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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 computationSat, 13 Dec 2008 04:14:49 -0700
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/Dec/13/t1229166949r434v4x71qlytd2.htm/, Retrieved Sat, 18 May 2024 11:56:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32969, Retrieved Sat, 18 May 2024 11:56:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact167
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper - central t...] [2008-12-13 11:14:49] [73ec5abea95a9c3c8c3a1ac44cab1f72] [Current]
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Dataseries X:
1529
2186
3069
3252
3541
3435
2320
3285
2681
3019
3833
3472
2971
2770
3060
4124
3282
3772
1500
2844
3449
4356
3150
2425
1212
1328
2097
2167
2773
2368
1387
2478
2702
3349
3114
3394
1249
2155
2188
2363
2040
2144
1440
2485
2904
2452
2855
3966
1621
1717
2370
1849
2262
2494
2010
1901
2027
1769
1271
1571




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32969&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32969&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32969&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2546.61666666667101.80450716401425.0147732905764
Geometric Mean2420.94212469075
Harmonic Mean2291.54625430678
Quadratic Mean2663.97104901686
Winsorized Mean ( 1 / 20 )2543.36666666667100.57091538171325.2892862415881
Winsorized Mean ( 2 / 20 )2538.8333333333399.066490730657225.6275690660724
Winsorized Mean ( 3 / 20 )2535.0333333333396.888936844525926.1643219122242
Winsorized Mean ( 4 / 20 )2534.995.161636800992826.6378352161084
Winsorized Mean ( 5 / 20 )2520.0666666666790.28966213533127.9109103641284
Winsorized Mean ( 6 / 20 )2519.1666666666787.794711649375528.6938315456565
Winsorized Mean ( 7 / 20 )2519.8666666666786.64325998565429.0832393319907
Winsorized Mean ( 8 / 20 )2523.685.231204996085529.6088738873973
Winsorized Mean ( 9 / 20 )2524.9582.721018530840530.5236812220661
Winsorized Mean ( 10 / 20 )2533.4578.498876975665632.2737101167111
Winsorized Mean ( 11 / 20 )2531.2574.799047642657833.8406715028338
Winsorized Mean ( 12 / 20 )2546.6571.998951753982635.3706538492643
Winsorized Mean ( 13 / 20 )2551.4166666666769.052339486162536.9490257050298
Winsorized Mean ( 14 / 20 )2553.0561.07652616204241.8008383978242
Winsorized Mean ( 15 / 20 )2548.358.960320373375543.2205928302711
Winsorized Mean ( 16 / 20 )2539.7666666666756.512177412101844.9419361095576
Winsorized Mean ( 17 / 20 )2553.3666666666753.732061606125347.5203554515316
Winsorized Mean ( 18 / 20 )2555.1666666666749.774401599757451.3349550078593
Winsorized Mean ( 19 / 20 )2543.4546.910953179919454.2186808749123
Winsorized Mean ( 20 / 20 )2525.1166666666742.950701550189958.7910459091326
Trimmed Mean ( 1 / 20 )2538.4310344827697.813609406665325.9517162272286
Trimmed Mean ( 2 / 20 )2533.1428571428694.408505245601326.8317229528521
Trimmed Mean ( 3 / 20 )2529.9814814814891.201528066648327.7405602199189
Trimmed Mean ( 4 / 20 )2528.0384615384688.26827748181528.6403964556722
Trimmed Mean ( 5 / 20 )2525.9885.267590752014729.6241511894754
Trimmed Mean ( 6 / 20 )2527.4583333333383.16424489964530.3911655349392
Trimmed Mean ( 7 / 20 )2529.2608695652281.220088866848431.140828640457
Trimmed Mean ( 8 / 20 )2531.0909090909179.002052708243532.0382929597828
Trimmed Mean ( 9 / 20 )2532.4285714285776.470046384364633.1166082821464
Trimmed Mean ( 10 / 20 )2533.67573.800731247680134.3312993945388
Trimmed Mean ( 11 / 20 )2533.7105263157971.385903632325135.4931491708185
Trimmed Mean ( 12 / 20 )2534.0833333333369.096658488567436.6744700650411
Trimmed Mean ( 13 / 20 )2532.2352941176566.667852825769437.9828536061514
Trimmed Mean ( 14 / 20 )2529.4687564.0539085013939.4896862530272
Trimmed Mean ( 15 / 20 )2526.162.65057906732640.3204573302568
Trimmed Mean ( 16 / 20 )2522.9285714285761.073117956769341.3099683761755
Trimmed Mean ( 17 / 20 )2520.559.332913424039942.4806377193467
Trimmed Mean ( 18 / 20 )2515.6666666666757.377521310098643.8441154170928
Trimmed Mean ( 19 / 20 )2509.6818181818255.537802981534545.1887126146537
Trimmed Mean ( 20 / 20 )2504.3553.455159516620746.8495468472286
Median2465
Midrange2784
Midmean - Weighted Average at Xnp2509.45161290323
Midmean - Weighted Average at X(n+1)p2526.1
Midmean - Empirical Distribution Function2509.45161290323
Midmean - Empirical Distribution Function - Averaging2526.1
Midmean - Empirical Distribution Function - Interpolation2526.1
Midmean - Closest Observation2509.45161290323
Midmean - True Basic - Statistics Graphics Toolkit2526.1
Midmean - MS Excel (old versions)2529.46875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2546.61666666667 & 101.804507164014 & 25.0147732905764 \tabularnewline
Geometric Mean & 2420.94212469075 &  &  \tabularnewline
Harmonic Mean & 2291.54625430678 &  &  \tabularnewline
Quadratic Mean & 2663.97104901686 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2543.36666666667 & 100.570915381713 & 25.2892862415881 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2538.83333333333 & 99.0664907306572 & 25.6275690660724 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2535.03333333333 & 96.8889368445259 & 26.1643219122242 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2534.9 & 95.1616368009928 & 26.6378352161084 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2520.06666666667 & 90.289662135331 & 27.9109103641284 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2519.16666666667 & 87.7947116493755 & 28.6938315456565 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2519.86666666667 & 86.643259985654 & 29.0832393319907 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2523.6 & 85.2312049960855 & 29.6088738873973 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2524.95 & 82.7210185308405 & 30.5236812220661 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2533.45 & 78.4988769756656 & 32.2737101167111 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2531.25 & 74.7990476426578 & 33.8406715028338 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2546.65 & 71.9989517539826 & 35.3706538492643 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2551.41666666667 & 69.0523394861625 & 36.9490257050298 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2553.05 & 61.076526162042 & 41.8008383978242 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2548.3 & 58.9603203733755 & 43.2205928302711 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2539.76666666667 & 56.5121774121018 & 44.9419361095576 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2553.36666666667 & 53.7320616061253 & 47.5203554515316 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2555.16666666667 & 49.7744015997574 & 51.3349550078593 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2543.45 & 46.9109531799194 & 54.2186808749123 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2525.11666666667 & 42.9507015501899 & 58.7910459091326 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2538.43103448276 & 97.8136094066653 & 25.9517162272286 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2533.14285714286 & 94.4085052456013 & 26.8317229528521 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2529.98148148148 & 91.2015280666483 & 27.7405602199189 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2528.03846153846 & 88.268277481815 & 28.6403964556722 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2525.98 & 85.2675907520147 & 29.6241511894754 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2527.45833333333 & 83.164244899645 & 30.3911655349392 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2529.26086956522 & 81.2200888668484 & 31.140828640457 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2531.09090909091 & 79.0020527082435 & 32.0382929597828 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2532.42857142857 & 76.4700463843646 & 33.1166082821464 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2533.675 & 73.8007312476801 & 34.3312993945388 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2533.71052631579 & 71.3859036323251 & 35.4931491708185 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2534.08333333333 & 69.0966584885674 & 36.6744700650411 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2532.23529411765 & 66.6678528257694 & 37.9828536061514 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2529.46875 & 64.05390850139 & 39.4896862530272 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2526.1 & 62.650579067326 & 40.3204573302568 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2522.92857142857 & 61.0731179567693 & 41.3099683761755 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2520.5 & 59.3329134240399 & 42.4806377193467 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2515.66666666667 & 57.3775213100986 & 43.8441154170928 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2509.68181818182 & 55.5378029815345 & 45.1887126146537 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2504.35 & 53.4551595166207 & 46.8495468472286 \tabularnewline
Median & 2465 &  &  \tabularnewline
Midrange & 2784 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2509.45161290323 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2526.1 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2509.45161290323 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2526.1 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2526.1 &  &  \tabularnewline
Midmean - Closest Observation & 2509.45161290323 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2526.1 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2529.46875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32969&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]2546.61666666667[/C][C]101.804507164014[/C][C]25.0147732905764[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2420.94212469075[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2291.54625430678[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2663.97104901686[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2543.36666666667[/C][C]100.570915381713[/C][C]25.2892862415881[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2538.83333333333[/C][C]99.0664907306572[/C][C]25.6275690660724[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2535.03333333333[/C][C]96.8889368445259[/C][C]26.1643219122242[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2534.9[/C][C]95.1616368009928[/C][C]26.6378352161084[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2520.06666666667[/C][C]90.289662135331[/C][C]27.9109103641284[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2519.16666666667[/C][C]87.7947116493755[/C][C]28.6938315456565[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2519.86666666667[/C][C]86.643259985654[/C][C]29.0832393319907[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2523.6[/C][C]85.2312049960855[/C][C]29.6088738873973[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2524.95[/C][C]82.7210185308405[/C][C]30.5236812220661[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2533.45[/C][C]78.4988769756656[/C][C]32.2737101167111[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2531.25[/C][C]74.7990476426578[/C][C]33.8406715028338[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2546.65[/C][C]71.9989517539826[/C][C]35.3706538492643[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2551.41666666667[/C][C]69.0523394861625[/C][C]36.9490257050298[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2553.05[/C][C]61.076526162042[/C][C]41.8008383978242[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2548.3[/C][C]58.9603203733755[/C][C]43.2205928302711[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2539.76666666667[/C][C]56.5121774121018[/C][C]44.9419361095576[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2553.36666666667[/C][C]53.7320616061253[/C][C]47.5203554515316[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2555.16666666667[/C][C]49.7744015997574[/C][C]51.3349550078593[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2543.45[/C][C]46.9109531799194[/C][C]54.2186808749123[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2525.11666666667[/C][C]42.9507015501899[/C][C]58.7910459091326[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2538.43103448276[/C][C]97.8136094066653[/C][C]25.9517162272286[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2533.14285714286[/C][C]94.4085052456013[/C][C]26.8317229528521[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2529.98148148148[/C][C]91.2015280666483[/C][C]27.7405602199189[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2528.03846153846[/C][C]88.268277481815[/C][C]28.6403964556722[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2525.98[/C][C]85.2675907520147[/C][C]29.6241511894754[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2527.45833333333[/C][C]83.164244899645[/C][C]30.3911655349392[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2529.26086956522[/C][C]81.2200888668484[/C][C]31.140828640457[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2531.09090909091[/C][C]79.0020527082435[/C][C]32.0382929597828[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2532.42857142857[/C][C]76.4700463843646[/C][C]33.1166082821464[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2533.675[/C][C]73.8007312476801[/C][C]34.3312993945388[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2533.71052631579[/C][C]71.3859036323251[/C][C]35.4931491708185[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2534.08333333333[/C][C]69.0966584885674[/C][C]36.6744700650411[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2532.23529411765[/C][C]66.6678528257694[/C][C]37.9828536061514[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2529.46875[/C][C]64.05390850139[/C][C]39.4896862530272[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2526.1[/C][C]62.650579067326[/C][C]40.3204573302568[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2522.92857142857[/C][C]61.0731179567693[/C][C]41.3099683761755[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2520.5[/C][C]59.3329134240399[/C][C]42.4806377193467[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2515.66666666667[/C][C]57.3775213100986[/C][C]43.8441154170928[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2509.68181818182[/C][C]55.5378029815345[/C][C]45.1887126146537[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2504.35[/C][C]53.4551595166207[/C][C]46.8495468472286[/C][/ROW]
[ROW][C]Median[/C][C]2465[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2509.45161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2526.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2509.45161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2526.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2526.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2509.45161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2526.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2529.46875[/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=32969&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32969&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 Mean2546.61666666667101.80450716401425.0147732905764
Geometric Mean2420.94212469075
Harmonic Mean2291.54625430678
Quadratic Mean2663.97104901686
Winsorized Mean ( 1 / 20 )2543.36666666667100.57091538171325.2892862415881
Winsorized Mean ( 2 / 20 )2538.8333333333399.066490730657225.6275690660724
Winsorized Mean ( 3 / 20 )2535.0333333333396.888936844525926.1643219122242
Winsorized Mean ( 4 / 20 )2534.995.161636800992826.6378352161084
Winsorized Mean ( 5 / 20 )2520.0666666666790.28966213533127.9109103641284
Winsorized Mean ( 6 / 20 )2519.1666666666787.794711649375528.6938315456565
Winsorized Mean ( 7 / 20 )2519.8666666666786.64325998565429.0832393319907
Winsorized Mean ( 8 / 20 )2523.685.231204996085529.6088738873973
Winsorized Mean ( 9 / 20 )2524.9582.721018530840530.5236812220661
Winsorized Mean ( 10 / 20 )2533.4578.498876975665632.2737101167111
Winsorized Mean ( 11 / 20 )2531.2574.799047642657833.8406715028338
Winsorized Mean ( 12 / 20 )2546.6571.998951753982635.3706538492643
Winsorized Mean ( 13 / 20 )2551.4166666666769.052339486162536.9490257050298
Winsorized Mean ( 14 / 20 )2553.0561.07652616204241.8008383978242
Winsorized Mean ( 15 / 20 )2548.358.960320373375543.2205928302711
Winsorized Mean ( 16 / 20 )2539.7666666666756.512177412101844.9419361095576
Winsorized Mean ( 17 / 20 )2553.3666666666753.732061606125347.5203554515316
Winsorized Mean ( 18 / 20 )2555.1666666666749.774401599757451.3349550078593
Winsorized Mean ( 19 / 20 )2543.4546.910953179919454.2186808749123
Winsorized Mean ( 20 / 20 )2525.1166666666742.950701550189958.7910459091326
Trimmed Mean ( 1 / 20 )2538.4310344827697.813609406665325.9517162272286
Trimmed Mean ( 2 / 20 )2533.1428571428694.408505245601326.8317229528521
Trimmed Mean ( 3 / 20 )2529.9814814814891.201528066648327.7405602199189
Trimmed Mean ( 4 / 20 )2528.0384615384688.26827748181528.6403964556722
Trimmed Mean ( 5 / 20 )2525.9885.267590752014729.6241511894754
Trimmed Mean ( 6 / 20 )2527.4583333333383.16424489964530.3911655349392
Trimmed Mean ( 7 / 20 )2529.2608695652281.220088866848431.140828640457
Trimmed Mean ( 8 / 20 )2531.0909090909179.002052708243532.0382929597828
Trimmed Mean ( 9 / 20 )2532.4285714285776.470046384364633.1166082821464
Trimmed Mean ( 10 / 20 )2533.67573.800731247680134.3312993945388
Trimmed Mean ( 11 / 20 )2533.7105263157971.385903632325135.4931491708185
Trimmed Mean ( 12 / 20 )2534.0833333333369.096658488567436.6744700650411
Trimmed Mean ( 13 / 20 )2532.2352941176566.667852825769437.9828536061514
Trimmed Mean ( 14 / 20 )2529.4687564.0539085013939.4896862530272
Trimmed Mean ( 15 / 20 )2526.162.65057906732640.3204573302568
Trimmed Mean ( 16 / 20 )2522.9285714285761.073117956769341.3099683761755
Trimmed Mean ( 17 / 20 )2520.559.332913424039942.4806377193467
Trimmed Mean ( 18 / 20 )2515.6666666666757.377521310098643.8441154170928
Trimmed Mean ( 19 / 20 )2509.6818181818255.537802981534545.1887126146537
Trimmed Mean ( 20 / 20 )2504.3553.455159516620746.8495468472286
Median2465
Midrange2784
Midmean - Weighted Average at Xnp2509.45161290323
Midmean - Weighted Average at X(n+1)p2526.1
Midmean - Empirical Distribution Function2509.45161290323
Midmean - Empirical Distribution Function - Averaging2526.1
Midmean - Empirical Distribution Function - Interpolation2526.1
Midmean - Closest Observation2509.45161290323
Midmean - True Basic - Statistics Graphics Toolkit2526.1
Midmean - MS Excel (old versions)2529.46875
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')