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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 computationMon, 28 Dec 2009 05:48:47 -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/2009/Dec/28/t126200457497bc988k2zdaag7.htm/, Retrieved Sun, 05 May 2024 10:55:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70950, Retrieved Sun, 05 May 2024 10:55:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsPaper
Estimated Impact140
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [SHW_WS3_Yt=c+Xt] [2009-10-16 08:10:06] [8b1aef4e7013bd33fbc2a5833375c5f5]
- RM D    [Central Tendency] [Basismodel] [2009-12-28 12:48:47] [5b5bced41faf164488f2c271c918b21f] [Current]
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Dataseries X:
2215
1878
2882
2395
2403
2027
2367
2320
1735
2307
2205
1960
2373
1969
2746
2325
2458
2310
2578
2254
1867
2116
2055
2038
2189
1729
2943
2428
2030
2650
2132
2605
1835
2095
2217
2075
1854
1994
2747
2418
2252
2397
2228
2414
1800
1929
2135
2017
1866
1757
2832
1896
2315
2333
1916
2329
1507
1983
2061
1533




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70950&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]2 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=70950&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70950&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2187.0666666666741.018811081302053.3186264792453
Geometric Mean2164.43039160004
Harmonic Mean2141.77464820376
Quadratic Mean2209.64491114146
Winsorized Mean ( 1 / 20 )2186.4833333333340.592333831813253.8644400785779
Winsorized Mean ( 2 / 20 )2191.3538.554267462215256.8380660363374
Winsorized Mean ( 3 / 20 )2187.437.354003559470158.5586494501858
Winsorized Mean ( 4 / 20 )2188.837.04159213671359.0903326164162
Winsorized Mean ( 5 / 20 )2184.3833333333334.406715706201663.4871212929983
Winsorized Mean ( 6 / 20 )2183.3833333333332.751832584830866.6644630549492
Winsorized Mean ( 7 / 20 )2182.4531.68004259577468.890374544229
Winsorized Mean ( 8 / 20 )2168.0528.295379281793876.6220511981261
Winsorized Mean ( 9 / 20 )2163.727.510596828369778.6496931890888
Winsorized Mean ( 10 / 20 )2163.8666666666726.908838220702680.4147190941105
Winsorized Mean ( 11 / 20 )2166.4333333333326.205622878175382.670552934561
Winsorized Mean ( 12 / 20 )2168.2333333333325.165737252266186.158148740033
Winsorized Mean ( 13 / 20 )2169.7524.486715238345988.6092715531807
Winsorized Mean ( 14 / 20 )2176.5166666666723.238185646217393.6612134786417
Winsorized Mean ( 15 / 20 )2173.2666666666722.022264884864498.6849753206047
Winsorized Mean ( 16 / 20 )2175.421.1959408756611102.632858468575
Winsorized Mean ( 17 / 20 )2168.8833333333319.2817511521981112.483732219834
Winsorized Mean ( 18 / 20 )2174.5833333333318.0672518251183120.360492806664
Winsorized Mean ( 19 / 20 )2176.4833333333317.4195567034262124.944817505330
Winsorized Mean ( 20 / 20 )2175.8166666666717.0343039017213127.731469346793
Trimmed Mean ( 1 / 20 )2185.7586206896638.585770068138656.6467538895771
Trimmed Mean ( 2 / 20 )2184.9821428571436.08835199959160.5453566536346
Trimmed Mean ( 3 / 20 )2181.4444444444434.386249615075363.4394407317999
Trimmed Mean ( 4 / 20 )2179.1538461538532.86605414090566.3040910482064
Trimmed Mean ( 5 / 20 )2176.2631.067297722124270.0498646346768
Trimmed Mean ( 6 / 20 )2174.2291666666729.763283576850373.0507156931358
Trimmed Mean ( 7 / 20 )2172.2391304347828.637855167282275.8520188661508
Trimmed Mean ( 8 / 20 )2170.2527.507160801304878.8976374434492
Trimmed Mean ( 9 / 20 )2170.6428571428627.009221581520880.3667314361985
Trimmed Mean ( 10 / 20 )2171.826.526600099155481.8725351866388
Trimmed Mean ( 11 / 20 )2173.0526315789526.003581856580283.5674348081805
Trimmed Mean ( 12 / 20 )2174.0555555555625.446300271962285.436999969344
Trimmed Mean ( 13 / 20 )2174.9117647058824.921172253033187.271647682672
Trimmed Mean ( 14 / 20 )2175.6562524.326020242462589.4374101605929
Trimmed Mean ( 15 / 20 )2175.5333333333323.790306793272191.4462075768008
Trimmed Mean ( 16 / 20 )2175.8571428571423.309211697571693.3475216188384
Trimmed Mean ( 17 / 20 )2175.9230769230822.770420966813995.559194100729
Trimmed Mean ( 18 / 20 )2176.9583333333322.490938526910396.792685228703
Trimmed Mean ( 19 / 20 )2177.3181818181822.337376357275497.4742130406475
Trimmed Mean ( 20 / 20 )2177.4522.130768650289498.3901659453445
Median2197
Midrange2225
Midmean - Weighted Average at Xnp2168.58064516129
Midmean - Weighted Average at X(n+1)p2175.53333333333
Midmean - Empirical Distribution Function2168.58064516129
Midmean - Empirical Distribution Function - Averaging2175.53333333333
Midmean - Empirical Distribution Function - Interpolation2175.53333333333
Midmean - Closest Observation2168.58064516129
Midmean - True Basic - Statistics Graphics Toolkit2175.53333333333
Midmean - MS Excel (old versions)2175.65625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2187.06666666667 & 41.0188110813020 & 53.3186264792453 \tabularnewline
Geometric Mean & 2164.43039160004 &  &  \tabularnewline
Harmonic Mean & 2141.77464820376 &  &  \tabularnewline
Quadratic Mean & 2209.64491114146 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2186.48333333333 & 40.5923338318132 & 53.8644400785779 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2191.35 & 38.5542674622152 & 56.8380660363374 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2187.4 & 37.3540035594701 & 58.5586494501858 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2188.8 & 37.041592136713 & 59.0903326164162 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2184.38333333333 & 34.4067157062016 & 63.4871212929983 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2183.38333333333 & 32.7518325848308 & 66.6644630549492 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2182.45 & 31.680042595774 & 68.890374544229 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2168.05 & 28.2953792817938 & 76.6220511981261 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2163.7 & 27.5105968283697 & 78.6496931890888 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2163.86666666667 & 26.9088382207026 & 80.4147190941105 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2166.43333333333 & 26.2056228781753 & 82.670552934561 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2168.23333333333 & 25.1657372522661 & 86.158148740033 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2169.75 & 24.4867152383459 & 88.6092715531807 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2176.51666666667 & 23.2381856462173 & 93.6612134786417 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2173.26666666667 & 22.0222648848644 & 98.6849753206047 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2175.4 & 21.1959408756611 & 102.632858468575 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2168.88333333333 & 19.2817511521981 & 112.483732219834 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2174.58333333333 & 18.0672518251183 & 120.360492806664 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2176.48333333333 & 17.4195567034262 & 124.944817505330 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2175.81666666667 & 17.0343039017213 & 127.731469346793 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2185.75862068966 & 38.5857700681386 & 56.6467538895771 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2184.98214285714 & 36.088351999591 & 60.5453566536346 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2181.44444444444 & 34.3862496150753 & 63.4394407317999 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2179.15384615385 & 32.866054140905 & 66.3040910482064 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2176.26 & 31.0672977221242 & 70.0498646346768 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2174.22916666667 & 29.7632835768503 & 73.0507156931358 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2172.23913043478 & 28.6378551672822 & 75.8520188661508 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2170.25 & 27.5071608013048 & 78.8976374434492 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2170.64285714286 & 27.0092215815208 & 80.3667314361985 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2171.8 & 26.5266000991554 & 81.8725351866388 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2173.05263157895 & 26.0035818565802 & 83.5674348081805 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2174.05555555556 & 25.4463002719622 & 85.436999969344 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2174.91176470588 & 24.9211722530331 & 87.271647682672 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2175.65625 & 24.3260202424625 & 89.4374101605929 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2175.53333333333 & 23.7903067932721 & 91.4462075768008 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2175.85714285714 & 23.3092116975716 & 93.3475216188384 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2175.92307692308 & 22.7704209668139 & 95.559194100729 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2176.95833333333 & 22.4909385269103 & 96.792685228703 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2177.31818181818 & 22.3373763572754 & 97.4742130406475 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2177.45 & 22.1307686502894 & 98.3901659453445 \tabularnewline
Median & 2197 &  &  \tabularnewline
Midrange & 2225 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2168.58064516129 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2175.53333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2168.58064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2175.53333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2175.53333333333 &  &  \tabularnewline
Midmean - Closest Observation & 2168.58064516129 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2175.53333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2175.65625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70950&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]2187.06666666667[/C][C]41.0188110813020[/C][C]53.3186264792453[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2164.43039160004[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2141.77464820376[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2209.64491114146[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2186.48333333333[/C][C]40.5923338318132[/C][C]53.8644400785779[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2191.35[/C][C]38.5542674622152[/C][C]56.8380660363374[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2187.4[/C][C]37.3540035594701[/C][C]58.5586494501858[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2188.8[/C][C]37.041592136713[/C][C]59.0903326164162[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2184.38333333333[/C][C]34.4067157062016[/C][C]63.4871212929983[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2183.38333333333[/C][C]32.7518325848308[/C][C]66.6644630549492[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2182.45[/C][C]31.680042595774[/C][C]68.890374544229[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2168.05[/C][C]28.2953792817938[/C][C]76.6220511981261[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2163.7[/C][C]27.5105968283697[/C][C]78.6496931890888[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2163.86666666667[/C][C]26.9088382207026[/C][C]80.4147190941105[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2166.43333333333[/C][C]26.2056228781753[/C][C]82.670552934561[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2168.23333333333[/C][C]25.1657372522661[/C][C]86.158148740033[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2169.75[/C][C]24.4867152383459[/C][C]88.6092715531807[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2176.51666666667[/C][C]23.2381856462173[/C][C]93.6612134786417[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2173.26666666667[/C][C]22.0222648848644[/C][C]98.6849753206047[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2175.4[/C][C]21.1959408756611[/C][C]102.632858468575[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2168.88333333333[/C][C]19.2817511521981[/C][C]112.483732219834[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2174.58333333333[/C][C]18.0672518251183[/C][C]120.360492806664[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2176.48333333333[/C][C]17.4195567034262[/C][C]124.944817505330[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2175.81666666667[/C][C]17.0343039017213[/C][C]127.731469346793[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2185.75862068966[/C][C]38.5857700681386[/C][C]56.6467538895771[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2184.98214285714[/C][C]36.088351999591[/C][C]60.5453566536346[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2181.44444444444[/C][C]34.3862496150753[/C][C]63.4394407317999[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2179.15384615385[/C][C]32.866054140905[/C][C]66.3040910482064[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2176.26[/C][C]31.0672977221242[/C][C]70.0498646346768[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2174.22916666667[/C][C]29.7632835768503[/C][C]73.0507156931358[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2172.23913043478[/C][C]28.6378551672822[/C][C]75.8520188661508[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2170.25[/C][C]27.5071608013048[/C][C]78.8976374434492[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2170.64285714286[/C][C]27.0092215815208[/C][C]80.3667314361985[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2171.8[/C][C]26.5266000991554[/C][C]81.8725351866388[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2173.05263157895[/C][C]26.0035818565802[/C][C]83.5674348081805[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2174.05555555556[/C][C]25.4463002719622[/C][C]85.436999969344[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2174.91176470588[/C][C]24.9211722530331[/C][C]87.271647682672[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2175.65625[/C][C]24.3260202424625[/C][C]89.4374101605929[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2175.53333333333[/C][C]23.7903067932721[/C][C]91.4462075768008[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2175.85714285714[/C][C]23.3092116975716[/C][C]93.3475216188384[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2175.92307692308[/C][C]22.7704209668139[/C][C]95.559194100729[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2176.95833333333[/C][C]22.4909385269103[/C][C]96.792685228703[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2177.31818181818[/C][C]22.3373763572754[/C][C]97.4742130406475[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2177.45[/C][C]22.1307686502894[/C][C]98.3901659453445[/C][/ROW]
[ROW][C]Median[/C][C]2197[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2168.58064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2175.53333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2168.58064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2175.53333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2175.53333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2168.58064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2175.53333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2175.65625[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70950&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70950&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 Mean2187.0666666666741.018811081302053.3186264792453
Geometric Mean2164.43039160004
Harmonic Mean2141.77464820376
Quadratic Mean2209.64491114146
Winsorized Mean ( 1 / 20 )2186.4833333333340.592333831813253.8644400785779
Winsorized Mean ( 2 / 20 )2191.3538.554267462215256.8380660363374
Winsorized Mean ( 3 / 20 )2187.437.354003559470158.5586494501858
Winsorized Mean ( 4 / 20 )2188.837.04159213671359.0903326164162
Winsorized Mean ( 5 / 20 )2184.3833333333334.406715706201663.4871212929983
Winsorized Mean ( 6 / 20 )2183.3833333333332.751832584830866.6644630549492
Winsorized Mean ( 7 / 20 )2182.4531.68004259577468.890374544229
Winsorized Mean ( 8 / 20 )2168.0528.295379281793876.6220511981261
Winsorized Mean ( 9 / 20 )2163.727.510596828369778.6496931890888
Winsorized Mean ( 10 / 20 )2163.8666666666726.908838220702680.4147190941105
Winsorized Mean ( 11 / 20 )2166.4333333333326.205622878175382.670552934561
Winsorized Mean ( 12 / 20 )2168.2333333333325.165737252266186.158148740033
Winsorized Mean ( 13 / 20 )2169.7524.486715238345988.6092715531807
Winsorized Mean ( 14 / 20 )2176.5166666666723.238185646217393.6612134786417
Winsorized Mean ( 15 / 20 )2173.2666666666722.022264884864498.6849753206047
Winsorized Mean ( 16 / 20 )2175.421.1959408756611102.632858468575
Winsorized Mean ( 17 / 20 )2168.8833333333319.2817511521981112.483732219834
Winsorized Mean ( 18 / 20 )2174.5833333333318.0672518251183120.360492806664
Winsorized Mean ( 19 / 20 )2176.4833333333317.4195567034262124.944817505330
Winsorized Mean ( 20 / 20 )2175.8166666666717.0343039017213127.731469346793
Trimmed Mean ( 1 / 20 )2185.7586206896638.585770068138656.6467538895771
Trimmed Mean ( 2 / 20 )2184.9821428571436.08835199959160.5453566536346
Trimmed Mean ( 3 / 20 )2181.4444444444434.386249615075363.4394407317999
Trimmed Mean ( 4 / 20 )2179.1538461538532.86605414090566.3040910482064
Trimmed Mean ( 5 / 20 )2176.2631.067297722124270.0498646346768
Trimmed Mean ( 6 / 20 )2174.2291666666729.763283576850373.0507156931358
Trimmed Mean ( 7 / 20 )2172.2391304347828.637855167282275.8520188661508
Trimmed Mean ( 8 / 20 )2170.2527.507160801304878.8976374434492
Trimmed Mean ( 9 / 20 )2170.6428571428627.009221581520880.3667314361985
Trimmed Mean ( 10 / 20 )2171.826.526600099155481.8725351866388
Trimmed Mean ( 11 / 20 )2173.0526315789526.003581856580283.5674348081805
Trimmed Mean ( 12 / 20 )2174.0555555555625.446300271962285.436999969344
Trimmed Mean ( 13 / 20 )2174.9117647058824.921172253033187.271647682672
Trimmed Mean ( 14 / 20 )2175.6562524.326020242462589.4374101605929
Trimmed Mean ( 15 / 20 )2175.5333333333323.790306793272191.4462075768008
Trimmed Mean ( 16 / 20 )2175.8571428571423.309211697571693.3475216188384
Trimmed Mean ( 17 / 20 )2175.9230769230822.770420966813995.559194100729
Trimmed Mean ( 18 / 20 )2176.9583333333322.490938526910396.792685228703
Trimmed Mean ( 19 / 20 )2177.3181818181822.337376357275497.4742130406475
Trimmed Mean ( 20 / 20 )2177.4522.130768650289498.3901659453445
Median2197
Midrange2225
Midmean - Weighted Average at Xnp2168.58064516129
Midmean - Weighted Average at X(n+1)p2175.53333333333
Midmean - Empirical Distribution Function2168.58064516129
Midmean - Empirical Distribution Function - Averaging2175.53333333333
Midmean - Empirical Distribution Function - Interpolation2175.53333333333
Midmean - Closest Observation2168.58064516129
Midmean - True Basic - Statistics Graphics Toolkit2175.53333333333
Midmean - MS Excel (old versions)2175.65625
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')