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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 02:28:59 -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/t1255941024qis5ag09bicj32r.htm/, Retrieved Mon, 29 Apr 2024 20:24:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47601, Retrieved Mon, 29 Apr 2024 20:24:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsJSSHWWS3P2
Estimated Impact122
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]
- RMPD        [Central Tendency] [Part 2] [2009-10-19 08:28:59] [c8fd62404619100d8e91184019148412] [Current]
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Post a new message
Dataseries X:
2 407
2 129
1 877
1 750
1 622
1 646
1 912
2 403
2 126
2 351
2 453
2 539
2 609
2 472
2 310
2 253
2 224
2 468
2 928
3 225
3 227
3 336
3 185
3 017
2 846
2 545
2 562
2 425
2 345
2 526
2 758
2 899
3 074
2 915
2 843
2 959
2 880
2 840
2 655
2 694
2 399
2 884
3 083
2 872
2 898
2 874
2 890
3 312
3 514
3 342
2 741
2 346
2 397
2 644
2 837
2 877
2 895
2 823
2 905
2 765




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47601&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47601&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47601&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' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2658.8833333333354.052684550874149.1905879499991
Geometric Mean2623.61835062661
Harmonic Mean2584.98519273334
Quadratic Mean2691.10394633875
Winsorized Mean ( 1 / 20 )2656.4166666666753.225499876467249.9087218125152
Winsorized Mean ( 2 / 20 )2659.6833333333352.110630315724251.0391702656259
Winsorized Mean ( 3 / 20 )2664.8333333333350.058971814587953.2338806958229
Winsorized Mean ( 4 / 20 )2661.548.255894520070855.1538838202039
Winsorized Mean ( 5 / 20 )2679.1666666666743.95165658721960.9571259583822
Winsorized Mean ( 6 / 20 )2675.4666666666743.065142265441962.1260380419926
Winsorized Mean ( 7 / 20 )2674.6538.498865087095169.4734765284431
Winsorized Mean ( 8 / 20 )2677.3166666666737.529276644526471.3394156787499
Winsorized Mean ( 9 / 20 )2677.3166666666734.453099961931177.7090209480413
Winsorized Mean ( 10 / 20 )2673.4833333333331.871435696733283.8833668734718
Winsorized Mean ( 11 / 20 )2667.9833333333331.003503462194786.054253080999
Winsorized Mean ( 12 / 20 )2666.3833333333330.463093273485587.5283185917992
Winsorized Mean ( 13 / 20 )2674.1833333333328.465654710839993.9442061142893
Winsorized Mean ( 14 / 20 )2673.2528.197483810090994.8045583784797
Winsorized Mean ( 15 / 20 )267427.999122262271595.5029938064589
Winsorized Mean ( 16 / 20 )2674.2666666666727.716226117694296.4874025529542
Winsorized Mean ( 17 / 20 )2677.9526.6988692390533100.302000658622
Winsorized Mean ( 18 / 20 )2684.5525.1255989050805106.845214322719
Winsorized Mean ( 19 / 20 )2688.0333333333324.218508198477110.990871580702
Winsorized Mean ( 20 / 20 )2688.3666666666723.879345573307112.581253887954
Trimmed Mean ( 1 / 20 )2662.0172413793150.812726227097452.3887899555311
Trimmed Mean ( 2 / 20 )2668.0178571428647.806383662410155.8088199262959
Trimmed Mean ( 3 / 20 )2672.6481481481544.819196974906659.631772288212
Trimmed Mean ( 4 / 20 )2675.6538461538542.128402844826063.5118747798068
Trimmed Mean ( 5 / 20 )2679.939.479907056938367.8800990117586
Trimmed Mean ( 6 / 20 )2680.0833333333337.749076280715670.9973222497759
Trimmed Mean ( 7 / 20 )2681.0869565217435.820969570261274.8468561484051
Trimmed Mean ( 8 / 20 )2682.3409090909134.756567256025777.1750814553147
Trimmed Mean ( 9 / 20 )2683.2380952381033.632291350936879.7816023666005
Trimmed Mean ( 10 / 20 )2684.22532.982755546823881.3826787816243
Trimmed Mean ( 11 / 20 )2685.9210526315832.73216412630182.0575456687688
Trimmed Mean ( 12 / 20 )2688.6388888888932.513322123712382.6934534299106
Trimmed Mean ( 13 / 20 )2691.9117647058832.241882385540583.4911477101945
Trimmed Mean ( 14 / 20 )2694.4687532.281741830247683.4672665486506
Trimmed Mean ( 15 / 20 )2697.532.241251152243983.6661079702628
Trimmed Mean ( 16 / 20 )2700.8571428571432.061395892505484.2401607189064
Trimmed Mean ( 17 / 20 )2704.6923076923131.688181210072185.3533464026209
Trimmed Mean ( 18 / 20 )2708.62531.270026191921986.6204902859894
Trimmed Mean ( 19 / 20 )2712.2727272727330.978290248904687.5539839507003
Trimmed Mean ( 20 / 20 )2716.130.5762980100688.8302435797285
Median2749.5
Midrange2568
Midmean - Weighted Average at Xnp2687.87096774194
Midmean - Weighted Average at X(n+1)p2697.5
Midmean - Empirical Distribution Function2687.87096774194
Midmean - Empirical Distribution Function - Averaging2697.5
Midmean - Empirical Distribution Function - Interpolation2697.5
Midmean - Closest Observation2687.87096774194
Midmean - True Basic - Statistics Graphics Toolkit2697.5
Midmean - MS Excel (old versions)2694.46875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2658.88333333333 & 54.0526845508741 & 49.1905879499991 \tabularnewline
Geometric Mean & 2623.61835062661 &  &  \tabularnewline
Harmonic Mean & 2584.98519273334 &  &  \tabularnewline
Quadratic Mean & 2691.10394633875 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2656.41666666667 & 53.2254998764672 & 49.9087218125152 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2659.68333333333 & 52.1106303157242 & 51.0391702656259 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2664.83333333333 & 50.0589718145879 & 53.2338806958229 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2661.5 & 48.2558945200708 & 55.1538838202039 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2679.16666666667 & 43.951656587219 & 60.9571259583822 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2675.46666666667 & 43.0651422654419 & 62.1260380419926 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2674.65 & 38.4988650870951 & 69.4734765284431 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2677.31666666667 & 37.5292766445264 & 71.3394156787499 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2677.31666666667 & 34.4530999619311 & 77.7090209480413 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2673.48333333333 & 31.8714356967332 & 83.8833668734718 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2667.98333333333 & 31.0035034621947 & 86.054253080999 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2666.38333333333 & 30.4630932734855 & 87.5283185917992 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2674.18333333333 & 28.4656547108399 & 93.9442061142893 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2673.25 & 28.1974838100909 & 94.8045583784797 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2674 & 27.9991222622715 & 95.5029938064589 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2674.26666666667 & 27.7162261176942 & 96.4874025529542 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2677.95 & 26.6988692390533 & 100.302000658622 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2684.55 & 25.1255989050805 & 106.845214322719 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2688.03333333333 & 24.218508198477 & 110.990871580702 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2688.36666666667 & 23.879345573307 & 112.581253887954 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2662.01724137931 & 50.8127262270974 & 52.3887899555311 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2668.01785714286 & 47.8063836624101 & 55.8088199262959 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2672.64814814815 & 44.8191969749066 & 59.631772288212 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2675.65384615385 & 42.1284028448260 & 63.5118747798068 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2679.9 & 39.4799070569383 & 67.8800990117586 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2680.08333333333 & 37.7490762807156 & 70.9973222497759 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2681.08695652174 & 35.8209695702612 & 74.8468561484051 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2682.34090909091 & 34.7565672560257 & 77.1750814553147 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2683.23809523810 & 33.6322913509368 & 79.7816023666005 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2684.225 & 32.9827555468238 & 81.3826787816243 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2685.92105263158 & 32.732164126301 & 82.0575456687688 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2688.63888888889 & 32.5133221237123 & 82.6934534299106 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2691.91176470588 & 32.2418823855405 & 83.4911477101945 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2694.46875 & 32.2817418302476 & 83.4672665486506 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2697.5 & 32.2412511522439 & 83.6661079702628 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2700.85714285714 & 32.0613958925054 & 84.2401607189064 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2704.69230769231 & 31.6881812100721 & 85.3533464026209 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2708.625 & 31.2700261919219 & 86.6204902859894 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2712.27272727273 & 30.9782902489046 & 87.5539839507003 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2716.1 & 30.57629801006 & 88.8302435797285 \tabularnewline
Median & 2749.5 &  &  \tabularnewline
Midrange & 2568 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2687.87096774194 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2697.5 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2687.87096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2697.5 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2697.5 &  &  \tabularnewline
Midmean - Closest Observation & 2687.87096774194 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2697.5 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2694.46875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47601&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]2658.88333333333[/C][C]54.0526845508741[/C][C]49.1905879499991[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2623.61835062661[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2584.98519273334[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2691.10394633875[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2656.41666666667[/C][C]53.2254998764672[/C][C]49.9087218125152[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2659.68333333333[/C][C]52.1106303157242[/C][C]51.0391702656259[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2664.83333333333[/C][C]50.0589718145879[/C][C]53.2338806958229[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2661.5[/C][C]48.2558945200708[/C][C]55.1538838202039[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2679.16666666667[/C][C]43.951656587219[/C][C]60.9571259583822[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2675.46666666667[/C][C]43.0651422654419[/C][C]62.1260380419926[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2674.65[/C][C]38.4988650870951[/C][C]69.4734765284431[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2677.31666666667[/C][C]37.5292766445264[/C][C]71.3394156787499[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2677.31666666667[/C][C]34.4530999619311[/C][C]77.7090209480413[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2673.48333333333[/C][C]31.8714356967332[/C][C]83.8833668734718[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2667.98333333333[/C][C]31.0035034621947[/C][C]86.054253080999[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2666.38333333333[/C][C]30.4630932734855[/C][C]87.5283185917992[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2674.18333333333[/C][C]28.4656547108399[/C][C]93.9442061142893[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2673.25[/C][C]28.1974838100909[/C][C]94.8045583784797[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2674[/C][C]27.9991222622715[/C][C]95.5029938064589[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2674.26666666667[/C][C]27.7162261176942[/C][C]96.4874025529542[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2677.95[/C][C]26.6988692390533[/C][C]100.302000658622[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2684.55[/C][C]25.1255989050805[/C][C]106.845214322719[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2688.03333333333[/C][C]24.218508198477[/C][C]110.990871580702[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2688.36666666667[/C][C]23.879345573307[/C][C]112.581253887954[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2662.01724137931[/C][C]50.8127262270974[/C][C]52.3887899555311[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2668.01785714286[/C][C]47.8063836624101[/C][C]55.8088199262959[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2672.64814814815[/C][C]44.8191969749066[/C][C]59.631772288212[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2675.65384615385[/C][C]42.1284028448260[/C][C]63.5118747798068[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2679.9[/C][C]39.4799070569383[/C][C]67.8800990117586[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2680.08333333333[/C][C]37.7490762807156[/C][C]70.9973222497759[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2681.08695652174[/C][C]35.8209695702612[/C][C]74.8468561484051[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2682.34090909091[/C][C]34.7565672560257[/C][C]77.1750814553147[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2683.23809523810[/C][C]33.6322913509368[/C][C]79.7816023666005[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2684.225[/C][C]32.9827555468238[/C][C]81.3826787816243[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2685.92105263158[/C][C]32.732164126301[/C][C]82.0575456687688[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2688.63888888889[/C][C]32.5133221237123[/C][C]82.6934534299106[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2691.91176470588[/C][C]32.2418823855405[/C][C]83.4911477101945[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2694.46875[/C][C]32.2817418302476[/C][C]83.4672665486506[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2697.5[/C][C]32.2412511522439[/C][C]83.6661079702628[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2700.85714285714[/C][C]32.0613958925054[/C][C]84.2401607189064[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2704.69230769231[/C][C]31.6881812100721[/C][C]85.3533464026209[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2708.625[/C][C]31.2700261919219[/C][C]86.6204902859894[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2712.27272727273[/C][C]30.9782902489046[/C][C]87.5539839507003[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2716.1[/C][C]30.57629801006[/C][C]88.8302435797285[/C][/ROW]
[ROW][C]Median[/C][C]2749.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2687.87096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2697.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2687.87096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2697.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2697.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2687.87096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2697.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2694.46875[/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=47601&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47601&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 Mean2658.8833333333354.052684550874149.1905879499991
Geometric Mean2623.61835062661
Harmonic Mean2584.98519273334
Quadratic Mean2691.10394633875
Winsorized Mean ( 1 / 20 )2656.4166666666753.225499876467249.9087218125152
Winsorized Mean ( 2 / 20 )2659.6833333333352.110630315724251.0391702656259
Winsorized Mean ( 3 / 20 )2664.8333333333350.058971814587953.2338806958229
Winsorized Mean ( 4 / 20 )2661.548.255894520070855.1538838202039
Winsorized Mean ( 5 / 20 )2679.1666666666743.95165658721960.9571259583822
Winsorized Mean ( 6 / 20 )2675.4666666666743.065142265441962.1260380419926
Winsorized Mean ( 7 / 20 )2674.6538.498865087095169.4734765284431
Winsorized Mean ( 8 / 20 )2677.3166666666737.529276644526471.3394156787499
Winsorized Mean ( 9 / 20 )2677.3166666666734.453099961931177.7090209480413
Winsorized Mean ( 10 / 20 )2673.4833333333331.871435696733283.8833668734718
Winsorized Mean ( 11 / 20 )2667.9833333333331.003503462194786.054253080999
Winsorized Mean ( 12 / 20 )2666.3833333333330.463093273485587.5283185917992
Winsorized Mean ( 13 / 20 )2674.1833333333328.465654710839993.9442061142893
Winsorized Mean ( 14 / 20 )2673.2528.197483810090994.8045583784797
Winsorized Mean ( 15 / 20 )267427.999122262271595.5029938064589
Winsorized Mean ( 16 / 20 )2674.2666666666727.716226117694296.4874025529542
Winsorized Mean ( 17 / 20 )2677.9526.6988692390533100.302000658622
Winsorized Mean ( 18 / 20 )2684.5525.1255989050805106.845214322719
Winsorized Mean ( 19 / 20 )2688.0333333333324.218508198477110.990871580702
Winsorized Mean ( 20 / 20 )2688.3666666666723.879345573307112.581253887954
Trimmed Mean ( 1 / 20 )2662.0172413793150.812726227097452.3887899555311
Trimmed Mean ( 2 / 20 )2668.0178571428647.806383662410155.8088199262959
Trimmed Mean ( 3 / 20 )2672.6481481481544.819196974906659.631772288212
Trimmed Mean ( 4 / 20 )2675.6538461538542.128402844826063.5118747798068
Trimmed Mean ( 5 / 20 )2679.939.479907056938367.8800990117586
Trimmed Mean ( 6 / 20 )2680.0833333333337.749076280715670.9973222497759
Trimmed Mean ( 7 / 20 )2681.0869565217435.820969570261274.8468561484051
Trimmed Mean ( 8 / 20 )2682.3409090909134.756567256025777.1750814553147
Trimmed Mean ( 9 / 20 )2683.2380952381033.632291350936879.7816023666005
Trimmed Mean ( 10 / 20 )2684.22532.982755546823881.3826787816243
Trimmed Mean ( 11 / 20 )2685.9210526315832.73216412630182.0575456687688
Trimmed Mean ( 12 / 20 )2688.6388888888932.513322123712382.6934534299106
Trimmed Mean ( 13 / 20 )2691.9117647058832.241882385540583.4911477101945
Trimmed Mean ( 14 / 20 )2694.4687532.281741830247683.4672665486506
Trimmed Mean ( 15 / 20 )2697.532.241251152243983.6661079702628
Trimmed Mean ( 16 / 20 )2700.8571428571432.061395892505484.2401607189064
Trimmed Mean ( 17 / 20 )2704.6923076923131.688181210072185.3533464026209
Trimmed Mean ( 18 / 20 )2708.62531.270026191921986.6204902859894
Trimmed Mean ( 19 / 20 )2712.2727272727330.978290248904687.5539839507003
Trimmed Mean ( 20 / 20 )2716.130.5762980100688.8302435797285
Median2749.5
Midrange2568
Midmean - Weighted Average at Xnp2687.87096774194
Midmean - Weighted Average at X(n+1)p2697.5
Midmean - Empirical Distribution Function2687.87096774194
Midmean - Empirical Distribution Function - Averaging2697.5
Midmean - Empirical Distribution Function - Interpolation2697.5
Midmean - Closest Observation2687.87096774194
Midmean - True Basic - Statistics Graphics Toolkit2697.5
Midmean - MS Excel (old versions)2694.46875
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')