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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 22 Oct 2007 09:22:26 -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/2007/Oct/22/ka5u30v2ys3os3w1193069871.htm/, Retrieved Sun, 05 May 2024 22:26:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1506, Retrieved Sun, 05 May 2024 22:26:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact207
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [WS2Q9BASISMETAAL] [2007-10-22 16:22:26] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
2354
2318
2250
2219
2206
2146
2212
2243
2275
2291
2141
2134
2180
2183
2169
2132
2092
2069
2099
2073
2051
2082
2059
2101
2158
2153
2145
2149
2135
2097
2143
2130
2132
2142
2094
2147
2203
2244
2260
2254
2231
2211
2209
2191
2210
2257
2252
2266
2264
2265
2255
2280
2288
2284
2282
2271
2296
2303
2316
2325
2415
2402
2425
2400
2424
2393
2419
2415
2425
2421
2378
2364




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

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1506&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1506&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1506&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2233.3611111111112.5062473520562178.579636899947
Geometric Mean2230.89112209359
Harmonic Mean2228.43836895438
Quadratic Mean2235.84585659308
Winsorized Mean ( 1 / 24 )2233.4722222222212.483901561972178.908189169461
Winsorized Mean ( 2 / 24 )2233.7222222222212.4246275677176179.781825253742
Winsorized Mean ( 3 / 24 )2233.7638888888912.366999683195180.622943811041
Winsorized Mean ( 4 / 24 )2234.1527777777812.2538464422392182.322570166754
Winsorized Mean ( 5 / 24 )2234.5694444444412.0766304282099185.032526889677
Winsorized Mean ( 6 / 24 )2234.7361111111112.0490649423172185.469671033356
Winsorized Mean ( 7 / 24 )2233.7638888888911.7403690269393190.263515888072
Winsorized Mean ( 8 / 24 )2233.7638888888911.6593117838786191.586255715154
Winsorized Mean ( 9 / 24 )2233.1388888888911.4446908636886195.124439400467
Winsorized Mean ( 10 / 24 )2235.0833333333310.4230121517783214.437371921512
Winsorized Mean ( 11 / 24 )2233.259.97531675910316223.877602479340
Winsorized Mean ( 12 / 24 )2231.583333333339.67285195509716230.705829438172
Winsorized Mean ( 13 / 24 )2226.708333333338.73551646144636254.902883322442
Winsorized Mean ( 14 / 24 )2225.541666666678.49415101854338262.008723627369
Winsorized Mean ( 15 / 24 )2226.3758.24529641370896270.017581939
Winsorized Mean ( 16 / 24 )2223.708333333337.78389245862966285.680762568605
Winsorized Mean ( 17 / 24 )2222.291666666677.51611303822946295.670335898802
Winsorized Mean ( 18 / 24 )2221.541666666677.27145084951855305.515599656946
Winsorized Mean ( 19 / 24 )2221.013888888897.1266623697147311.648535270488
Winsorized Mean ( 20 / 24 )2220.180555555566.93992008329174319.914426810298
Winsorized Mean ( 21 / 24 )2220.180555555566.77821369560751327.546556549892
Winsorized Mean ( 22 / 24 )2220.791666666676.51998065117572340.613229621502
Winsorized Mean ( 23 / 24 )2220.791666666676.08449688210079364.991832471758
Winsorized Mean ( 24 / 24 )2223.1255.39129803327251412.354313614260
Trimmed Mean ( 1 / 24 )2233.2285714285712.2901965919411181.708124416248
Trimmed Mean ( 2 / 24 )2232.9705882352912.0580788437913185.184606699188
Trimmed Mean ( 3 / 24 )2232.5606060606111.8167856745112188.931293801515
Trimmed Mean ( 4 / 24 )2232.10937511.5519254988896193.224010595858
Trimmed Mean ( 5 / 24 )2231.5161290322611.2724948013177197.961158409353
Trimmed Mean ( 6 / 24 )2230.7833333333310.9880801278668203.018480696719
Trimmed Mean ( 7 / 24 )2229.9655172413810.6464938608390209.455389388226
Trimmed Mean ( 8 / 24 )2229.2678571428610.3105195011718216.21295191668
Trimmed Mean ( 9 / 24 )2228.518518518529.91359388084564224.794211393338
Trimmed Mean ( 10 / 24 )2227.807692307699.4719972482812235.199360167883
Trimmed Mean ( 11 / 24 )2226.769.16415198655353242.9859307514
Trimmed Mean ( 12 / 24 )2225.8758.8801927671397250.65615785241
Trimmed Mean ( 13 / 24 )2225.130434782618.58740841469784259.115477840109
Trimmed Mean ( 14 / 24 )2224.931818181828.42730371558214264.014671035043
Trimmed Mean ( 15 / 24 )2224.857142857148.26461127752588269.202878168903
Trimmed Mean ( 16 / 24 )2224.6758.09711783955824274.748996381331
Trimmed Mean ( 17 / 24 )2224.789473684217.96990765412454279.148714167704
Trimmed Mean ( 18 / 24 )2225.083333333337.84496350411857283.632082184343
Trimmed Mean ( 19 / 24 )2225.57.71486631189022288.469029796412
Trimmed Mean ( 20 / 24 )2226.031257.54989910942524294.842516136545
Trimmed Mean ( 21 / 24 )2226.733333333337.344077813259303.201217355457
Trimmed Mean ( 22 / 24 )2227.535714285717.07190621549707314.983774728854
Trimmed Mean ( 23 / 24 )2228.384615384626.73477243589667330.877492386708
Trimmed Mean ( 24 / 24 )2229.3756.3604907351009350.503615656102
Median2237
Midrange2238
Midmean - Weighted Average at Xnp2222.86486486487
Midmean - Weighted Average at X(n+1)p2225.08333333333
Midmean - Empirical Distribution Function2222.86486486487
Midmean - Empirical Distribution Function - Averaging2225.08333333333
Midmean - Empirical Distribution Function - Interpolation2225.08333333333
Midmean - Closest Observation2222.86486486487
Midmean - True Basic - Statistics Graphics Toolkit2225.08333333333
Midmean - MS Excel (old versions)2224.78947368421
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2233.36111111111 & 12.5062473520562 & 178.579636899947 \tabularnewline
Geometric Mean & 2230.89112209359 &  &  \tabularnewline
Harmonic Mean & 2228.43836895438 &  &  \tabularnewline
Quadratic Mean & 2235.84585659308 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 2233.47222222222 & 12.483901561972 & 178.908189169461 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 2233.72222222222 & 12.4246275677176 & 179.781825253742 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 2233.76388888889 & 12.366999683195 & 180.622943811041 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 2234.15277777778 & 12.2538464422392 & 182.322570166754 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 2234.56944444444 & 12.0766304282099 & 185.032526889677 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 2234.73611111111 & 12.0490649423172 & 185.469671033356 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 2233.76388888889 & 11.7403690269393 & 190.263515888072 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 2233.76388888889 & 11.6593117838786 & 191.586255715154 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 2233.13888888889 & 11.4446908636886 & 195.124439400467 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 2235.08333333333 & 10.4230121517783 & 214.437371921512 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 2233.25 & 9.97531675910316 & 223.877602479340 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 2231.58333333333 & 9.67285195509716 & 230.705829438172 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 2226.70833333333 & 8.73551646144636 & 254.902883322442 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 2225.54166666667 & 8.49415101854338 & 262.008723627369 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 2226.375 & 8.24529641370896 & 270.017581939 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 2223.70833333333 & 7.78389245862966 & 285.680762568605 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 2222.29166666667 & 7.51611303822946 & 295.670335898802 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 2221.54166666667 & 7.27145084951855 & 305.515599656946 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 2221.01388888889 & 7.1266623697147 & 311.648535270488 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 2220.18055555556 & 6.93992008329174 & 319.914426810298 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 2220.18055555556 & 6.77821369560751 & 327.546556549892 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 2220.79166666667 & 6.51998065117572 & 340.613229621502 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 2220.79166666667 & 6.08449688210079 & 364.991832471758 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 2223.125 & 5.39129803327251 & 412.354313614260 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 2233.22857142857 & 12.2901965919411 & 181.708124416248 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 2232.97058823529 & 12.0580788437913 & 185.184606699188 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 2232.56060606061 & 11.8167856745112 & 188.931293801515 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 2232.109375 & 11.5519254988896 & 193.224010595858 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 2231.51612903226 & 11.2724948013177 & 197.961158409353 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 2230.78333333333 & 10.9880801278668 & 203.018480696719 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 2229.96551724138 & 10.6464938608390 & 209.455389388226 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 2229.26785714286 & 10.3105195011718 & 216.21295191668 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 2228.51851851852 & 9.91359388084564 & 224.794211393338 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 2227.80769230769 & 9.4719972482812 & 235.199360167883 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 2226.76 & 9.16415198655353 & 242.9859307514 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 2225.875 & 8.8801927671397 & 250.65615785241 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 2225.13043478261 & 8.58740841469784 & 259.115477840109 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 2224.93181818182 & 8.42730371558214 & 264.014671035043 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 2224.85714285714 & 8.26461127752588 & 269.202878168903 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 2224.675 & 8.09711783955824 & 274.748996381331 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 2224.78947368421 & 7.96990765412454 & 279.148714167704 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 2225.08333333333 & 7.84496350411857 & 283.632082184343 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 2225.5 & 7.71486631189022 & 288.469029796412 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 2226.03125 & 7.54989910942524 & 294.842516136545 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 2226.73333333333 & 7.344077813259 & 303.201217355457 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 2227.53571428571 & 7.07190621549707 & 314.983774728854 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 2228.38461538462 & 6.73477243589667 & 330.877492386708 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 2229.375 & 6.3604907351009 & 350.503615656102 \tabularnewline
Median & 2237 &  &  \tabularnewline
Midrange & 2238 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2222.86486486487 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2225.08333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2222.86486486487 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2225.08333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2225.08333333333 &  &  \tabularnewline
Midmean - Closest Observation & 2222.86486486487 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2225.08333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2224.78947368421 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1506&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]2233.36111111111[/C][C]12.5062473520562[/C][C]178.579636899947[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2230.89112209359[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2228.43836895438[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2235.84585659308[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]2233.47222222222[/C][C]12.483901561972[/C][C]178.908189169461[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]2233.72222222222[/C][C]12.4246275677176[/C][C]179.781825253742[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]2233.76388888889[/C][C]12.366999683195[/C][C]180.622943811041[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]2234.15277777778[/C][C]12.2538464422392[/C][C]182.322570166754[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]2234.56944444444[/C][C]12.0766304282099[/C][C]185.032526889677[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]2234.73611111111[/C][C]12.0490649423172[/C][C]185.469671033356[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]2233.76388888889[/C][C]11.7403690269393[/C][C]190.263515888072[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]2233.76388888889[/C][C]11.6593117838786[/C][C]191.586255715154[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]2233.13888888889[/C][C]11.4446908636886[/C][C]195.124439400467[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]2235.08333333333[/C][C]10.4230121517783[/C][C]214.437371921512[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]2233.25[/C][C]9.97531675910316[/C][C]223.877602479340[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]2231.58333333333[/C][C]9.67285195509716[/C][C]230.705829438172[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]2226.70833333333[/C][C]8.73551646144636[/C][C]254.902883322442[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]2225.54166666667[/C][C]8.49415101854338[/C][C]262.008723627369[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]2226.375[/C][C]8.24529641370896[/C][C]270.017581939[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]2223.70833333333[/C][C]7.78389245862966[/C][C]285.680762568605[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]2222.29166666667[/C][C]7.51611303822946[/C][C]295.670335898802[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]2221.54166666667[/C][C]7.27145084951855[/C][C]305.515599656946[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]2221.01388888889[/C][C]7.1266623697147[/C][C]311.648535270488[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]2220.18055555556[/C][C]6.93992008329174[/C][C]319.914426810298[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]2220.18055555556[/C][C]6.77821369560751[/C][C]327.546556549892[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]2220.79166666667[/C][C]6.51998065117572[/C][C]340.613229621502[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]2220.79166666667[/C][C]6.08449688210079[/C][C]364.991832471758[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]2223.125[/C][C]5.39129803327251[/C][C]412.354313614260[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]2233.22857142857[/C][C]12.2901965919411[/C][C]181.708124416248[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]2232.97058823529[/C][C]12.0580788437913[/C][C]185.184606699188[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]2232.56060606061[/C][C]11.8167856745112[/C][C]188.931293801515[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]2232.109375[/C][C]11.5519254988896[/C][C]193.224010595858[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]2231.51612903226[/C][C]11.2724948013177[/C][C]197.961158409353[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]2230.78333333333[/C][C]10.9880801278668[/C][C]203.018480696719[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]2229.96551724138[/C][C]10.6464938608390[/C][C]209.455389388226[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]2229.26785714286[/C][C]10.3105195011718[/C][C]216.21295191668[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]2228.51851851852[/C][C]9.91359388084564[/C][C]224.794211393338[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]2227.80769230769[/C][C]9.4719972482812[/C][C]235.199360167883[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]2226.76[/C][C]9.16415198655353[/C][C]242.9859307514[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]2225.875[/C][C]8.8801927671397[/C][C]250.65615785241[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]2225.13043478261[/C][C]8.58740841469784[/C][C]259.115477840109[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]2224.93181818182[/C][C]8.42730371558214[/C][C]264.014671035043[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]2224.85714285714[/C][C]8.26461127752588[/C][C]269.202878168903[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]2224.675[/C][C]8.09711783955824[/C][C]274.748996381331[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]2224.78947368421[/C][C]7.96990765412454[/C][C]279.148714167704[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]2225.08333333333[/C][C]7.84496350411857[/C][C]283.632082184343[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]2225.5[/C][C]7.71486631189022[/C][C]288.469029796412[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]2226.03125[/C][C]7.54989910942524[/C][C]294.842516136545[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]2226.73333333333[/C][C]7.344077813259[/C][C]303.201217355457[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]2227.53571428571[/C][C]7.07190621549707[/C][C]314.983774728854[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]2228.38461538462[/C][C]6.73477243589667[/C][C]330.877492386708[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]2229.375[/C][C]6.3604907351009[/C][C]350.503615656102[/C][/ROW]
[ROW][C]Median[/C][C]2237[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2238[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2222.86486486487[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2225.08333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2222.86486486487[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2225.08333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2225.08333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2222.86486486487[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2225.08333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2224.78947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1506&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1506&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 Mean2233.3611111111112.5062473520562178.579636899947
Geometric Mean2230.89112209359
Harmonic Mean2228.43836895438
Quadratic Mean2235.84585659308
Winsorized Mean ( 1 / 24 )2233.4722222222212.483901561972178.908189169461
Winsorized Mean ( 2 / 24 )2233.7222222222212.4246275677176179.781825253742
Winsorized Mean ( 3 / 24 )2233.7638888888912.366999683195180.622943811041
Winsorized Mean ( 4 / 24 )2234.1527777777812.2538464422392182.322570166754
Winsorized Mean ( 5 / 24 )2234.5694444444412.0766304282099185.032526889677
Winsorized Mean ( 6 / 24 )2234.7361111111112.0490649423172185.469671033356
Winsorized Mean ( 7 / 24 )2233.7638888888911.7403690269393190.263515888072
Winsorized Mean ( 8 / 24 )2233.7638888888911.6593117838786191.586255715154
Winsorized Mean ( 9 / 24 )2233.1388888888911.4446908636886195.124439400467
Winsorized Mean ( 10 / 24 )2235.0833333333310.4230121517783214.437371921512
Winsorized Mean ( 11 / 24 )2233.259.97531675910316223.877602479340
Winsorized Mean ( 12 / 24 )2231.583333333339.67285195509716230.705829438172
Winsorized Mean ( 13 / 24 )2226.708333333338.73551646144636254.902883322442
Winsorized Mean ( 14 / 24 )2225.541666666678.49415101854338262.008723627369
Winsorized Mean ( 15 / 24 )2226.3758.24529641370896270.017581939
Winsorized Mean ( 16 / 24 )2223.708333333337.78389245862966285.680762568605
Winsorized Mean ( 17 / 24 )2222.291666666677.51611303822946295.670335898802
Winsorized Mean ( 18 / 24 )2221.541666666677.27145084951855305.515599656946
Winsorized Mean ( 19 / 24 )2221.013888888897.1266623697147311.648535270488
Winsorized Mean ( 20 / 24 )2220.180555555566.93992008329174319.914426810298
Winsorized Mean ( 21 / 24 )2220.180555555566.77821369560751327.546556549892
Winsorized Mean ( 22 / 24 )2220.791666666676.51998065117572340.613229621502
Winsorized Mean ( 23 / 24 )2220.791666666676.08449688210079364.991832471758
Winsorized Mean ( 24 / 24 )2223.1255.39129803327251412.354313614260
Trimmed Mean ( 1 / 24 )2233.2285714285712.2901965919411181.708124416248
Trimmed Mean ( 2 / 24 )2232.9705882352912.0580788437913185.184606699188
Trimmed Mean ( 3 / 24 )2232.5606060606111.8167856745112188.931293801515
Trimmed Mean ( 4 / 24 )2232.10937511.5519254988896193.224010595858
Trimmed Mean ( 5 / 24 )2231.5161290322611.2724948013177197.961158409353
Trimmed Mean ( 6 / 24 )2230.7833333333310.9880801278668203.018480696719
Trimmed Mean ( 7 / 24 )2229.9655172413810.6464938608390209.455389388226
Trimmed Mean ( 8 / 24 )2229.2678571428610.3105195011718216.21295191668
Trimmed Mean ( 9 / 24 )2228.518518518529.91359388084564224.794211393338
Trimmed Mean ( 10 / 24 )2227.807692307699.4719972482812235.199360167883
Trimmed Mean ( 11 / 24 )2226.769.16415198655353242.9859307514
Trimmed Mean ( 12 / 24 )2225.8758.8801927671397250.65615785241
Trimmed Mean ( 13 / 24 )2225.130434782618.58740841469784259.115477840109
Trimmed Mean ( 14 / 24 )2224.931818181828.42730371558214264.014671035043
Trimmed Mean ( 15 / 24 )2224.857142857148.26461127752588269.202878168903
Trimmed Mean ( 16 / 24 )2224.6758.09711783955824274.748996381331
Trimmed Mean ( 17 / 24 )2224.789473684217.96990765412454279.148714167704
Trimmed Mean ( 18 / 24 )2225.083333333337.84496350411857283.632082184343
Trimmed Mean ( 19 / 24 )2225.57.71486631189022288.469029796412
Trimmed Mean ( 20 / 24 )2226.031257.54989910942524294.842516136545
Trimmed Mean ( 21 / 24 )2226.733333333337.344077813259303.201217355457
Trimmed Mean ( 22 / 24 )2227.535714285717.07190621549707314.983774728854
Trimmed Mean ( 23 / 24 )2228.384615384626.73477243589667330.877492386708
Trimmed Mean ( 24 / 24 )2229.3756.3604907351009350.503615656102
Median2237
Midrange2238
Midmean - Weighted Average at Xnp2222.86486486487
Midmean - Weighted Average at X(n+1)p2225.08333333333
Midmean - Empirical Distribution Function2222.86486486487
Midmean - Empirical Distribution Function - Averaging2225.08333333333
Midmean - Empirical Distribution Function - Interpolation2225.08333333333
Midmean - Closest Observation2222.86486486487
Midmean - True Basic - Statistics Graphics Toolkit2225.08333333333
Midmean - MS Excel (old versions)2224.78947368421
Number of observations72



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')