Free Statistics

of Irreproducible Research!

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, 16 Dec 2008 14:44:07 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/16/t12294639598f3symej623x322.htm/, Retrieved Wed, 15 May 2024 14:46:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34221, Retrieved Wed, 15 May 2024 14:46:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central tendency:...] [2008-12-16 21:44:07] [e515c0250d6233b5d2604259ab52cebe] [Current]
Feedback Forum

Post a new message
Dataseries X:
101,3
91,5
152,6
86,6
86,6
98,5
86,7
89,1
111
92,6
85,1
116,1
98,3
97,7
177,9
94,2
83,8
109,5
102,3
102,5
250
85,3
88,2
104,7
99,4
113,8
166,6
89,2
93,2
115
97,2
112,5
121,8
100,2
93,8
113,6
110,7
127,6
185,9
105,9
108
125,2
106,2
123,3
145,2
114,3
108,4
120,9
126,3
141,3
208,2
131,6
119,8
122,5
137,6
141
154,1
127
106,1
129,9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34221&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34221&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34221&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean117.2566666666674.0311109112635129.0879286747071
Geometric Mean113.985099478859
Harmonic Mean111.306293789856
Quadratic Mean121.275996525831
Winsorized Mean ( 1 / 20 )116.5816666666673.6846662657074131.6396813876126
Winsorized Mean ( 2 / 20 )115.8453.3960058169082434.1121323830554
Winsorized Mean ( 3 / 20 )115.513.2510647538765435.5298982778694
Winsorized Mean ( 4 / 20 )114.7566666666673.0184183820653838.0188072496906
Winsorized Mean ( 5 / 20 )113.7233333333332.7340222709001141.5956133729272
Winsorized Mean ( 6 / 20 )113.7233333333332.6720391149859842.5605047080046
Winsorized Mean ( 7 / 20 )112.9652.4518030088794446.0742562069164
Winsorized Mean ( 8 / 20 )112.4583333333332.3371747535486648.1172121008845
Winsorized Mean ( 9 / 20 )112.7583333333332.2712415923890949.6461203031794
Winsorized Mean ( 10 / 20 )112.3752.1254439549538252.8713070688528
Winsorized Mean ( 11 / 20 )111.3851.8972487142216858.7086970543523
Winsorized Mean ( 12 / 20 )111.1651.8173579646705361.1684666208031
Winsorized Mean ( 13 / 20 )110.7533333333331.7182642448313764.4565198085716
Winsorized Mean ( 14 / 20 )111.3133333333331.5847373495451370.2408720065089
Winsorized Mean ( 15 / 20 )111.2633333333331.5367585790618372.4013093854063
Winsorized Mean ( 16 / 20 )111.131.4646981525099675.8722879588284
Winsorized Mean ( 17 / 20 )110.6483333333331.3702313130359180.7515725853463
Winsorized Mean ( 18 / 20 )110.6783333333331.2925844379344185.625611824788
Winsorized Mean ( 19 / 20 )110.711.2211222494175690.6625033265962
Winsorized Mean ( 20 / 20 )110.7766666666671.1220803083807198.7243656619643
Trimmed Mean ( 1 / 20 )115.5448275862073.4176149266904433.8086150911386
Trimmed Mean ( 2 / 20 )114.4339285714293.0702492356058737.2718694118808
Trimmed Mean ( 3 / 20 )113.652.8375560467871440.0520723207147
Trimmed Mean ( 4 / 20 )112.9346153846152.6166350373462643.1602473301556
Trimmed Mean ( 5 / 20 )112.3882.4385704075652746.0876584294365
Trimmed Mean ( 6 / 20 )112.0541666666672.3220458207656548.2566561196105
Trimmed Mean ( 7 / 20 )111.6913043478262.1918906891336350.9566033112598
Trimmed Mean ( 8 / 20 )111.4431818181822.0956473509460553.178404166079
Trimmed Mean ( 9 / 20 )111.2619047619052.0048719764751155.4957653493274
Trimmed Mean ( 10 / 20 )111.01251.9021283204442158.3622560091399
Trimmed Mean ( 11 / 20 )110.7973684210531.8081036443329661.278217522717
Trimmed Mean ( 12 / 20 )110.7083333333331.7488879686772863.3021298768866
Trimmed Mean ( 13 / 20 )110.6411764705881.6886647239338165.5199193199497
Trimmed Mean ( 14 / 20 )110.6251.6318280862964167.792067638126
Trimmed Mean ( 15 / 20 )110.5266666666671.5876313111288269.617338667931
Trimmed Mean ( 16 / 20 )110.4214285714291.5341212359987271.9769898104197
Trimmed Mean ( 17 / 20 )110.3192307692311.4747413773870774.8058150810775
Trimmed Mean ( 18 / 20 )110.2708333333331.4151161058355577.9235236448845
Trimmed Mean ( 19 / 20 )110.2090909090911.3464706003209081.8503507487092
Trimmed Mean ( 20 / 20 )110.131.2596386282121687.42983704486
Median110.1
Midrange166.9
Midmean - Weighted Average at Xnp110.096774193548
Midmean - Weighted Average at X(n+1)p110.526666666667
Midmean - Empirical Distribution Function110.096774193548
Midmean - Empirical Distribution Function - Averaging110.526666666667
Midmean - Empirical Distribution Function - Interpolation110.526666666667
Midmean - Closest Observation110.096774193548
Midmean - True Basic - Statistics Graphics Toolkit110.526666666667
Midmean - MS Excel (old versions)110.625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 117.256666666667 & 4.03111091126351 & 29.0879286747071 \tabularnewline
Geometric Mean & 113.985099478859 &  &  \tabularnewline
Harmonic Mean & 111.306293789856 &  &  \tabularnewline
Quadratic Mean & 121.275996525831 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 116.581666666667 & 3.68466626570741 & 31.6396813876126 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 115.845 & 3.39600581690824 & 34.1121323830554 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 115.51 & 3.25106475387654 & 35.5298982778694 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 114.756666666667 & 3.01841838206538 & 38.0188072496906 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 113.723333333333 & 2.73402227090011 & 41.5956133729272 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 113.723333333333 & 2.67203911498598 & 42.5605047080046 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 112.965 & 2.45180300887944 & 46.0742562069164 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 112.458333333333 & 2.33717475354866 & 48.1172121008845 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 112.758333333333 & 2.27124159238909 & 49.6461203031794 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 112.375 & 2.12544395495382 & 52.8713070688528 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 111.385 & 1.89724871422168 & 58.7086970543523 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 111.165 & 1.81735796467053 & 61.1684666208031 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 110.753333333333 & 1.71826424483137 & 64.4565198085716 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 111.313333333333 & 1.58473734954513 & 70.2408720065089 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 111.263333333333 & 1.53675857906183 & 72.4013093854063 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 111.13 & 1.46469815250996 & 75.8722879588284 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 110.648333333333 & 1.37023131303591 & 80.7515725853463 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 110.678333333333 & 1.29258443793441 & 85.625611824788 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 110.71 & 1.22112224941756 & 90.6625033265962 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 110.776666666667 & 1.12208030838071 & 98.7243656619643 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 115.544827586207 & 3.41761492669044 & 33.8086150911386 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 114.433928571429 & 3.07024923560587 & 37.2718694118808 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 113.65 & 2.83755604678714 & 40.0520723207147 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 112.934615384615 & 2.61663503734626 & 43.1602473301556 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 112.388 & 2.43857040756527 & 46.0876584294365 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 112.054166666667 & 2.32204582076565 & 48.2566561196105 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 111.691304347826 & 2.19189068913363 & 50.9566033112598 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 111.443181818182 & 2.09564735094605 & 53.178404166079 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 111.261904761905 & 2.00487197647511 & 55.4957653493274 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 111.0125 & 1.90212832044421 & 58.3622560091399 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 110.797368421053 & 1.80810364433296 & 61.278217522717 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 110.708333333333 & 1.74888796867728 & 63.3021298768866 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 110.641176470588 & 1.68866472393381 & 65.5199193199497 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 110.625 & 1.63182808629641 & 67.792067638126 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 110.526666666667 & 1.58763131112882 & 69.617338667931 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 110.421428571429 & 1.53412123599872 & 71.9769898104197 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 110.319230769231 & 1.47474137738707 & 74.8058150810775 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 110.270833333333 & 1.41511610583555 & 77.9235236448845 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 110.209090909091 & 1.34647060032090 & 81.8503507487092 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 110.13 & 1.25963862821216 & 87.42983704486 \tabularnewline
Median & 110.1 &  &  \tabularnewline
Midrange & 166.9 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 110.096774193548 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 110.526666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 110.096774193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 110.526666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 110.526666666667 &  &  \tabularnewline
Midmean - Closest Observation & 110.096774193548 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 110.526666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 110.625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34221&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]117.256666666667[/C][C]4.03111091126351[/C][C]29.0879286747071[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]113.985099478859[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]111.306293789856[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]121.275996525831[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]116.581666666667[/C][C]3.68466626570741[/C][C]31.6396813876126[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]115.845[/C][C]3.39600581690824[/C][C]34.1121323830554[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]115.51[/C][C]3.25106475387654[/C][C]35.5298982778694[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]114.756666666667[/C][C]3.01841838206538[/C][C]38.0188072496906[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]113.723333333333[/C][C]2.73402227090011[/C][C]41.5956133729272[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]113.723333333333[/C][C]2.67203911498598[/C][C]42.5605047080046[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]112.965[/C][C]2.45180300887944[/C][C]46.0742562069164[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]112.458333333333[/C][C]2.33717475354866[/C][C]48.1172121008845[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]112.758333333333[/C][C]2.27124159238909[/C][C]49.6461203031794[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]112.375[/C][C]2.12544395495382[/C][C]52.8713070688528[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]111.385[/C][C]1.89724871422168[/C][C]58.7086970543523[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]111.165[/C][C]1.81735796467053[/C][C]61.1684666208031[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]110.753333333333[/C][C]1.71826424483137[/C][C]64.4565198085716[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]111.313333333333[/C][C]1.58473734954513[/C][C]70.2408720065089[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]111.263333333333[/C][C]1.53675857906183[/C][C]72.4013093854063[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]111.13[/C][C]1.46469815250996[/C][C]75.8722879588284[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]110.648333333333[/C][C]1.37023131303591[/C][C]80.7515725853463[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]110.678333333333[/C][C]1.29258443793441[/C][C]85.625611824788[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]110.71[/C][C]1.22112224941756[/C][C]90.6625033265962[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]110.776666666667[/C][C]1.12208030838071[/C][C]98.7243656619643[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]115.544827586207[/C][C]3.41761492669044[/C][C]33.8086150911386[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]114.433928571429[/C][C]3.07024923560587[/C][C]37.2718694118808[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]113.65[/C][C]2.83755604678714[/C][C]40.0520723207147[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]112.934615384615[/C][C]2.61663503734626[/C][C]43.1602473301556[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]112.388[/C][C]2.43857040756527[/C][C]46.0876584294365[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]112.054166666667[/C][C]2.32204582076565[/C][C]48.2566561196105[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]111.691304347826[/C][C]2.19189068913363[/C][C]50.9566033112598[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]111.443181818182[/C][C]2.09564735094605[/C][C]53.178404166079[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]111.261904761905[/C][C]2.00487197647511[/C][C]55.4957653493274[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]111.0125[/C][C]1.90212832044421[/C][C]58.3622560091399[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]110.797368421053[/C][C]1.80810364433296[/C][C]61.278217522717[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]110.708333333333[/C][C]1.74888796867728[/C][C]63.3021298768866[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]110.641176470588[/C][C]1.68866472393381[/C][C]65.5199193199497[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]110.625[/C][C]1.63182808629641[/C][C]67.792067638126[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]110.526666666667[/C][C]1.58763131112882[/C][C]69.617338667931[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]110.421428571429[/C][C]1.53412123599872[/C][C]71.9769898104197[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]110.319230769231[/C][C]1.47474137738707[/C][C]74.8058150810775[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]110.270833333333[/C][C]1.41511610583555[/C][C]77.9235236448845[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]110.209090909091[/C][C]1.34647060032090[/C][C]81.8503507487092[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]110.13[/C][C]1.25963862821216[/C][C]87.42983704486[/C][/ROW]
[ROW][C]Median[/C][C]110.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]166.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]110.096774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]110.526666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]110.096774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]110.526666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]110.526666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]110.096774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]110.526666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]110.625[/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=34221&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34221&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 Mean117.2566666666674.0311109112635129.0879286747071
Geometric Mean113.985099478859
Harmonic Mean111.306293789856
Quadratic Mean121.275996525831
Winsorized Mean ( 1 / 20 )116.5816666666673.6846662657074131.6396813876126
Winsorized Mean ( 2 / 20 )115.8453.3960058169082434.1121323830554
Winsorized Mean ( 3 / 20 )115.513.2510647538765435.5298982778694
Winsorized Mean ( 4 / 20 )114.7566666666673.0184183820653838.0188072496906
Winsorized Mean ( 5 / 20 )113.7233333333332.7340222709001141.5956133729272
Winsorized Mean ( 6 / 20 )113.7233333333332.6720391149859842.5605047080046
Winsorized Mean ( 7 / 20 )112.9652.4518030088794446.0742562069164
Winsorized Mean ( 8 / 20 )112.4583333333332.3371747535486648.1172121008845
Winsorized Mean ( 9 / 20 )112.7583333333332.2712415923890949.6461203031794
Winsorized Mean ( 10 / 20 )112.3752.1254439549538252.8713070688528
Winsorized Mean ( 11 / 20 )111.3851.8972487142216858.7086970543523
Winsorized Mean ( 12 / 20 )111.1651.8173579646705361.1684666208031
Winsorized Mean ( 13 / 20 )110.7533333333331.7182642448313764.4565198085716
Winsorized Mean ( 14 / 20 )111.3133333333331.5847373495451370.2408720065089
Winsorized Mean ( 15 / 20 )111.2633333333331.5367585790618372.4013093854063
Winsorized Mean ( 16 / 20 )111.131.4646981525099675.8722879588284
Winsorized Mean ( 17 / 20 )110.6483333333331.3702313130359180.7515725853463
Winsorized Mean ( 18 / 20 )110.6783333333331.2925844379344185.625611824788
Winsorized Mean ( 19 / 20 )110.711.2211222494175690.6625033265962
Winsorized Mean ( 20 / 20 )110.7766666666671.1220803083807198.7243656619643
Trimmed Mean ( 1 / 20 )115.5448275862073.4176149266904433.8086150911386
Trimmed Mean ( 2 / 20 )114.4339285714293.0702492356058737.2718694118808
Trimmed Mean ( 3 / 20 )113.652.8375560467871440.0520723207147
Trimmed Mean ( 4 / 20 )112.9346153846152.6166350373462643.1602473301556
Trimmed Mean ( 5 / 20 )112.3882.4385704075652746.0876584294365
Trimmed Mean ( 6 / 20 )112.0541666666672.3220458207656548.2566561196105
Trimmed Mean ( 7 / 20 )111.6913043478262.1918906891336350.9566033112598
Trimmed Mean ( 8 / 20 )111.4431818181822.0956473509460553.178404166079
Trimmed Mean ( 9 / 20 )111.2619047619052.0048719764751155.4957653493274
Trimmed Mean ( 10 / 20 )111.01251.9021283204442158.3622560091399
Trimmed Mean ( 11 / 20 )110.7973684210531.8081036443329661.278217522717
Trimmed Mean ( 12 / 20 )110.7083333333331.7488879686772863.3021298768866
Trimmed Mean ( 13 / 20 )110.6411764705881.6886647239338165.5199193199497
Trimmed Mean ( 14 / 20 )110.6251.6318280862964167.792067638126
Trimmed Mean ( 15 / 20 )110.5266666666671.5876313111288269.617338667931
Trimmed Mean ( 16 / 20 )110.4214285714291.5341212359987271.9769898104197
Trimmed Mean ( 17 / 20 )110.3192307692311.4747413773870774.8058150810775
Trimmed Mean ( 18 / 20 )110.2708333333331.4151161058355577.9235236448845
Trimmed Mean ( 19 / 20 )110.2090909090911.3464706003209081.8503507487092
Trimmed Mean ( 20 / 20 )110.131.2596386282121687.42983704486
Median110.1
Midrange166.9
Midmean - Weighted Average at Xnp110.096774193548
Midmean - Weighted Average at X(n+1)p110.526666666667
Midmean - Empirical Distribution Function110.096774193548
Midmean - Empirical Distribution Function - Averaging110.526666666667
Midmean - Empirical Distribution Function - Interpolation110.526666666667
Midmean - Closest Observation110.096774193548
Midmean - True Basic - Statistics Graphics Toolkit110.526666666667
Midmean - MS Excel (old versions)110.625
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')