Quadratic Mean & 2399.35055796355 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2370.48333333333 & 39.3641014271583 & 60.2194194047543 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2369.88333333333 & 38.9280597654162 & 60.8785371686761 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2372.83333333333 & 37.8825509276161 & 62.6365774012213 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2369.36666666667 & 36.0524254703834 & 65.7200350809426 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2374.28333333333 & 35.0225923182884 & 67.7929066973581 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2376.38333333333 & 32.9497913855922 & 72.1213468553989 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2375.91666666667 & 32.8042154145503 & 72.4271754907703 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2367.38333333333 & 30.7916920674497 & 76.8838337350068 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2362.88333333333 & 29.9252655913967 & 78.9594774394465 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2360.88333333333 & 29.2569861439923 & 80.6946867908377 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2359.6 & 28.8934258352514 & 81.6656361019388 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2362.2 & 24.7991570842719 & 95.253237518228 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2352.88333333333 & 23.1109836639069 & 101.808013347692 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2347.75 & 22.3115285874725 & 105.225869702097 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2350 & 21.8035398566950 & 107.780663848417 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2349.73333333333 & 21.3541282830026 & 110.036490471197 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2350.3 & 21.0076835553466 & 111.878113253559 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2352.7 & 20.2785865741754 & 116.018934130061 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2354.28333333333 & 18.8082217216687 & 125.173095477761 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2350.61666666667 & 17.1850199460501 & 136.782888471826 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2369.68965517241 & 38.0798044969276 & 62.2295646334951 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2368.83928571429 & 36.4960839100573 & 64.9066703033719 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2368.25925925926 & 34.8269976602547 & 68.0006724197753 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2366.5 & 33.2645538522077 & 71.1417928679943 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2365.64 & 32.0566177700821 & 73.7956829060055 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2363.47916666667 & 30.8830008667943 & 76.5301007133638 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2360.67391304348 & 30.0379157235051 & 78.5898041253315 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2357.70454545455 & 28.9705430978468 & 81.3828217680108 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2355.97619047619 & 28.1655444751384 & 83.6474577140095 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2354.825 & 27.3302895623903 & 86.161728898786 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2353.86842105263 & 26.3806302884032 & 89.227148681409 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2353 & 25.1751326031722 & 93.4652475158567 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2351.64705882353 & 24.6763319583341 & 95.2997010574457 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2351.46875 & 24.3941089024204 & 96.394943525348 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2352 & 24.129344942545 & 97.474672669333 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2352.28571428571 & 23.7962502683292 & 98.8511083788866 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2352.65384615385 & 23.3347507318158 & 100.821897486401 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2353 & 22.6356618724922 & 103.951013814156 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2353.04545454545 & 21.7058730130479 & 108.405934796126 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2352.85 & 20.7244166954928 & 113.530336441831 \tabularnewline
Median & 2334.5 &  &  \tabularnewline
Midrange & 2599 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2338.6875 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2352 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2338.6875 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2352 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2352 &  &  \tabularnewline
Midmean - Closest Observation & 2338.6875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2352 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2345.03030303030 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48166&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]2377.33333333333[/C][C]42.2200294306199[/C][C]56.3081874975952[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2355.81164589092[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2334.78198448044[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2399.35055796355[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2370.48333333333[/C][C]39.3641014271583[/C][C]60.2194194047543[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2369.88333333333[/C][C]38.9280597654162[/C][C]60.8785371686761[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2372.83333333333[/C][C]37.8825509276161[/C][C]62.6365774012213[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2369.36666666667[/C][C]36.0524254703834[/C][C]65.7200350809426[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2374.28333333333[/C][C]35.0225923182884[/C][C]67.7929066973581[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2376.38333333333[/C][C]32.9497913855922[/C][C]72.1213468553989[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2375.91666666667[/C][C]32.8042154145503[/C][C]72.4271754907703[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2367.38333333333[/C][C]30.7916920674497[/C][C]76.8838337350068[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2362.88333333333[/C][C]29.9252655913967[/C][C]78.9594774394465[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2360.88333333333[/C][C]29.2569861439923[/C][C]80.6946867908377[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2359.6[/C][C]28.8934258352514[/C][C]81.6656361019388[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2362.2[/C][C]24.7991570842719[/C][C]95.253237518228[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2352.88333333333[/C][C]23.1109836639069[/C][C]101.808013347692[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2347.75[/C][C]22.3115285874725[/C][C]105.225869702097[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2350[/C][C]21.8035398566950[/C][C]107.780663848417[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2349.73333333333[/C][C]21.3541282830026[/C][C]110.036490471197[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2350.3[/C][C]21.0076835553466[/C][C]111.878113253559[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2352.7[/C][C]20.2785865741754[/C][C]116.018934130061[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2354.28333333333[/C][C]18.8082217216687[/C][C]125.173095477761[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2350.61666666667[/C][C]17.1850199460501[/C][C]136.782888471826[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2369.68965517241[/C][C]38.0798044969276[/C][C]62.2295646334951[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2368.83928571429[/C][C]36.4960839100573[/C][C]64.9066703033719[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2368.25925925926[/C][C]34.8269976602547[/C][C]68.0006724197753[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2366.5[/C][C]33.2645538522077[/C][C]71.1417928679943[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2365.64[/C][C]32.0566177700821[/C][C]73.7956829060055[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2363.47916666667[/C][C]30.8830008667943[/C][C]76.5301007133638[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2360.67391304348[/C][C]30.0379157235051[/C][C]78.5898041253315[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2357.70454545455[/C][C]28.9705430978468[/C][C]81.3828217680108[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2355.97619047619[/C][C]28.1655444751384[/C][C]83.6474577140095[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2354.825[/C][C]27.3302895623903[/C][C]86.161728898786[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2353.86842105263[/C][C]26.3806302884032[/C][C]89.227148681409[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2353[/C][C]25.1751326031722[/C][C]93.4652475158567[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2351.64705882353[/C][C]24.6763319583341[/C][C]95.2997010574457[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2351.46875[/C][C]24.3941089024204[/C][C]96.394943525348[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2352[/C][C]24.129344942545[/C][C]97.474672669333[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2352.28571428571[/C][C]23.7962502683292[/C][C]98.8511083788866[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2352.65384615385[/C][C]23.3347507318158[/C][C]100.821897486401[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2353[/C][C]22.6356618724922[/C][C]103.951013814156[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2353.04545454545[/C][C]21.7058730130479[/C][C]108.405934796126[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2352.85[/C][C]20.7244166954928[/C][C]113.530336441831[/C][/ROW]
[ROW][C]Median[/C][C]2334.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2599[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2338.6875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2352[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2338.6875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2352[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2352[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2338.6875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2352[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2345.03030303030[/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=48166&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48166&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 Mean2377.3333333333342.220029430619956.3081874975952
Geometric Mean2355.81164589092
Harmonic Mean2334.78198448044
Quadratic Mean2399.35055796355
Winsorized Mean ( 1 / 20 )2370.4833333333339.364101427158360.2194194047543
Winsorized Mean ( 2 / 20 )2369.8833333333338.928059765416260.8785371686761
Winsorized Mean ( 3 / 20 )2372.8333333333337.882550927616162.6365774012213
Winsorized Mean ( 4 / 20 )2369.3666666666736.052425470383465.7200350809426
Winsorized Mean ( 5 / 20 )2374.2833333333335.022592318288467.7929066973581
Winsorized Mean ( 6 / 20 )2376.3833333333332.949791385592272.1213468553989
Winsorized Mean ( 7 / 20 )2375.9166666666732.804215414550372.4271754907703
Winsorized Mean ( 8 / 20 )2367.3833333333330.791692067449776.8838337350068
Winsorized Mean ( 9 / 20 )2362.8833333333329.925265591396778.9594774394465
Winsorized Mean ( 10 / 20 )2360.8833333333329.256986143992380.6946867908377
Winsorized Mean ( 11 / 20 )2359.628.893425835251481.6656361019388
Winsorized Mean ( 12 / 20 )2362.224.799157084271995.253237518228
Winsorized Mean ( 13 / 20 )2352.8833333333323.1109836639069101.808013347692
Winsorized Mean ( 14 / 20 )2347.7522.3115285874725105.225869702097
Winsorized Mean ( 15 / 20 )235021.8035398566950107.780663848417
Winsorized Mean ( 16 / 20 )2349.7333333333321.3541282830026110.036490471197
Winsorized Mean ( 17 / 20 )2350.321.0076835553466111.878113253559
Winsorized Mean ( 18 / 20 )2352.720.2785865741754116.018934130061
Winsorized Mean ( 19 / 20 )2354.2833333333318.8082217216687125.173095477761
Winsorized Mean ( 20 / 20 )2350.6166666666717.1850199460501136.782888471826
Trimmed Mean ( 1 / 20 )2369.6896551724138.079804496927662.2295646334951
Trimmed Mean ( 2 / 20 )2368.8392857142936.496083910057364.9066703033719
Trimmed Mean ( 3 / 20 )2368.2592592592634.826997660254768.0006724197753
Trimmed Mean ( 4 / 20 )2366.533.264553852207771.1417928679943
Trimmed Mean ( 5 / 20 )2365.6432.056617770082173.7956829060055
Trimmed Mean ( 6 / 20 )2363.4791666666730.883000866794376.5301007133638
Trimmed Mean ( 7 / 20 )2360.6739130434830.037915723505178.5898041253315
Trimmed Mean ( 8 / 20 )2357.7045454545528.970543097846881.3828217680108
Trimmed Mean ( 9 / 20 )2355.9761904761928.165544475138483.6474577140095
Trimmed Mean ( 10 / 20 )2354.82527.330289562390386.161728898786
Trimmed Mean ( 11 / 20 )2353.8684210526326.380630288403289.227148681409
Trimmed Mean ( 12 / 20 )235325.175132603172293.4652475158567
Trimmed Mean ( 13 / 20 )2351.6470588235324.676331958334195.2997010574457
Trimmed Mean ( 14 / 20 )2351.4687524.394108902420496.394943525348
Trimmed Mean ( 15 / 20 )235224.12934494254597.474672669333
Trimmed Mean ( 16 / 20 )2352.2857142857123.796250268329298.8511083788866
Trimmed Mean ( 17 / 20 )2352.6538461538523.3347507318158100.821897486401
Trimmed Mean ( 18 / 20 )235322.6356618724922103.951013814156
Trimmed Mean ( 19 / 20 )2353.0454545454521.7058730130479108.405934796126
Trimmed Mean ( 20 / 20 )2352.8520.7244166954928113.530336441831
Median2334.5
Midrange2599
Midmean - Weighted Average at Xnp2338.6875
Midmean - Weighted Average at X(n+1)p2352
Midmean - Empirical Distribution Function2338.6875
Midmean - Empirical Distribution Function - Averaging2352
Midmean - Empirical Distribution Function - Interpolation2352
Midmean - Closest Observation2338.6875
Midmean - True Basic - Statistics Graphics Toolkit2352
Midmean - MS Excel (old versions)2345.03030303030
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')