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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 computationThu, 22 Oct 2009 09:31:13 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/22/t1256225642fkoc7i51mrruct7.htm/, Retrieved Thu, 02 May 2024 23:35:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49763, Retrieved Thu, 02 May 2024 23:35:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact128
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [workshop 3/part 2] [2009-10-22 15:31:13] [bebfa40a4e66abcf3fcee16e050bb8d6] [Current]
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Dataseries X:
8362
7751
7045
6505
6002
5389
4777
4079
3684
3382
5579
6737
7939
7286
6677
6189
5793
5438
4718
4364
4027
3938
5928
7161
8360
8258
6963
5941
6079
5768
4958
4989
3810
3181
5257
6103
7432
6953
5723
5925
5766
5557
4649
4687
3271
2790
4830
5444
6773
5798
5438
5338
5178
4878
5020
4776
3846
3608
5393
6056




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49763&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49763&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49763&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean5559.1173.67083726842032.009404039482
Geometric Mean5392.6516480107
Harmonic Mean5219.00001892452
Quadratic Mean5716.91567484892
Winsorized Mean ( 1 / 20 )5565.58333333333172.01500770760632.3552195096477
Winsorized Mean ( 2 / 20 )5565.18333333333170.39673130811432.6601531062839
Winsorized Mean ( 3 / 20 )5554.78333333333165.05250164834433.6546449030393
Winsorized Mean ( 4 / 20 )5557.31666666667158.79923986865534.9958644088171
Winsorized Mean ( 5 / 20 )5537.06666666667151.54816292975136.5366795586519
Winsorized Mean ( 6 / 20 )5535.06666666667145.94692338122337.9252027958734
Winsorized Mean ( 7 / 20 )5524.68333333333142.20042053317438.8513853378124
Winsorized Mean ( 8 / 20 )5521.48333333333136.80052386093140.3615657126165
Winsorized Mean ( 9 / 20 )5522.53333333333131.90820825443941.8664873582459
Winsorized Mean ( 10 / 20 )5529.53333333333129.94659586837142.5523523443004
Winsorized Mean ( 11 / 20 )5548.78333333333114.33018664033048.5329683820876
Winsorized Mean ( 12 / 20 )5598.58333333333103.54252733559954.0703755007578
Winsorized Mean ( 13 / 20 )5593.8166666666799.862369955579456.0152604945676
Winsorized Mean ( 14 / 20 )5560.9166666666791.53675835906160.7506401401444
Winsorized Mean ( 15 / 20 )5496.4166666666776.179394620746572.1509627902686
Winsorized Mean ( 16 / 20 )5473.7572.68491953802175.3079185447363
Winsorized Mean ( 17 / 20 )5481.9666666666769.271120365999879.1378374956581
Winsorized Mean ( 18 / 20 )5489.4666666666765.985199790082583.1923929021994
Winsorized Mean ( 19 / 20 )5497.759.576842560608492.2791434340802
Winsorized Mean ( 20 / 20 )5487.755.113638637290299.5706350675782
Trimmed Mean ( 1 / 20 )5558.51724137931166.1344240336433.4579499324823
Trimmed Mean ( 2 / 20 )5550.94642857143158.87554841096534.9389599852882
Trimmed Mean ( 3 / 20 )5543.03703703704150.95082053007336.7208142199713
Trimmed Mean ( 4 / 20 )5538.51923076923143.75142596285238.528447239198
Trimmed Mean ( 5 / 20 )5532.88137.28952764140540.3008160567912
Trimmed Mean ( 6 / 20 )5531.83333333333131.73950202881141.9906956390616
Trimmed Mean ( 7 / 20 )5531.13043478261126.47528489614543.7328956350997
Trimmed Mean ( 8 / 20 )5532.38636363636120.81363181379545.792732828057
Trimmed Mean ( 9 / 20 )5534.33333333333115.02986365093448.1121437310197
Trimmed Mean ( 10 / 20 )5536.3108.81642504224450.8774295594688
Trimmed Mean ( 11 / 20 )5537.36842105263100.99496784115354.8281616343687
Trimmed Mean ( 12 / 20 )5535.6388888888995.275249978036958.1015414828613
Trimmed Mean ( 13 / 20 )5526.3823529411890.5773717645261.0128362667497
Trimmed Mean ( 14 / 20 )5516.6562585.038352464455464.8725673784175
Trimmed Mean ( 15 / 20 )5510.3333333333379.926652199380768.9423763125666
Trimmed Mean ( 16 / 20 )5512.3214285714377.646006066799570.9929809374758
Trimmed Mean ( 17 / 20 )5517.8846153846275.114749692066373.4594022879027
Trimmed Mean ( 18 / 20 )5523.1666666666772.215726203584776.4814945029592
Trimmed Mean ( 19 / 20 )5528.2727272727368.660914160911480.5155712654343
Trimmed Mean ( 20 / 20 )5533.165.452308873271384.5363608289692
Median5500.5
Midrange5576
Midmean - Weighted Average at Xnp5484.77419354839
Midmean - Weighted Average at X(n+1)p5510.33333333333
Midmean - Empirical Distribution Function5484.77419354839
Midmean - Empirical Distribution Function - Averaging5510.33333333333
Midmean - Empirical Distribution Function - Interpolation5510.33333333333
Midmean - Closest Observation5484.77419354839
Midmean - True Basic - Statistics Graphics Toolkit5510.33333333333
Midmean - MS Excel (old versions)5516.65625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 5559.1 & 173.670837268420 & 32.009404039482 \tabularnewline
Geometric Mean & 5392.6516480107 &  &  \tabularnewline
Harmonic Mean & 5219.00001892452 &  &  \tabularnewline
Quadratic Mean & 5716.91567484892 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 5565.58333333333 & 172.015007707606 & 32.3552195096477 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 5565.18333333333 & 170.396731308114 & 32.6601531062839 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 5554.78333333333 & 165.052501648344 & 33.6546449030393 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 5557.31666666667 & 158.799239868655 & 34.9958644088171 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 5537.06666666667 & 151.548162929751 & 36.5366795586519 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 5535.06666666667 & 145.946923381223 & 37.9252027958734 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 5524.68333333333 & 142.200420533174 & 38.8513853378124 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 5521.48333333333 & 136.800523860931 & 40.3615657126165 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 5522.53333333333 & 131.908208254439 & 41.8664873582459 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 5529.53333333333 & 129.946595868371 & 42.5523523443004 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 5548.78333333333 & 114.330186640330 & 48.5329683820876 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 5598.58333333333 & 103.542527335599 & 54.0703755007578 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 5593.81666666667 & 99.8623699555794 & 56.0152604945676 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 5560.91666666667 & 91.536758359061 & 60.7506401401444 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 5496.41666666667 & 76.1793946207465 & 72.1509627902686 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 5473.75 & 72.684919538021 & 75.3079185447363 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 5481.96666666667 & 69.2711203659998 & 79.1378374956581 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 5489.46666666667 & 65.9851997900825 & 83.1923929021994 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 5497.7 & 59.5768425606084 & 92.2791434340802 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 5487.7 & 55.1136386372902 & 99.5706350675782 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 5558.51724137931 & 166.13442403364 & 33.4579499324823 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 5550.94642857143 & 158.875548410965 & 34.9389599852882 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 5543.03703703704 & 150.950820530073 & 36.7208142199713 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 5538.51923076923 & 143.751425962852 & 38.528447239198 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 5532.88 & 137.289527641405 & 40.3008160567912 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 5531.83333333333 & 131.739502028811 & 41.9906956390616 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 5531.13043478261 & 126.475284896145 & 43.7328956350997 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 5532.38636363636 & 120.813631813795 & 45.792732828057 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 5534.33333333333 & 115.029863650934 & 48.1121437310197 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 5536.3 & 108.816425042244 & 50.8774295594688 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 5537.36842105263 & 100.994967841153 & 54.8281616343687 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 5535.63888888889 & 95.2752499780369 & 58.1015414828613 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 5526.38235294118 & 90.57737176452 & 61.0128362667497 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 5516.65625 & 85.0383524644554 & 64.8725673784175 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 5510.33333333333 & 79.9266521993807 & 68.9423763125666 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 5512.32142857143 & 77.6460060667995 & 70.9929809374758 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 5517.88461538462 & 75.1147496920663 & 73.4594022879027 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 5523.16666666667 & 72.2157262035847 & 76.4814945029592 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 5528.27272727273 & 68.6609141609114 & 80.5155712654343 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 5533.1 & 65.4523088732713 & 84.5363608289692 \tabularnewline
Median & 5500.5 &  &  \tabularnewline
Midrange & 5576 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 5484.77419354839 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 5510.33333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 5484.77419354839 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 5510.33333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 5510.33333333333 &  &  \tabularnewline
Midmean - Closest Observation & 5484.77419354839 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 5510.33333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 5516.65625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49763&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]5559.1[/C][C]173.670837268420[/C][C]32.009404039482[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]5392.6516480107[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]5219.00001892452[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]5716.91567484892[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]5565.58333333333[/C][C]172.015007707606[/C][C]32.3552195096477[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]5565.18333333333[/C][C]170.396731308114[/C][C]32.6601531062839[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]5554.78333333333[/C][C]165.052501648344[/C][C]33.6546449030393[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]5557.31666666667[/C][C]158.799239868655[/C][C]34.9958644088171[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]5537.06666666667[/C][C]151.548162929751[/C][C]36.5366795586519[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]5535.06666666667[/C][C]145.946923381223[/C][C]37.9252027958734[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]5524.68333333333[/C][C]142.200420533174[/C][C]38.8513853378124[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]5521.48333333333[/C][C]136.800523860931[/C][C]40.3615657126165[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]5522.53333333333[/C][C]131.908208254439[/C][C]41.8664873582459[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]5529.53333333333[/C][C]129.946595868371[/C][C]42.5523523443004[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]5548.78333333333[/C][C]114.330186640330[/C][C]48.5329683820876[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]5598.58333333333[/C][C]103.542527335599[/C][C]54.0703755007578[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]5593.81666666667[/C][C]99.8623699555794[/C][C]56.0152604945676[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]5560.91666666667[/C][C]91.536758359061[/C][C]60.7506401401444[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]5496.41666666667[/C][C]76.1793946207465[/C][C]72.1509627902686[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]5473.75[/C][C]72.684919538021[/C][C]75.3079185447363[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]5481.96666666667[/C][C]69.2711203659998[/C][C]79.1378374956581[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]5489.46666666667[/C][C]65.9851997900825[/C][C]83.1923929021994[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]5497.7[/C][C]59.5768425606084[/C][C]92.2791434340802[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]5487.7[/C][C]55.1136386372902[/C][C]99.5706350675782[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]5558.51724137931[/C][C]166.13442403364[/C][C]33.4579499324823[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]5550.94642857143[/C][C]158.875548410965[/C][C]34.9389599852882[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]5543.03703703704[/C][C]150.950820530073[/C][C]36.7208142199713[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]5538.51923076923[/C][C]143.751425962852[/C][C]38.528447239198[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]5532.88[/C][C]137.289527641405[/C][C]40.3008160567912[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]5531.83333333333[/C][C]131.739502028811[/C][C]41.9906956390616[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]5531.13043478261[/C][C]126.475284896145[/C][C]43.7328956350997[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]5532.38636363636[/C][C]120.813631813795[/C][C]45.792732828057[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]5534.33333333333[/C][C]115.029863650934[/C][C]48.1121437310197[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]5536.3[/C][C]108.816425042244[/C][C]50.8774295594688[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]5537.36842105263[/C][C]100.994967841153[/C][C]54.8281616343687[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]5535.63888888889[/C][C]95.2752499780369[/C][C]58.1015414828613[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]5526.38235294118[/C][C]90.57737176452[/C][C]61.0128362667497[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]5516.65625[/C][C]85.0383524644554[/C][C]64.8725673784175[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]5510.33333333333[/C][C]79.9266521993807[/C][C]68.9423763125666[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]5512.32142857143[/C][C]77.6460060667995[/C][C]70.9929809374758[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]5517.88461538462[/C][C]75.1147496920663[/C][C]73.4594022879027[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]5523.16666666667[/C][C]72.2157262035847[/C][C]76.4814945029592[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]5528.27272727273[/C][C]68.6609141609114[/C][C]80.5155712654343[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]5533.1[/C][C]65.4523088732713[/C][C]84.5363608289692[/C][/ROW]
[ROW][C]Median[/C][C]5500.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]5576[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]5484.77419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]5510.33333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]5484.77419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]5510.33333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]5510.33333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]5484.77419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]5510.33333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]5516.65625[/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=49763&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49763&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 Mean5559.1173.67083726842032.009404039482
Geometric Mean5392.6516480107
Harmonic Mean5219.00001892452
Quadratic Mean5716.91567484892
Winsorized Mean ( 1 / 20 )5565.58333333333172.01500770760632.3552195096477
Winsorized Mean ( 2 / 20 )5565.18333333333170.39673130811432.6601531062839
Winsorized Mean ( 3 / 20 )5554.78333333333165.05250164834433.6546449030393
Winsorized Mean ( 4 / 20 )5557.31666666667158.79923986865534.9958644088171
Winsorized Mean ( 5 / 20 )5537.06666666667151.54816292975136.5366795586519
Winsorized Mean ( 6 / 20 )5535.06666666667145.94692338122337.9252027958734
Winsorized Mean ( 7 / 20 )5524.68333333333142.20042053317438.8513853378124
Winsorized Mean ( 8 / 20 )5521.48333333333136.80052386093140.3615657126165
Winsorized Mean ( 9 / 20 )5522.53333333333131.90820825443941.8664873582459
Winsorized Mean ( 10 / 20 )5529.53333333333129.94659586837142.5523523443004
Winsorized Mean ( 11 / 20 )5548.78333333333114.33018664033048.5329683820876
Winsorized Mean ( 12 / 20 )5598.58333333333103.54252733559954.0703755007578
Winsorized Mean ( 13 / 20 )5593.8166666666799.862369955579456.0152604945676
Winsorized Mean ( 14 / 20 )5560.9166666666791.53675835906160.7506401401444
Winsorized Mean ( 15 / 20 )5496.4166666666776.179394620746572.1509627902686
Winsorized Mean ( 16 / 20 )5473.7572.68491953802175.3079185447363
Winsorized Mean ( 17 / 20 )5481.9666666666769.271120365999879.1378374956581
Winsorized Mean ( 18 / 20 )5489.4666666666765.985199790082583.1923929021994
Winsorized Mean ( 19 / 20 )5497.759.576842560608492.2791434340802
Winsorized Mean ( 20 / 20 )5487.755.113638637290299.5706350675782
Trimmed Mean ( 1 / 20 )5558.51724137931166.1344240336433.4579499324823
Trimmed Mean ( 2 / 20 )5550.94642857143158.87554841096534.9389599852882
Trimmed Mean ( 3 / 20 )5543.03703703704150.95082053007336.7208142199713
Trimmed Mean ( 4 / 20 )5538.51923076923143.75142596285238.528447239198
Trimmed Mean ( 5 / 20 )5532.88137.28952764140540.3008160567912
Trimmed Mean ( 6 / 20 )5531.83333333333131.73950202881141.9906956390616
Trimmed Mean ( 7 / 20 )5531.13043478261126.47528489614543.7328956350997
Trimmed Mean ( 8 / 20 )5532.38636363636120.81363181379545.792732828057
Trimmed Mean ( 9 / 20 )5534.33333333333115.02986365093448.1121437310197
Trimmed Mean ( 10 / 20 )5536.3108.81642504224450.8774295594688
Trimmed Mean ( 11 / 20 )5537.36842105263100.99496784115354.8281616343687
Trimmed Mean ( 12 / 20 )5535.6388888888995.275249978036958.1015414828613
Trimmed Mean ( 13 / 20 )5526.3823529411890.5773717645261.0128362667497
Trimmed Mean ( 14 / 20 )5516.6562585.038352464455464.8725673784175
Trimmed Mean ( 15 / 20 )5510.3333333333379.926652199380768.9423763125666
Trimmed Mean ( 16 / 20 )5512.3214285714377.646006066799570.9929809374758
Trimmed Mean ( 17 / 20 )5517.8846153846275.114749692066373.4594022879027
Trimmed Mean ( 18 / 20 )5523.1666666666772.215726203584776.4814945029592
Trimmed Mean ( 19 / 20 )5528.2727272727368.660914160911480.5155712654343
Trimmed Mean ( 20 / 20 )5533.165.452308873271384.5363608289692
Median5500.5
Midrange5576
Midmean - Weighted Average at Xnp5484.77419354839
Midmean - Weighted Average at X(n+1)p5510.33333333333
Midmean - Empirical Distribution Function5484.77419354839
Midmean - Empirical Distribution Function - Averaging5510.33333333333
Midmean - Empirical Distribution Function - Interpolation5510.33333333333
Midmean - Closest Observation5484.77419354839
Midmean - True Basic - Statistics Graphics Toolkit5510.33333333333
Midmean - MS Excel (old versions)5516.65625
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')