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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 22 Dec 2008 01:00:21 -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/22/t1229932838c06i1kryt0htgoz.htm/, Retrieved Sun, 12 May 2024 18:23:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35940, Retrieved Sun, 12 May 2024 18:23:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact195
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Paper central ten...] [2007-11-09 08:56:17] [74be16979710d4c4e7c6647856088456]
-   PD  [Central Tendency] [CT Frankrijk] [2008-12-21 19:03:14] [d7f17de546c455a6cc3e244ffe795733]
-   PD      [Central Tendency] [CT Nederland] [2008-12-22 08:00:21] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
3032.9
2630.8
2851.4
3029.7
2856.4
2899.2
2784.9
2764.2
2770.0
2335.6
2700.9
2941.0
2489.2
2378.3
2404.6
2661.4
2559.3
2431.0
2670.2
2333.8
2441.9
2215.9
2482.9
2520.4
2423.8
2262.3
2190.8
2606.3
2547.9
2281.4
2594.1
2174.8
2158.6
2282.5
2368.1
2316.1
2404.9
2025.7
1931.9
2376.5
2091.7
2232.5
2355.8
2066.1
2014.4
2330.4
2198.2
2287.0
2371.4
1872.4
1983.8
2285.6
1965.0
2213.0
2246.3
1889.4
1907.4
1955.1
1863.6
2161.5




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35940&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35940&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35940&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2373.7033333333339.00460359376360.8570044207012
Geometric Mean2355.00467489666
Harmonic Mean2336.53426154054
Quadratic Mean2392.53583080101
Winsorized Mean ( 1 / 20 )2373.7966666666738.957102654962760.9336040128814
Winsorized Mean ( 2 / 20 )2371.4066666666738.036790387406762.3450780813461
Winsorized Mean ( 3 / 20 )2370.2166666666737.329200121789163.4949760223544
Winsorized Mean ( 4 / 20 )2368.9966666666736.323577187533265.2192556486354
Winsorized Mean ( 5 / 20 )2370.5133333333335.841717279614166.138386027659
Winsorized Mean ( 6 / 20 )2364.8533333333334.196533794238469.1547671925678
Winsorized Mean ( 7 / 20 )2365.3083333333333.40742730872870.8018702390583
Winsorized Mean ( 8 / 20 )2368.61532.475984332015872.9343559161947
Winsorized Mean ( 9 / 20 )2360.81530.273634258454877.9825434847047
Winsorized Mean ( 10 / 20 )2362.4316666666728.075712556338484.1450296916264
Winsorized Mean ( 11 / 20 )2365.5116666666726.951532255390887.7690976621012
Winsorized Mean ( 12 / 20 )2372.7716666666723.6275956744238100.423746002862
Winsorized Mean ( 13 / 20 )2368.0916666666722.5640196928358104.949902495367
Winsorized Mean ( 14 / 20 )2368.3483333333321.5801449982388109.746636712896
Winsorized Mean ( 15 / 20 )2363.6483333333319.4608085796656121.456840996991
Winsorized Mean ( 16 / 20 )2362.5816666666718.6497808247624126.681470890517
Winsorized Mean ( 17 / 20 )2358.9833333333316.7321560517275140.985018669473
Winsorized Mean ( 18 / 20 )2350.4933333333315.1067846595339155.591900348559
Winsorized Mean ( 19 / 20 )2353.75514.0129529314402167.969949768332
Winsorized Mean ( 20 / 20 )2344.6883333333311.2607821756375208.217182142641
Trimmed Mean ( 1 / 20 )2371.1327586206937.666678609653762.9504072603042
Trimmed Mean ( 2 / 20 )2368.2785714285736.071632081205565.6548771094425
Trimmed Mean ( 3 / 20 )2366.5407407407434.720020879671568.1606946304098
Trimmed Mean ( 4 / 20 )2365.1269230769233.382937915297370.8483755707173
Trimmed Mean ( 5 / 20 )2363.96632.111674348582173.6170270767703
Trimmed Mean ( 6 / 20 )2362.3291666666730.665268280395577.0359856325445
Trimmed Mean ( 7 / 20 )2361.7804347826129.365255624124880.4277158357955
Trimmed Mean ( 8 / 20 )2361.0931818181827.925693723788484.5491326078283
Trimmed Mean ( 9 / 20 )2359.7526.317750410007389.6638186485236
Trimmed Mean ( 10 / 20 )2359.572524.867914140230994.8842145221468
Trimmed Mean ( 11 / 20 )2359.1210526315823.5851597498352100.025655015886
Trimmed Mean ( 12 / 20 )2358.1527777777822.1678461863449106.377171600476
Trimmed Mean ( 13 / 20 )2356.0029411764721.2124876975561111.066791164146
Trimmed Mean ( 14 / 20 )2354.25937520.1878436050729116.617674530053
Trimmed Mean ( 15 / 20 )2352.2466666666719.0111254380548123.730006113059
Trimmed Mean ( 16 / 20 )2350.6178571428618.0177573004192130.461178822082
Trimmed Mean ( 17 / 20 )2348.8923076923116.7882128274819139.913183840940
Trimmed Mean ( 18 / 20 )2347.4083333333315.6538761193637149.957002050732
Trimmed Mean ( 19 / 20 )2346.9409090909114.5539802191835161.257667919420
Trimmed Mean ( 20 / 20 )2345.86513.2043977422994177.657856555258
Median2345.7
Midrange2448.25
Midmean - Weighted Average at Xnp2346.52258064516
Midmean - Weighted Average at X(n+1)p2352.24666666667
Midmean - Empirical Distribution Function2346.52258064516
Midmean - Empirical Distribution Function - Averaging2352.24666666667
Midmean - Empirical Distribution Function - Interpolation2352.24666666667
Midmean - Closest Observation2346.52258064516
Midmean - True Basic - Statistics Graphics Toolkit2352.24666666667
Midmean - MS Excel (old versions)2354.259375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2373.70333333333 & 39.004603593763 & 60.8570044207012 \tabularnewline
Geometric Mean & 2355.00467489666 &  &  \tabularnewline
Harmonic Mean & 2336.53426154054 &  &  \tabularnewline
Quadratic Mean & 2392.53583080101 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2373.79666666667 & 38.9571026549627 & 60.9336040128814 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2371.40666666667 & 38.0367903874067 & 62.3450780813461 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2370.21666666667 & 37.3292001217891 & 63.4949760223544 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2368.99666666667 & 36.3235771875332 & 65.2192556486354 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2370.51333333333 & 35.8417172796141 & 66.138386027659 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2364.85333333333 & 34.1965337942384 & 69.1547671925678 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2365.30833333333 & 33.407427308728 & 70.8018702390583 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2368.615 & 32.4759843320158 & 72.9343559161947 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2360.815 & 30.2736342584548 & 77.9825434847047 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2362.43166666667 & 28.0757125563384 & 84.1450296916264 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2365.51166666667 & 26.9515322553908 & 87.7690976621012 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2372.77166666667 & 23.6275956744238 & 100.423746002862 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2368.09166666667 & 22.5640196928358 & 104.949902495367 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2368.34833333333 & 21.5801449982388 & 109.746636712896 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2363.64833333333 & 19.4608085796656 & 121.456840996991 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2362.58166666667 & 18.6497808247624 & 126.681470890517 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2358.98333333333 & 16.7321560517275 & 140.985018669473 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2350.49333333333 & 15.1067846595339 & 155.591900348559 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2353.755 & 14.0129529314402 & 167.969949768332 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2344.68833333333 & 11.2607821756375 & 208.217182142641 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2371.13275862069 & 37.6666786096537 & 62.9504072603042 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2368.27857142857 & 36.0716320812055 & 65.6548771094425 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2366.54074074074 & 34.7200208796715 & 68.1606946304098 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2365.12692307692 & 33.3829379152973 & 70.8483755707173 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2363.966 & 32.1116743485821 & 73.6170270767703 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2362.32916666667 & 30.6652682803955 & 77.0359856325445 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2361.78043478261 & 29.3652556241248 & 80.4277158357955 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2361.09318181818 & 27.9256937237884 & 84.5491326078283 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2359.75 & 26.3177504100073 & 89.6638186485236 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2359.5725 & 24.8679141402309 & 94.8842145221468 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2359.12105263158 & 23.5851597498352 & 100.025655015886 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2358.15277777778 & 22.1678461863449 & 106.377171600476 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2356.00294117647 & 21.2124876975561 & 111.066791164146 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2354.259375 & 20.1878436050729 & 116.617674530053 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2352.24666666667 & 19.0111254380548 & 123.730006113059 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2350.61785714286 & 18.0177573004192 & 130.461178822082 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2348.89230769231 & 16.7882128274819 & 139.913183840940 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2347.40833333333 & 15.6538761193637 & 149.957002050732 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2346.94090909091 & 14.5539802191835 & 161.257667919420 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2345.865 & 13.2043977422994 & 177.657856555258 \tabularnewline
Median & 2345.7 &  &  \tabularnewline
Midrange & 2448.25 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2346.52258064516 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2352.24666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2346.52258064516 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2352.24666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2352.24666666667 &  &  \tabularnewline
Midmean - Closest Observation & 2346.52258064516 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2352.24666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2354.259375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35940&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]2373.70333333333[/C][C]39.004603593763[/C][C]60.8570044207012[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2355.00467489666[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2336.53426154054[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2392.53583080101[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2373.79666666667[/C][C]38.9571026549627[/C][C]60.9336040128814[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2371.40666666667[/C][C]38.0367903874067[/C][C]62.3450780813461[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2370.21666666667[/C][C]37.3292001217891[/C][C]63.4949760223544[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2368.99666666667[/C][C]36.3235771875332[/C][C]65.2192556486354[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2370.51333333333[/C][C]35.8417172796141[/C][C]66.138386027659[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2364.85333333333[/C][C]34.1965337942384[/C][C]69.1547671925678[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2365.30833333333[/C][C]33.407427308728[/C][C]70.8018702390583[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2368.615[/C][C]32.4759843320158[/C][C]72.9343559161947[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2360.815[/C][C]30.2736342584548[/C][C]77.9825434847047[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2362.43166666667[/C][C]28.0757125563384[/C][C]84.1450296916264[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2365.51166666667[/C][C]26.9515322553908[/C][C]87.7690976621012[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2372.77166666667[/C][C]23.6275956744238[/C][C]100.423746002862[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2368.09166666667[/C][C]22.5640196928358[/C][C]104.949902495367[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2368.34833333333[/C][C]21.5801449982388[/C][C]109.746636712896[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2363.64833333333[/C][C]19.4608085796656[/C][C]121.456840996991[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2362.58166666667[/C][C]18.6497808247624[/C][C]126.681470890517[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2358.98333333333[/C][C]16.7321560517275[/C][C]140.985018669473[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2350.49333333333[/C][C]15.1067846595339[/C][C]155.591900348559[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2353.755[/C][C]14.0129529314402[/C][C]167.969949768332[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2344.68833333333[/C][C]11.2607821756375[/C][C]208.217182142641[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2371.13275862069[/C][C]37.6666786096537[/C][C]62.9504072603042[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2368.27857142857[/C][C]36.0716320812055[/C][C]65.6548771094425[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2366.54074074074[/C][C]34.7200208796715[/C][C]68.1606946304098[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2365.12692307692[/C][C]33.3829379152973[/C][C]70.8483755707173[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2363.966[/C][C]32.1116743485821[/C][C]73.6170270767703[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2362.32916666667[/C][C]30.6652682803955[/C][C]77.0359856325445[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2361.78043478261[/C][C]29.3652556241248[/C][C]80.4277158357955[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2361.09318181818[/C][C]27.9256937237884[/C][C]84.5491326078283[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2359.75[/C][C]26.3177504100073[/C][C]89.6638186485236[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2359.5725[/C][C]24.8679141402309[/C][C]94.8842145221468[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2359.12105263158[/C][C]23.5851597498352[/C][C]100.025655015886[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2358.15277777778[/C][C]22.1678461863449[/C][C]106.377171600476[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2356.00294117647[/C][C]21.2124876975561[/C][C]111.066791164146[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2354.259375[/C][C]20.1878436050729[/C][C]116.617674530053[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2352.24666666667[/C][C]19.0111254380548[/C][C]123.730006113059[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2350.61785714286[/C][C]18.0177573004192[/C][C]130.461178822082[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2348.89230769231[/C][C]16.7882128274819[/C][C]139.913183840940[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2347.40833333333[/C][C]15.6538761193637[/C][C]149.957002050732[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2346.94090909091[/C][C]14.5539802191835[/C][C]161.257667919420[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2345.865[/C][C]13.2043977422994[/C][C]177.657856555258[/C][/ROW]
[ROW][C]Median[/C][C]2345.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2448.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2346.52258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2352.24666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2346.52258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2352.24666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2352.24666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2346.52258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2352.24666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2354.259375[/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=35940&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35940&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 Mean2373.7033333333339.00460359376360.8570044207012
Geometric Mean2355.00467489666
Harmonic Mean2336.53426154054
Quadratic Mean2392.53583080101
Winsorized Mean ( 1 / 20 )2373.7966666666738.957102654962760.9336040128814
Winsorized Mean ( 2 / 20 )2371.4066666666738.036790387406762.3450780813461
Winsorized Mean ( 3 / 20 )2370.2166666666737.329200121789163.4949760223544
Winsorized Mean ( 4 / 20 )2368.9966666666736.323577187533265.2192556486354
Winsorized Mean ( 5 / 20 )2370.5133333333335.841717279614166.138386027659
Winsorized Mean ( 6 / 20 )2364.8533333333334.196533794238469.1547671925678
Winsorized Mean ( 7 / 20 )2365.3083333333333.40742730872870.8018702390583
Winsorized Mean ( 8 / 20 )2368.61532.475984332015872.9343559161947
Winsorized Mean ( 9 / 20 )2360.81530.273634258454877.9825434847047
Winsorized Mean ( 10 / 20 )2362.4316666666728.075712556338484.1450296916264
Winsorized Mean ( 11 / 20 )2365.5116666666726.951532255390887.7690976621012
Winsorized Mean ( 12 / 20 )2372.7716666666723.6275956744238100.423746002862
Winsorized Mean ( 13 / 20 )2368.0916666666722.5640196928358104.949902495367
Winsorized Mean ( 14 / 20 )2368.3483333333321.5801449982388109.746636712896
Winsorized Mean ( 15 / 20 )2363.6483333333319.4608085796656121.456840996991
Winsorized Mean ( 16 / 20 )2362.5816666666718.6497808247624126.681470890517
Winsorized Mean ( 17 / 20 )2358.9833333333316.7321560517275140.985018669473
Winsorized Mean ( 18 / 20 )2350.4933333333315.1067846595339155.591900348559
Winsorized Mean ( 19 / 20 )2353.75514.0129529314402167.969949768332
Winsorized Mean ( 20 / 20 )2344.6883333333311.2607821756375208.217182142641
Trimmed Mean ( 1 / 20 )2371.1327586206937.666678609653762.9504072603042
Trimmed Mean ( 2 / 20 )2368.2785714285736.071632081205565.6548771094425
Trimmed Mean ( 3 / 20 )2366.5407407407434.720020879671568.1606946304098
Trimmed Mean ( 4 / 20 )2365.1269230769233.382937915297370.8483755707173
Trimmed Mean ( 5 / 20 )2363.96632.111674348582173.6170270767703
Trimmed Mean ( 6 / 20 )2362.3291666666730.665268280395577.0359856325445
Trimmed Mean ( 7 / 20 )2361.7804347826129.365255624124880.4277158357955
Trimmed Mean ( 8 / 20 )2361.0931818181827.925693723788484.5491326078283
Trimmed Mean ( 9 / 20 )2359.7526.317750410007389.6638186485236
Trimmed Mean ( 10 / 20 )2359.572524.867914140230994.8842145221468
Trimmed Mean ( 11 / 20 )2359.1210526315823.5851597498352100.025655015886
Trimmed Mean ( 12 / 20 )2358.1527777777822.1678461863449106.377171600476
Trimmed Mean ( 13 / 20 )2356.0029411764721.2124876975561111.066791164146
Trimmed Mean ( 14 / 20 )2354.25937520.1878436050729116.617674530053
Trimmed Mean ( 15 / 20 )2352.2466666666719.0111254380548123.730006113059
Trimmed Mean ( 16 / 20 )2350.6178571428618.0177573004192130.461178822082
Trimmed Mean ( 17 / 20 )2348.8923076923116.7882128274819139.913183840940
Trimmed Mean ( 18 / 20 )2347.4083333333315.6538761193637149.957002050732
Trimmed Mean ( 19 / 20 )2346.9409090909114.5539802191835161.257667919420
Trimmed Mean ( 20 / 20 )2345.86513.2043977422994177.657856555258
Median2345.7
Midrange2448.25
Midmean - Weighted Average at Xnp2346.52258064516
Midmean - Weighted Average at X(n+1)p2352.24666666667
Midmean - Empirical Distribution Function2346.52258064516
Midmean - Empirical Distribution Function - Averaging2352.24666666667
Midmean - Empirical Distribution Function - Interpolation2352.24666666667
Midmean - Closest Observation2346.52258064516
Midmean - True Basic - Statistics Graphics Toolkit2352.24666666667
Midmean - MS Excel (old versions)2354.259375
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')