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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 computationTue, 20 Oct 2009 10:20:25 -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/20/t1256055659lk9bius6rn2g6ix.htm/, Retrieved Thu, 02 May 2024 14:06:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48786, Retrieved Thu, 02 May 2024 14:06:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact130
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [] [2009-10-20 16:20:25] [244731fa3e7e6c85774b8c0902c58f85] [Current]
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Post a new message
Dataseries X:
3062,1
3379,8
2644,4
3182,3
2876,9
3286,7
3809,7
3218,1
3945,2
3802
2868,5
3506,4
3699,5
3442
3352,2
4102
4376,8
3720,7
4300,8
3497,9
3682
3903,2
2944,2
3316,3
3409,4
3490,4
2762,4
2899,2
3171
3006
3475,1
3008,3
2609,6
3527,1
2842,3
3122,5
2571,6
3619,3
2806,2
2584,1
2883,1
3362,3
2919,6
3009,8
2872,1
3191,9
2553,3
2566,2
3114,4
2651,6
2862,6
3069,3
2160,9
2333,9
2563,1
2619,6
2484
2750




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=48786&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=48786&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48786&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 Mean3151.5844827586264.81450804041548.6246764504246
Geometric Mean3114.33494161013
Harmonic Mean3077.8136223509
Quadratic Mean3189.34745955323
Winsorized Mean ( 1 / 19 )3153.2568965517263.652623225670749.5385223225181
Winsorized Mean ( 2 / 19 )3151.577586206960.5336406620652.0632420541356
Winsorized Mean ( 3 / 19 )3147.0517241379357.7598794979854.4850811928718
Winsorized Mean ( 4 / 19 )3144.8310344827656.948824800339255.2220532295168
Winsorized Mean ( 5 / 19 )3137.0379310344855.094495396857956.9392261139284
Winsorized Mean ( 6 / 19 )3136.854.823113399873757.2167431849506
Winsorized Mean ( 7 / 19 )3128.4965517241452.533366976516959.5525611964414
Winsorized Mean ( 8 / 19 )3129.0896551724151.327026350025560.9637821960216
Winsorized Mean ( 9 / 19 )3127.9258620689750.526349559018261.9068246443439
Winsorized Mean ( 10 / 19 )3121.3913793103547.743945513954565.377742574669
Winsorized Mean ( 11 / 19 )3105.2706896551744.441375565132169.8734152615095
Winsorized Mean ( 12 / 19 )3121.3465517241440.245986390465677.5567163751661
Winsorized Mean ( 13 / 19 )3122.2206896551739.479881447037279.0838415724138
Winsorized Mean ( 14 / 19 )3130.9827586206937.527765170992683.4311007957598
Winsorized Mean ( 15 / 19 )3136.3620689655235.475417460067288.4094478238616
Winsorized Mean ( 16 / 19 )3132.8310344827633.155322219083994.4895366656858
Winsorized Mean ( 17 / 19 )3125.0051724137931.365475085814199.6320050585544
Winsorized Mean ( 18 / 19 )3116.9362068965529.7618772722345104.729153285112
Winsorized Mean ( 19 / 19 )3112.7758620689728.652662131982108.638277578909
Trimmed Mean ( 1 / 19 )3147.3964285714360.850711451746251.7232478221273
Trimmed Mean ( 2 / 19 )3141.1018518518557.341511805808654.7788461261613
Trimmed Mean ( 3 / 19 )3135.2596153846255.106893332479656.894145646507
Trimmed Mean ( 4 / 19 )3130.753.672450653791458.3297382896536
Trimmed Mean ( 5 / 19 )3126.4312552.160726710425259.9384143429722
Trimmed Mean ( 6 / 19 )3123.7565217391350.871384157578861.40498383262
Trimmed Mean ( 7 / 19 )3120.8909090909149.263582904768863.3508714768856
Trimmed Mean ( 8 / 19 )3119.3904761904847.855800849085865.1831213947821
Trimmed Mean ( 9 / 19 )3117.632546.320711348593867.3053674961459
Trimmed Mean ( 10 / 19 )3115.8868421052644.470058840762670.0670726176135
Trimmed Mean ( 11 / 19 )311542.768601633842272.8338051982309
Trimmed Mean ( 12 / 19 )3116.5088235294141.367982221489775.3362541794571
Trimmed Mean ( 13 / 19 )3115.77812540.582065832400776.777218238909
Trimmed Mean ( 14 / 19 )3114.8239.578353366106878.7000907083568
Trimmed Mean ( 15 / 19 )3112.4285714285738.598826933796380.6353150775005
Trimmed Mean ( 16 / 19 )3108.8692307692337.652498035110882.567409680766
Trimmed Mean ( 17 / 19 )3105.2536.849991642576784.2673189757844
Trimmed Mean ( 18 / 19 )3102.1863636363636.061773776975586.024231165718
Trimmed Mean ( 19 / 19 )3099.8135.194444761997188.0766842881741
Median3091.85
Midrange3268.85
Midmean - Weighted Average at Xnp3101.86896551724
Midmean - Weighted Average at X(n+1)p3114.82
Midmean - Empirical Distribution Function3114.82
Midmean - Empirical Distribution Function - Averaging3114.82
Midmean - Empirical Distribution Function - Interpolation3112.42857142857
Midmean - Closest Observation3114.82
Midmean - True Basic - Statistics Graphics Toolkit3114.82
Midmean - MS Excel (old versions)3114.82
Number of observations58

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3151.58448275862 & 64.814508040415 & 48.6246764504246 \tabularnewline
Geometric Mean & 3114.33494161013 &  &  \tabularnewline
Harmonic Mean & 3077.8136223509 &  &  \tabularnewline
Quadratic Mean & 3189.34745955323 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 3153.25689655172 & 63.6526232256707 & 49.5385223225181 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 3151.5775862069 & 60.53364066206 & 52.0632420541356 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 3147.05172413793 & 57.75987949798 & 54.4850811928718 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 3144.83103448276 & 56.9488248003392 & 55.2220532295168 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 3137.03793103448 & 55.0944953968579 & 56.9392261139284 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 3136.8 & 54.8231133998737 & 57.2167431849506 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 3128.49655172414 & 52.5333669765169 & 59.5525611964414 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 3129.08965517241 & 51.3270263500255 & 60.9637821960216 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 3127.92586206897 & 50.5263495590182 & 61.9068246443439 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 3121.39137931035 & 47.7439455139545 & 65.377742574669 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 3105.27068965517 & 44.4413755651321 & 69.8734152615095 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 3121.34655172414 & 40.2459863904656 & 77.5567163751661 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 3122.22068965517 & 39.4798814470372 & 79.0838415724138 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 3130.98275862069 & 37.5277651709926 & 83.4311007957598 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 3136.36206896552 & 35.4754174600672 & 88.4094478238616 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 3132.83103448276 & 33.1553222190839 & 94.4895366656858 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 3125.00517241379 & 31.3654750858141 & 99.6320050585544 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 3116.93620689655 & 29.7618772722345 & 104.729153285112 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 3112.77586206897 & 28.652662131982 & 108.638277578909 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 3147.39642857143 & 60.8507114517462 & 51.7232478221273 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 3141.10185185185 & 57.3415118058086 & 54.7788461261613 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 3135.25961538462 & 55.1068933324796 & 56.894145646507 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 3130.7 & 53.6724506537914 & 58.3297382896536 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 3126.43125 & 52.1607267104252 & 59.9384143429722 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 3123.75652173913 & 50.8713841575788 & 61.40498383262 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 3120.89090909091 & 49.2635829047688 & 63.3508714768856 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 3119.39047619048 & 47.8558008490858 & 65.1831213947821 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 3117.6325 & 46.3207113485938 & 67.3053674961459 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 3115.88684210526 & 44.4700588407626 & 70.0670726176135 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 3115 & 42.7686016338422 & 72.8338051982309 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 3116.50882352941 & 41.3679822214897 & 75.3362541794571 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 3115.778125 & 40.5820658324007 & 76.777218238909 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 3114.82 & 39.5783533661068 & 78.7000907083568 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 3112.42857142857 & 38.5988269337963 & 80.6353150775005 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 3108.86923076923 & 37.6524980351108 & 82.567409680766 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 3105.25 & 36.8499916425767 & 84.2673189757844 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 3102.18636363636 & 36.0617737769755 & 86.024231165718 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 3099.81 & 35.1944447619971 & 88.0766842881741 \tabularnewline
Median & 3091.85 &  &  \tabularnewline
Midrange & 3268.85 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3101.86896551724 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3114.82 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3114.82 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3114.82 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3112.42857142857 &  &  \tabularnewline
Midmean - Closest Observation & 3114.82 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3114.82 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3114.82 &  &  \tabularnewline
Number of observations & 58 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48786&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]3151.58448275862[/C][C]64.814508040415[/C][C]48.6246764504246[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3114.33494161013[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3077.8136223509[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3189.34745955323[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]3153.25689655172[/C][C]63.6526232256707[/C][C]49.5385223225181[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]3151.5775862069[/C][C]60.53364066206[/C][C]52.0632420541356[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]3147.05172413793[/C][C]57.75987949798[/C][C]54.4850811928718[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]3144.83103448276[/C][C]56.9488248003392[/C][C]55.2220532295168[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]3137.03793103448[/C][C]55.0944953968579[/C][C]56.9392261139284[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]3136.8[/C][C]54.8231133998737[/C][C]57.2167431849506[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]3128.49655172414[/C][C]52.5333669765169[/C][C]59.5525611964414[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]3129.08965517241[/C][C]51.3270263500255[/C][C]60.9637821960216[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]3127.92586206897[/C][C]50.5263495590182[/C][C]61.9068246443439[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]3121.39137931035[/C][C]47.7439455139545[/C][C]65.377742574669[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]3105.27068965517[/C][C]44.4413755651321[/C][C]69.8734152615095[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]3121.34655172414[/C][C]40.2459863904656[/C][C]77.5567163751661[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]3122.22068965517[/C][C]39.4798814470372[/C][C]79.0838415724138[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]3130.98275862069[/C][C]37.5277651709926[/C][C]83.4311007957598[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]3136.36206896552[/C][C]35.4754174600672[/C][C]88.4094478238616[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]3132.83103448276[/C][C]33.1553222190839[/C][C]94.4895366656858[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]3125.00517241379[/C][C]31.3654750858141[/C][C]99.6320050585544[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]3116.93620689655[/C][C]29.7618772722345[/C][C]104.729153285112[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]3112.77586206897[/C][C]28.652662131982[/C][C]108.638277578909[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]3147.39642857143[/C][C]60.8507114517462[/C][C]51.7232478221273[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]3141.10185185185[/C][C]57.3415118058086[/C][C]54.7788461261613[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]3135.25961538462[/C][C]55.1068933324796[/C][C]56.894145646507[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]3130.7[/C][C]53.6724506537914[/C][C]58.3297382896536[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]3126.43125[/C][C]52.1607267104252[/C][C]59.9384143429722[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]3123.75652173913[/C][C]50.8713841575788[/C][C]61.40498383262[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]3120.89090909091[/C][C]49.2635829047688[/C][C]63.3508714768856[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]3119.39047619048[/C][C]47.8558008490858[/C][C]65.1831213947821[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]3117.6325[/C][C]46.3207113485938[/C][C]67.3053674961459[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]3115.88684210526[/C][C]44.4700588407626[/C][C]70.0670726176135[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]3115[/C][C]42.7686016338422[/C][C]72.8338051982309[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]3116.50882352941[/C][C]41.3679822214897[/C][C]75.3362541794571[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]3115.778125[/C][C]40.5820658324007[/C][C]76.777218238909[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]3114.82[/C][C]39.5783533661068[/C][C]78.7000907083568[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]3112.42857142857[/C][C]38.5988269337963[/C][C]80.6353150775005[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]3108.86923076923[/C][C]37.6524980351108[/C][C]82.567409680766[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]3105.25[/C][C]36.8499916425767[/C][C]84.2673189757844[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]3102.18636363636[/C][C]36.0617737769755[/C][C]86.024231165718[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]3099.81[/C][C]35.1944447619971[/C][C]88.0766842881741[/C][/ROW]
[ROW][C]Median[/C][C]3091.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3268.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3101.86896551724[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3114.82[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3114.82[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3114.82[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3112.42857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3114.82[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3114.82[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3114.82[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]58[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48786&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48786&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 Mean3151.5844827586264.81450804041548.6246764504246
Geometric Mean3114.33494161013
Harmonic Mean3077.8136223509
Quadratic Mean3189.34745955323
Winsorized Mean ( 1 / 19 )3153.2568965517263.652623225670749.5385223225181
Winsorized Mean ( 2 / 19 )3151.577586206960.5336406620652.0632420541356
Winsorized Mean ( 3 / 19 )3147.0517241379357.7598794979854.4850811928718
Winsorized Mean ( 4 / 19 )3144.8310344827656.948824800339255.2220532295168
Winsorized Mean ( 5 / 19 )3137.0379310344855.094495396857956.9392261139284
Winsorized Mean ( 6 / 19 )3136.854.823113399873757.2167431849506
Winsorized Mean ( 7 / 19 )3128.4965517241452.533366976516959.5525611964414
Winsorized Mean ( 8 / 19 )3129.0896551724151.327026350025560.9637821960216
Winsorized Mean ( 9 / 19 )3127.9258620689750.526349559018261.9068246443439
Winsorized Mean ( 10 / 19 )3121.3913793103547.743945513954565.377742574669
Winsorized Mean ( 11 / 19 )3105.2706896551744.441375565132169.8734152615095
Winsorized Mean ( 12 / 19 )3121.3465517241440.245986390465677.5567163751661
Winsorized Mean ( 13 / 19 )3122.2206896551739.479881447037279.0838415724138
Winsorized Mean ( 14 / 19 )3130.9827586206937.527765170992683.4311007957598
Winsorized Mean ( 15 / 19 )3136.3620689655235.475417460067288.4094478238616
Winsorized Mean ( 16 / 19 )3132.8310344827633.155322219083994.4895366656858
Winsorized Mean ( 17 / 19 )3125.0051724137931.365475085814199.6320050585544
Winsorized Mean ( 18 / 19 )3116.9362068965529.7618772722345104.729153285112
Winsorized Mean ( 19 / 19 )3112.7758620689728.652662131982108.638277578909
Trimmed Mean ( 1 / 19 )3147.3964285714360.850711451746251.7232478221273
Trimmed Mean ( 2 / 19 )3141.1018518518557.341511805808654.7788461261613
Trimmed Mean ( 3 / 19 )3135.2596153846255.106893332479656.894145646507
Trimmed Mean ( 4 / 19 )3130.753.672450653791458.3297382896536
Trimmed Mean ( 5 / 19 )3126.4312552.160726710425259.9384143429722
Trimmed Mean ( 6 / 19 )3123.7565217391350.871384157578861.40498383262
Trimmed Mean ( 7 / 19 )3120.8909090909149.263582904768863.3508714768856
Trimmed Mean ( 8 / 19 )3119.3904761904847.855800849085865.1831213947821
Trimmed Mean ( 9 / 19 )3117.632546.320711348593867.3053674961459
Trimmed Mean ( 10 / 19 )3115.8868421052644.470058840762670.0670726176135
Trimmed Mean ( 11 / 19 )311542.768601633842272.8338051982309
Trimmed Mean ( 12 / 19 )3116.5088235294141.367982221489775.3362541794571
Trimmed Mean ( 13 / 19 )3115.77812540.582065832400776.777218238909
Trimmed Mean ( 14 / 19 )3114.8239.578353366106878.7000907083568
Trimmed Mean ( 15 / 19 )3112.4285714285738.598826933796380.6353150775005
Trimmed Mean ( 16 / 19 )3108.8692307692337.652498035110882.567409680766
Trimmed Mean ( 17 / 19 )3105.2536.849991642576784.2673189757844
Trimmed Mean ( 18 / 19 )3102.1863636363636.061773776975586.024231165718
Trimmed Mean ( 19 / 19 )3099.8135.194444761997188.0766842881741
Median3091.85
Midrange3268.85
Midmean - Weighted Average at Xnp3101.86896551724
Midmean - Weighted Average at X(n+1)p3114.82
Midmean - Empirical Distribution Function3114.82
Midmean - Empirical Distribution Function - Averaging3114.82
Midmean - Empirical Distribution Function - Interpolation3112.42857142857
Midmean - Closest Observation3114.82
Midmean - True Basic - Statistics Graphics Toolkit3114.82
Midmean - MS Excel (old versions)3114.82
Number of observations58



Parameters (Session):
par1 = 10 ; par2 = grey ; par3 = FALSE ; par4 = Unknown ;
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')