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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, 17 Nov 2011 18:03:34 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/17/t13215710375fzsajqrju6pdqw.htm/, Retrieved Fri, 19 Apr 2024 05:03:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=145338, Retrieved Fri, 19 Apr 2024 05:03:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central tendency Dow] [2011-11-17 23:03:34] [0956ee981dded61b2e7128dae94e5715] [Current]
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Dataseries X:
10539.51
10723.78
10682.06
10283.19
10377.18
10486.64
10545.38
10554.27
10532.54
10324.31
10695.25
10827.81
10872.48
10971.19
11145.65
11234.68
11333.88
10997.97
11036.89
11257.35
11533.59
11963.12
12185.15
12377.62
12512.89
12631.48
12268.53
12754.80
13407.75
13480.21
13673.28
13239.71
13557.69
13901.28
13200.58
13406.97
12538.12
12419.57
12193.88
12656.63
12812.48
12056.67
11322.38
11530.75
11114.08
9181.73
8614.55
8595.56
8396.20
7690.50
7235.47
7992.12
8398.37
8593.00
8679.75
9374.63
9634.97
9857.34
10238.83
10433.44
10471.24




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=145338&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=145338&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=145338&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean11041.7855737705209.60603153896852.678758777596
Geometric Mean10916.0685236883
Harmonic Mean10783.6877337066
Quadratic Mean11160.5156675029
Winsorized Mean ( 1 / 20 )11045.5073770492206.64589580421653.4513755236354
Winsorized Mean ( 2 / 20 )11051.6067213115203.27571645679454.3675698895419
Winsorized Mean ( 3 / 20 )11067.6690163934197.7636878786755.9641111829568
Winsorized Mean ( 4 / 20 )11063.0598360656196.77675161734956.2213764844473
Winsorized Mean ( 5 / 20 )11078.9491803279193.25273054890157.3288105625209
Winsorized Mean ( 6 / 20 )11062.7491803279189.97520819362958.2325940606541
Winsorized Mean ( 7 / 20 )11060.4380327869188.65060718711458.6292204287292
Winsorized Mean ( 8 / 20 )11018.0904918033177.67821185564762.0114890662838
Winsorized Mean ( 9 / 20 )11083.6429508197160.76049249482168.9450671543368
Winsorized Mean ( 10 / 20 )11099.1724590164151.87700133645673.0800079100073
Winsorized Mean ( 11 / 20 )11141.5837704918142.50644734396878.1830154224485
Winsorized Mean ( 12 / 20 )11166.9627868852131.82964945972584.7075209002728
Winsorized Mean ( 13 / 20 )11242.8870491803118.35239384766394.9950117920857
Winsorized Mean ( 14 / 20 )11231.6503278689113.13087840427599.2801477924745
Winsorized Mean ( 15 / 20 )11231.4462295082109.929932749326102.169135817807
Winsorized Mean ( 16 / 20 )11216.7103.114855426714108.778700736985
Winsorized Mean ( 17 / 20 )11211.574918032897.4917791643182115.000208367684
Winsorized Mean ( 18 / 20 )11220.152950819795.5884930457168117.379745127412
Winsorized Mean ( 19 / 20 )11184.931311475488.2972830326899126.67356148812
Winsorized Mean ( 20 / 20 )11169.308360655781.302632144118137.379418920373
Trimmed Mean ( 1 / 20 )11057.8333898305200.90460146586655.0402196323475
Trimmed Mean ( 2 / 20 )11071.0243859649193.83642098623557.1152951010744
Trimmed Mean ( 3 / 20 )11081.7923636364187.36348129907659.1459567616979
Trimmed Mean ( 4 / 20 )11087.210754717182.00593762022360.916753044902
Trimmed Mean ( 5 / 20 )11094.4323529412175.65370779018163.1608207564483
Trimmed Mean ( 6 / 20 )11098.2873469388168.87048675564965.7207044295295
Trimmed Mean ( 7 / 20 )11105.9746808511161.2572580941868.8711615967376
Trimmed Mean ( 8 / 20 )11114.7928888889151.79460353213273.2225825573314
Trimmed Mean ( 9 / 20 )11131.9406976744142.74277343000277.9860193982658
Trimmed Mean ( 10 / 20 )11139.9248780488136.05626558215281.8773382496108
Trimmed Mean ( 11 / 20 )11146.298974359129.72591051344385.9219174507465
Trimmed Mean ( 12 / 20 )11147.0056756757123.90784969543889.96206215405
Trimmed Mean ( 13 / 20 )11144.1071428571119.00028980020693.6477311237426
Trimmed Mean ( 14 / 20 )11130.0615151515115.76519401399996.1434186669756
Trimmed Mean ( 15 / 20 )11115.7829032258112.47807383003598.8262202998145
Trimmed Mean ( 16 / 20 )11099.5634482759108.388518638867102.405343182683
Trimmed Mean ( 17 / 20 )11083.0233333333104.347971779666106.212158648713
Trimmed Mean ( 18 / 20 )11064.572499.8269710069712110.837505018832
Trimmed Mean ( 19 / 20 )11041.648695652292.8195854760534118.958177188809
Trimmed Mean ( 20 / 20 )11019.743333333384.6709447728686130.147872601327
Median10997.97
Midrange10568.375
Midmean - Weighted Average at Xnp11073.7216666667
Midmean - Weighted Average at X(n+1)p11115.7829032258
Midmean - Empirical Distribution Function11115.7829032258
Midmean - Empirical Distribution Function - Averaging11115.7829032258
Midmean - Empirical Distribution Function - Interpolation11115.7829032258
Midmean - Closest Observation11089.764375
Midmean - True Basic - Statistics Graphics Toolkit11115.7829032258
Midmean - MS Excel (old versions)11115.7829032258
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 11041.7855737705 & 209.606031538968 & 52.678758777596 \tabularnewline
Geometric Mean & 10916.0685236883 &  &  \tabularnewline
Harmonic Mean & 10783.6877337066 &  &  \tabularnewline
Quadratic Mean & 11160.5156675029 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 11045.5073770492 & 206.645895804216 & 53.4513755236354 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 11051.6067213115 & 203.275716456794 & 54.3675698895419 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 11067.6690163934 & 197.76368787867 & 55.9641111829568 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 11063.0598360656 & 196.776751617349 & 56.2213764844473 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 11078.9491803279 & 193.252730548901 & 57.3288105625209 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 11062.7491803279 & 189.975208193629 & 58.2325940606541 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 11060.4380327869 & 188.650607187114 & 58.6292204287292 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 11018.0904918033 & 177.678211855647 & 62.0114890662838 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 11083.6429508197 & 160.760492494821 & 68.9450671543368 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 11099.1724590164 & 151.877001336456 & 73.0800079100073 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 11141.5837704918 & 142.506447343968 & 78.1830154224485 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 11166.9627868852 & 131.829649459725 & 84.7075209002728 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 11242.8870491803 & 118.352393847663 & 94.9950117920857 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 11231.6503278689 & 113.130878404275 & 99.2801477924745 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 11231.4462295082 & 109.929932749326 & 102.169135817807 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 11216.7 & 103.114855426714 & 108.778700736985 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 11211.5749180328 & 97.4917791643182 & 115.000208367684 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 11220.1529508197 & 95.5884930457168 & 117.379745127412 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 11184.9313114754 & 88.2972830326899 & 126.67356148812 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 11169.3083606557 & 81.302632144118 & 137.379418920373 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 11057.8333898305 & 200.904601465866 & 55.0402196323475 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 11071.0243859649 & 193.836420986235 & 57.1152951010744 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 11081.7923636364 & 187.363481299076 & 59.1459567616979 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 11087.210754717 & 182.005937620223 & 60.916753044902 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 11094.4323529412 & 175.653707790181 & 63.1608207564483 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 11098.2873469388 & 168.870486755649 & 65.7207044295295 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 11105.9746808511 & 161.25725809418 & 68.8711615967376 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 11114.7928888889 & 151.794603532132 & 73.2225825573314 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 11131.9406976744 & 142.742773430002 & 77.9860193982658 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 11139.9248780488 & 136.056265582152 & 81.8773382496108 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 11146.298974359 & 129.725910513443 & 85.9219174507465 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 11147.0056756757 & 123.907849695438 & 89.96206215405 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 11144.1071428571 & 119.000289800206 & 93.6477311237426 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 11130.0615151515 & 115.765194013999 & 96.1434186669756 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 11115.7829032258 & 112.478073830035 & 98.8262202998145 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 11099.5634482759 & 108.388518638867 & 102.405343182683 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 11083.0233333333 & 104.347971779666 & 106.212158648713 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 11064.5724 & 99.8269710069712 & 110.837505018832 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 11041.6486956522 & 92.8195854760534 & 118.958177188809 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 11019.7433333333 & 84.6709447728686 & 130.147872601327 \tabularnewline
Median & 10997.97 &  &  \tabularnewline
Midrange & 10568.375 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 11073.7216666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 11115.7829032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 11115.7829032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 11115.7829032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 11115.7829032258 &  &  \tabularnewline
Midmean - Closest Observation & 11089.764375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 11115.7829032258 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 11115.7829032258 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=145338&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]11041.7855737705[/C][C]209.606031538968[/C][C]52.678758777596[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]10916.0685236883[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]10783.6877337066[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]11160.5156675029[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]11045.5073770492[/C][C]206.645895804216[/C][C]53.4513755236354[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]11051.6067213115[/C][C]203.275716456794[/C][C]54.3675698895419[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]11067.6690163934[/C][C]197.76368787867[/C][C]55.9641111829568[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]11063.0598360656[/C][C]196.776751617349[/C][C]56.2213764844473[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]11078.9491803279[/C][C]193.252730548901[/C][C]57.3288105625209[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]11062.7491803279[/C][C]189.975208193629[/C][C]58.2325940606541[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]11060.4380327869[/C][C]188.650607187114[/C][C]58.6292204287292[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]11018.0904918033[/C][C]177.678211855647[/C][C]62.0114890662838[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]11083.6429508197[/C][C]160.760492494821[/C][C]68.9450671543368[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]11099.1724590164[/C][C]151.877001336456[/C][C]73.0800079100073[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]11141.5837704918[/C][C]142.506447343968[/C][C]78.1830154224485[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]11166.9627868852[/C][C]131.829649459725[/C][C]84.7075209002728[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]11242.8870491803[/C][C]118.352393847663[/C][C]94.9950117920857[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]11231.6503278689[/C][C]113.130878404275[/C][C]99.2801477924745[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]11231.4462295082[/C][C]109.929932749326[/C][C]102.169135817807[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]11216.7[/C][C]103.114855426714[/C][C]108.778700736985[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]11211.5749180328[/C][C]97.4917791643182[/C][C]115.000208367684[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]11220.1529508197[/C][C]95.5884930457168[/C][C]117.379745127412[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]11184.9313114754[/C][C]88.2972830326899[/C][C]126.67356148812[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]11169.3083606557[/C][C]81.302632144118[/C][C]137.379418920373[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]11057.8333898305[/C][C]200.904601465866[/C][C]55.0402196323475[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]11071.0243859649[/C][C]193.836420986235[/C][C]57.1152951010744[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]11081.7923636364[/C][C]187.363481299076[/C][C]59.1459567616979[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]11087.210754717[/C][C]182.005937620223[/C][C]60.916753044902[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]11094.4323529412[/C][C]175.653707790181[/C][C]63.1608207564483[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]11098.2873469388[/C][C]168.870486755649[/C][C]65.7207044295295[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]11105.9746808511[/C][C]161.25725809418[/C][C]68.8711615967376[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]11114.7928888889[/C][C]151.794603532132[/C][C]73.2225825573314[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]11131.9406976744[/C][C]142.742773430002[/C][C]77.9860193982658[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]11139.9248780488[/C][C]136.056265582152[/C][C]81.8773382496108[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]11146.298974359[/C][C]129.725910513443[/C][C]85.9219174507465[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]11147.0056756757[/C][C]123.907849695438[/C][C]89.96206215405[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]11144.1071428571[/C][C]119.000289800206[/C][C]93.6477311237426[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]11130.0615151515[/C][C]115.765194013999[/C][C]96.1434186669756[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]11115.7829032258[/C][C]112.478073830035[/C][C]98.8262202998145[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]11099.5634482759[/C][C]108.388518638867[/C][C]102.405343182683[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]11083.0233333333[/C][C]104.347971779666[/C][C]106.212158648713[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]11064.5724[/C][C]99.8269710069712[/C][C]110.837505018832[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]11041.6486956522[/C][C]92.8195854760534[/C][C]118.958177188809[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]11019.7433333333[/C][C]84.6709447728686[/C][C]130.147872601327[/C][/ROW]
[ROW][C]Median[/C][C]10997.97[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]10568.375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]11073.7216666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]11115.7829032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]11115.7829032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]11115.7829032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]11115.7829032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]11089.764375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]11115.7829032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]11115.7829032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=145338&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=145338&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 Mean11041.7855737705209.60603153896852.678758777596
Geometric Mean10916.0685236883
Harmonic Mean10783.6877337066
Quadratic Mean11160.5156675029
Winsorized Mean ( 1 / 20 )11045.5073770492206.64589580421653.4513755236354
Winsorized Mean ( 2 / 20 )11051.6067213115203.27571645679454.3675698895419
Winsorized Mean ( 3 / 20 )11067.6690163934197.7636878786755.9641111829568
Winsorized Mean ( 4 / 20 )11063.0598360656196.77675161734956.2213764844473
Winsorized Mean ( 5 / 20 )11078.9491803279193.25273054890157.3288105625209
Winsorized Mean ( 6 / 20 )11062.7491803279189.97520819362958.2325940606541
Winsorized Mean ( 7 / 20 )11060.4380327869188.65060718711458.6292204287292
Winsorized Mean ( 8 / 20 )11018.0904918033177.67821185564762.0114890662838
Winsorized Mean ( 9 / 20 )11083.6429508197160.76049249482168.9450671543368
Winsorized Mean ( 10 / 20 )11099.1724590164151.87700133645673.0800079100073
Winsorized Mean ( 11 / 20 )11141.5837704918142.50644734396878.1830154224485
Winsorized Mean ( 12 / 20 )11166.9627868852131.82964945972584.7075209002728
Winsorized Mean ( 13 / 20 )11242.8870491803118.35239384766394.9950117920857
Winsorized Mean ( 14 / 20 )11231.6503278689113.13087840427599.2801477924745
Winsorized Mean ( 15 / 20 )11231.4462295082109.929932749326102.169135817807
Winsorized Mean ( 16 / 20 )11216.7103.114855426714108.778700736985
Winsorized Mean ( 17 / 20 )11211.574918032897.4917791643182115.000208367684
Winsorized Mean ( 18 / 20 )11220.152950819795.5884930457168117.379745127412
Winsorized Mean ( 19 / 20 )11184.931311475488.2972830326899126.67356148812
Winsorized Mean ( 20 / 20 )11169.308360655781.302632144118137.379418920373
Trimmed Mean ( 1 / 20 )11057.8333898305200.90460146586655.0402196323475
Trimmed Mean ( 2 / 20 )11071.0243859649193.83642098623557.1152951010744
Trimmed Mean ( 3 / 20 )11081.7923636364187.36348129907659.1459567616979
Trimmed Mean ( 4 / 20 )11087.210754717182.00593762022360.916753044902
Trimmed Mean ( 5 / 20 )11094.4323529412175.65370779018163.1608207564483
Trimmed Mean ( 6 / 20 )11098.2873469388168.87048675564965.7207044295295
Trimmed Mean ( 7 / 20 )11105.9746808511161.2572580941868.8711615967376
Trimmed Mean ( 8 / 20 )11114.7928888889151.79460353213273.2225825573314
Trimmed Mean ( 9 / 20 )11131.9406976744142.74277343000277.9860193982658
Trimmed Mean ( 10 / 20 )11139.9248780488136.05626558215281.8773382496108
Trimmed Mean ( 11 / 20 )11146.298974359129.72591051344385.9219174507465
Trimmed Mean ( 12 / 20 )11147.0056756757123.90784969543889.96206215405
Trimmed Mean ( 13 / 20 )11144.1071428571119.00028980020693.6477311237426
Trimmed Mean ( 14 / 20 )11130.0615151515115.76519401399996.1434186669756
Trimmed Mean ( 15 / 20 )11115.7829032258112.47807383003598.8262202998145
Trimmed Mean ( 16 / 20 )11099.5634482759108.388518638867102.405343182683
Trimmed Mean ( 17 / 20 )11083.0233333333104.347971779666106.212158648713
Trimmed Mean ( 18 / 20 )11064.572499.8269710069712110.837505018832
Trimmed Mean ( 19 / 20 )11041.648695652292.8195854760534118.958177188809
Trimmed Mean ( 20 / 20 )11019.743333333384.6709447728686130.147872601327
Median10997.97
Midrange10568.375
Midmean - Weighted Average at Xnp11073.7216666667
Midmean - Weighted Average at X(n+1)p11115.7829032258
Midmean - Empirical Distribution Function11115.7829032258
Midmean - Empirical Distribution Function - Averaging11115.7829032258
Midmean - Empirical Distribution Function - Interpolation11115.7829032258
Midmean - Closest Observation11089.764375
Midmean - True Basic - Statistics Graphics Toolkit11115.7829032258
Midmean - MS Excel (old versions)11115.7829032258
Number of observations61



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')