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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 computationFri, 12 Nov 2010 18:32:54 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/12/t128958678332atlk87x61a59n.htm/, Retrieved Tue, 30 Apr 2024 08:35:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=94274, Retrieved Tue, 30 Apr 2024 08:35:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact144
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
-  M D    [Central Tendency] [WS 6 Mini Tut Cen...] [2010-11-12 18:32:54] [89d441ae0711e9b79b5d358f420c1317] [Current]
-           [Central Tendency] [Paper - Central T...] [2010-12-19 18:23:18] [18fa53e8b37a5effc0c5f8a5122cdd2d]
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Dataseries X:
1576.23
1546.37
1545.05
1552.34
1594.3
1605.78
1673.21
1612.94
1566.34
1530.17
1582.54
1702.16
1701.93
1811.15
1924.2
2034.25
2011.13
2013.04
2151.67
1902.09
1944.01
1916.67
1967.31
2119.88
2216.38
2522.83
2647.64
2631.23
2693.41
3021.76
2953.67
2796.8
2672.05
2251.23
2046.08
2420.04
2608.89
2660.47
2493.98
2541.7
2554.6
2699.61
2805.48
2956.66
3149.51
3372.5
3379.33
3517.54
3527.34
3281.06
3089.65
3222.76
3165.76
3232.43
3229.54
3071.74
2850.17




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=94274&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=94274&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=94274&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 Mean2401.2035087719383.000706046190528.9299166616203
Geometric Mean2319.34483166832
Harmonic Mean2238.36342101962
Quadratic Mean2480.23564484747
Winsorized Mean ( 1 / 19 )2401.2926315789582.91067921778128.9624045326114
Winsorized Mean ( 2 / 19 )2396.4894736842181.798491272914929.2974776966056
Winsorized Mean ( 3 / 19 )2396.4442105263281.663410146933529.3453849920607
Winsorized Mean ( 4 / 19 )2391.0098245614080.161121070997429.8275497225610
Winsorized Mean ( 5 / 19 )2387.6115789473779.172637770907630.1570295770126
Winsorized Mean ( 6 / 19 )2387.9715789473778.993472499588230.2299861417007
Winsorized Mean ( 7 / 19 )2388.5831578947478.573514687110630.3993421626405
Winsorized Mean ( 8 / 19 )2382.1943859649176.795176577797731.0201042841749
Winsorized Mean ( 9 / 19 )2380.7591228070276.12621547493631.2738405285741
Winsorized Mean ( 10 / 19 )2380.8310526315872.384553940070832.8914239715110
Winsorized Mean ( 11 / 19 )2382.9171929824670.82250610664133.6463269090531
Winsorized Mean ( 12 / 19 )2372.4435087719369.016154978114434.3751909900552
Winsorized Mean ( 13 / 19 )2382.4535087719362.351563428659938.2100043328959
Winsorized Mean ( 14 / 19 )2404.0552631578958.693236622242740.9596642051061
Winsorized Mean ( 15 / 19 )2380.6552631578953.693925767188144.3375154478403
Winsorized Mean ( 16 / 19 )2370.2243859649151.439404182934846.0779906690918
Winsorized Mean ( 17 / 19 )2373.5438596491250.13930320603947.3389877377323
Winsorized Mean ( 18 / 19 )2350.2101754386044.539177978136552.7672553048076
Winsorized Mean ( 19 / 19 )2362.7501754386042.036335996560656.207329193294
Trimmed Mean ( 1 / 19 )2396.5652727272781.982991004213429.2324693618961
Trimmed Mean ( 2 / 19 )2391.4811320754780.768630541711429.6090340524028
Trimmed Mean ( 3 / 19 )2388.6823529411879.922771169540229.8873815057547
Trimmed Mean ( 4 / 19 )2385.6726530612278.84340453501130.2583667857956
Trimmed Mean ( 5 / 19 )2384.0544680851177.982032394603730.57184321667
Trimmed Mean ( 6 / 19 )2383.1533333333377.117222759650930.9029973856922
Trimmed Mean ( 7 / 19 )2382.088837209375.950200603245531.3638254841885
Trimmed Mean ( 8 / 19 )2380.7990243902474.450763245940231.9781681287206
Trimmed Mean ( 9 / 19 )2380.544102564172.888920196497132.659889817911
Trimmed Mean ( 10 / 19 )2380.5072972973070.885842047619833.58226732636
Trimmed Mean ( 11 / 19 )2380.4545714285769.147778238723934.4256118137354
Trimmed Mean ( 12 / 19 )2380.0678787878867.079272823784635.4814203940501
Trimmed Mean ( 13 / 19 )2381.2361290322664.593333972586336.8650444648494
Trimmed Mean ( 14 / 19 )2381.0520689655263.012686089560637.7868682757199
Trimmed Mean ( 15 / 19 )2377.5833333333361.631489666553738.5774114206362
Trimmed Mean ( 16 / 19 )2377.116460.974318842389238.9855343221553
Trimmed Mean ( 17 / 19 )2378.1839130434860.336108744879839.4155997546874
Trimmed Mean ( 18 / 19 )2378.9247619047659.327736714188940.0980198075855
Trimmed Mean ( 19 / 19 )2383.7105263157959.373110136614540.1479814823747
Median2493.98
Midrange2528.755
Midmean - Weighted Average at Xnp2360.60142857143
Midmean - Weighted Average at X(n+1)p2381.05206896552
Midmean - Empirical Distribution Function2381.05206896552
Midmean - Empirical Distribution Function - Averaging2381.05206896552
Midmean - Empirical Distribution Function - Interpolation2381.05206896552
Midmean - Closest Observation2362.05533333333
Midmean - True Basic - Statistics Graphics Toolkit2381.05206896552
Midmean - MS Excel (old versions)2381.05206896552
Number of observations57

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2401.20350877193 & 83.0007060461905 & 28.9299166616203 \tabularnewline
Geometric Mean & 2319.34483166832 &  &  \tabularnewline
Harmonic Mean & 2238.36342101962 &  &  \tabularnewline
Quadratic Mean & 2480.23564484747 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 2401.29263157895 & 82.910679217781 & 28.9624045326114 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 2396.48947368421 & 81.7984912729149 & 29.2974776966056 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 2396.44421052632 & 81.6634101469335 & 29.3453849920607 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 2391.00982456140 & 80.1611210709974 & 29.8275497225610 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 2387.61157894737 & 79.1726377709076 & 30.1570295770126 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 2387.97157894737 & 78.9934724995882 & 30.2299861417007 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 2388.58315789474 & 78.5735146871106 & 30.3993421626405 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 2382.19438596491 & 76.7951765777977 & 31.0201042841749 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 2380.75912280702 & 76.126215474936 & 31.2738405285741 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 2380.83105263158 & 72.3845539400708 & 32.8914239715110 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 2382.91719298246 & 70.822506106641 & 33.6463269090531 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 2372.44350877193 & 69.0161549781144 & 34.3751909900552 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 2382.45350877193 & 62.3515634286599 & 38.2100043328959 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 2404.05526315789 & 58.6932366222427 & 40.9596642051061 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 2380.65526315789 & 53.6939257671881 & 44.3375154478403 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 2370.22438596491 & 51.4394041829348 & 46.0779906690918 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 2373.54385964912 & 50.139303206039 & 47.3389877377323 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 2350.21017543860 & 44.5391779781365 & 52.7672553048076 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 2362.75017543860 & 42.0363359965606 & 56.207329193294 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 2396.56527272727 & 81.9829910042134 & 29.2324693618961 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 2391.48113207547 & 80.7686305417114 & 29.6090340524028 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 2388.68235294118 & 79.9227711695402 & 29.8873815057547 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 2385.67265306122 & 78.843404535011 & 30.2583667857956 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 2384.05446808511 & 77.9820323946037 & 30.57184321667 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 2383.15333333333 & 77.1172227596509 & 30.9029973856922 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 2382.0888372093 & 75.9502006032455 & 31.3638254841885 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 2380.79902439024 & 74.4507632459402 & 31.9781681287206 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 2380.5441025641 & 72.8889201964971 & 32.659889817911 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 2380.50729729730 & 70.8858420476198 & 33.58226732636 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 2380.45457142857 & 69.1477782387239 & 34.4256118137354 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 2380.06787878788 & 67.0792728237846 & 35.4814203940501 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 2381.23612903226 & 64.5933339725863 & 36.8650444648494 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 2381.05206896552 & 63.0126860895606 & 37.7868682757199 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 2377.58333333333 & 61.6314896665537 & 38.5774114206362 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 2377.1164 & 60.9743188423892 & 38.9855343221553 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 2378.18391304348 & 60.3361087448798 & 39.4155997546874 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 2378.92476190476 & 59.3277367141889 & 40.0980198075855 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 2383.71052631579 & 59.3731101366145 & 40.1479814823747 \tabularnewline
Median & 2493.98 &  &  \tabularnewline
Midrange & 2528.755 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2360.60142857143 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2381.05206896552 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2381.05206896552 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2381.05206896552 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2381.05206896552 &  &  \tabularnewline
Midmean - Closest Observation & 2362.05533333333 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2381.05206896552 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2381.05206896552 &  &  \tabularnewline
Number of observations & 57 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=94274&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]2401.20350877193[/C][C]83.0007060461905[/C][C]28.9299166616203[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2319.34483166832[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2238.36342101962[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2480.23564484747[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]2401.29263157895[/C][C]82.910679217781[/C][C]28.9624045326114[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]2396.48947368421[/C][C]81.7984912729149[/C][C]29.2974776966056[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]2396.44421052632[/C][C]81.6634101469335[/C][C]29.3453849920607[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]2391.00982456140[/C][C]80.1611210709974[/C][C]29.8275497225610[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]2387.61157894737[/C][C]79.1726377709076[/C][C]30.1570295770126[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]2387.97157894737[/C][C]78.9934724995882[/C][C]30.2299861417007[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]2388.58315789474[/C][C]78.5735146871106[/C][C]30.3993421626405[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]2382.19438596491[/C][C]76.7951765777977[/C][C]31.0201042841749[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]2380.75912280702[/C][C]76.126215474936[/C][C]31.2738405285741[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]2380.83105263158[/C][C]72.3845539400708[/C][C]32.8914239715110[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]2382.91719298246[/C][C]70.822506106641[/C][C]33.6463269090531[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]2372.44350877193[/C][C]69.0161549781144[/C][C]34.3751909900552[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]2382.45350877193[/C][C]62.3515634286599[/C][C]38.2100043328959[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]2404.05526315789[/C][C]58.6932366222427[/C][C]40.9596642051061[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]2380.65526315789[/C][C]53.6939257671881[/C][C]44.3375154478403[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]2370.22438596491[/C][C]51.4394041829348[/C][C]46.0779906690918[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]2373.54385964912[/C][C]50.139303206039[/C][C]47.3389877377323[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]2350.21017543860[/C][C]44.5391779781365[/C][C]52.7672553048076[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]2362.75017543860[/C][C]42.0363359965606[/C][C]56.207329193294[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]2396.56527272727[/C][C]81.9829910042134[/C][C]29.2324693618961[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]2391.48113207547[/C][C]80.7686305417114[/C][C]29.6090340524028[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]2388.68235294118[/C][C]79.9227711695402[/C][C]29.8873815057547[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]2385.67265306122[/C][C]78.843404535011[/C][C]30.2583667857956[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]2384.05446808511[/C][C]77.9820323946037[/C][C]30.57184321667[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]2383.15333333333[/C][C]77.1172227596509[/C][C]30.9029973856922[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]2382.0888372093[/C][C]75.9502006032455[/C][C]31.3638254841885[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]2380.79902439024[/C][C]74.4507632459402[/C][C]31.9781681287206[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]2380.5441025641[/C][C]72.8889201964971[/C][C]32.659889817911[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]2380.50729729730[/C][C]70.8858420476198[/C][C]33.58226732636[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]2380.45457142857[/C][C]69.1477782387239[/C][C]34.4256118137354[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]2380.06787878788[/C][C]67.0792728237846[/C][C]35.4814203940501[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]2381.23612903226[/C][C]64.5933339725863[/C][C]36.8650444648494[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]2381.05206896552[/C][C]63.0126860895606[/C][C]37.7868682757199[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]2377.58333333333[/C][C]61.6314896665537[/C][C]38.5774114206362[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]2377.1164[/C][C]60.9743188423892[/C][C]38.9855343221553[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]2378.18391304348[/C][C]60.3361087448798[/C][C]39.4155997546874[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]2378.92476190476[/C][C]59.3277367141889[/C][C]40.0980198075855[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]2383.71052631579[/C][C]59.3731101366145[/C][C]40.1479814823747[/C][/ROW]
[ROW][C]Median[/C][C]2493.98[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2528.755[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2360.60142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2381.05206896552[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2381.05206896552[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2381.05206896552[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2381.05206896552[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2362.05533333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2381.05206896552[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2381.05206896552[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]57[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=94274&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=94274&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 Mean2401.2035087719383.000706046190528.9299166616203
Geometric Mean2319.34483166832
Harmonic Mean2238.36342101962
Quadratic Mean2480.23564484747
Winsorized Mean ( 1 / 19 )2401.2926315789582.91067921778128.9624045326114
Winsorized Mean ( 2 / 19 )2396.4894736842181.798491272914929.2974776966056
Winsorized Mean ( 3 / 19 )2396.4442105263281.663410146933529.3453849920607
Winsorized Mean ( 4 / 19 )2391.0098245614080.161121070997429.8275497225610
Winsorized Mean ( 5 / 19 )2387.6115789473779.172637770907630.1570295770126
Winsorized Mean ( 6 / 19 )2387.9715789473778.993472499588230.2299861417007
Winsorized Mean ( 7 / 19 )2388.5831578947478.573514687110630.3993421626405
Winsorized Mean ( 8 / 19 )2382.1943859649176.795176577797731.0201042841749
Winsorized Mean ( 9 / 19 )2380.7591228070276.12621547493631.2738405285741
Winsorized Mean ( 10 / 19 )2380.8310526315872.384553940070832.8914239715110
Winsorized Mean ( 11 / 19 )2382.9171929824670.82250610664133.6463269090531
Winsorized Mean ( 12 / 19 )2372.4435087719369.016154978114434.3751909900552
Winsorized Mean ( 13 / 19 )2382.4535087719362.351563428659938.2100043328959
Winsorized Mean ( 14 / 19 )2404.0552631578958.693236622242740.9596642051061
Winsorized Mean ( 15 / 19 )2380.6552631578953.693925767188144.3375154478403
Winsorized Mean ( 16 / 19 )2370.2243859649151.439404182934846.0779906690918
Winsorized Mean ( 17 / 19 )2373.5438596491250.13930320603947.3389877377323
Winsorized Mean ( 18 / 19 )2350.2101754386044.539177978136552.7672553048076
Winsorized Mean ( 19 / 19 )2362.7501754386042.036335996560656.207329193294
Trimmed Mean ( 1 / 19 )2396.5652727272781.982991004213429.2324693618961
Trimmed Mean ( 2 / 19 )2391.4811320754780.768630541711429.6090340524028
Trimmed Mean ( 3 / 19 )2388.6823529411879.922771169540229.8873815057547
Trimmed Mean ( 4 / 19 )2385.6726530612278.84340453501130.2583667857956
Trimmed Mean ( 5 / 19 )2384.0544680851177.982032394603730.57184321667
Trimmed Mean ( 6 / 19 )2383.1533333333377.117222759650930.9029973856922
Trimmed Mean ( 7 / 19 )2382.088837209375.950200603245531.3638254841885
Trimmed Mean ( 8 / 19 )2380.7990243902474.450763245940231.9781681287206
Trimmed Mean ( 9 / 19 )2380.544102564172.888920196497132.659889817911
Trimmed Mean ( 10 / 19 )2380.5072972973070.885842047619833.58226732636
Trimmed Mean ( 11 / 19 )2380.4545714285769.147778238723934.4256118137354
Trimmed Mean ( 12 / 19 )2380.0678787878867.079272823784635.4814203940501
Trimmed Mean ( 13 / 19 )2381.2361290322664.593333972586336.8650444648494
Trimmed Mean ( 14 / 19 )2381.0520689655263.012686089560637.7868682757199
Trimmed Mean ( 15 / 19 )2377.5833333333361.631489666553738.5774114206362
Trimmed Mean ( 16 / 19 )2377.116460.974318842389238.9855343221553
Trimmed Mean ( 17 / 19 )2378.1839130434860.336108744879839.4155997546874
Trimmed Mean ( 18 / 19 )2378.9247619047659.327736714188940.0980198075855
Trimmed Mean ( 19 / 19 )2383.7105263157959.373110136614540.1479814823747
Median2493.98
Midrange2528.755
Midmean - Weighted Average at Xnp2360.60142857143
Midmean - Weighted Average at X(n+1)p2381.05206896552
Midmean - Empirical Distribution Function2381.05206896552
Midmean - Empirical Distribution Function - Averaging2381.05206896552
Midmean - Empirical Distribution Function - Interpolation2381.05206896552
Midmean - Closest Observation2362.05533333333
Midmean - True Basic - Statistics Graphics Toolkit2381.05206896552
Midmean - MS Excel (old versions)2381.05206896552
Number of observations57



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')