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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 21 Dec 2008 05:24:39 -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/21/t1229862749mbfnmaor56gw493.htm/, Retrieved Mon, 27 May 2024 23:10:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35532, Retrieved Mon, 27 May 2024 23:10:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact121
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency V4] [2008-12-21 12:24:39] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
104
107,9
113,8
113,8
123,1
125,1
137,6
134
140,3
152,1
150,6
167,3
153,2
142
154,4
158,5
180,9
181,3
172,4
192
199,3
215,4
214,3
201,5
190,5
196
215,7
209,4
214,1
237,8
239
237,8
251,5
248,8
215,4
201,2
203,1
214,2
188,9
203
213,3
228,5
228,2
240,9
258,8
248,5
269,2
289,6
323,4
317,2
322,8
340,9
368,2
388,5
441,2
474,3
483,9
417,9
365,9
263
199,4




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35532&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35532&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35532&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean227.61967213114811.451190984822819.8773797793462
Geometric Mean212.475434306261
Harmonic Mean199.102572198468
Quadratic Mean244.291837029697
Winsorized Mean ( 1 / 20 )227.52622950819711.382051324725519.9899142093953
Winsorized Mean ( 2 / 20 )226.63442622950810.975298864508320.6494993008703
Winsorized Mean ( 3 / 20 )225.48852459016410.615299840391921.2418422447349
Winsorized Mean ( 4 / 20 )224.1704918032799.9528701806079222.5232006180539
Winsorized Mean ( 5 / 20 )222.6704918032799.482816309509723.4814726485819
Winsorized Mean ( 6 / 20 )223.3196721311489.2795868041114324.0656913767112
Winsorized Mean ( 7 / 20 )220.8639344262308.5068005687725125.9632199721474
Winsorized Mean ( 8 / 20 )218.9229508196727.9260535296155627.6206752833135
Winsorized Mean ( 9 / 20 )219.0852459016397.8653826992602727.8543656778765
Winsorized Mean ( 10 / 20 )219.5770491803287.4398658081215329.5135765675548
Winsorized Mean ( 11 / 20 )214.8704918032796.360886861329633.7799581233811
Winsorized Mean ( 12 / 20 )211.0737704918035.5802941250994437.8248468198873
Winsorized Mean ( 13 / 20 )210.0081967213115.3112111011617439.5405478564721
Winsorized Mean ( 14 / 20 )209.9852459016394.9893716743971342.0865110088260
Winsorized Mean ( 15 / 20 )210.3540983606564.3350626480686848.5238889118178
Winsorized Mean ( 16 / 20 )210.9836065573774.0050761372512852.6790501171788
Winsorized Mean ( 17 / 20 )213.2688524590163.6245802779311258.839599651728
Winsorized Mean ( 18 / 20 )211.1442622950823.2536406885212364.894769431669
Winsorized Mean ( 19 / 20 )212.9196721311482.8125293632197775.7039819443514
Winsorized Mean ( 20 / 20 )213.0508196721312.6776555920574779.5661773321738
Trimmed Mean ( 1 / 20 )225.37118644067810.793682550332620.8799161351779
Trimmed Mean ( 2 / 20 )223.06491228070210.053226919697122.1883892666995
Trimmed Mean ( 3 / 20 )221.0854545454559.4078878067496823.5000096819646
Trimmed Mean ( 4 / 20 )219.3962264150948.780347316619424.9871922491975
Trimmed Mean ( 5 / 20 )217.9686274509808.2723126624814926.3491766262127
Trimmed Mean ( 6 / 20 )216.7979591836737.8038846999317727.7807742579242
Trimmed Mean ( 7 / 20 )215.3872340425537.2633109277979729.6541393014346
Trimmed Mean ( 8 / 20 )214.3266666666676.8240094556283431.4077329552780
Trimmed Mean ( 9 / 20 )213.5116279069776.4355293298442833.1770110838952
Trimmed Mean ( 10 / 20 )212.5902439024395.9317611468594135.8393129188952
Trimmed Mean ( 11 / 20 )211.4974358974365.3785279194236839.3225505316514
Trimmed Mean ( 12 / 20 )210.9918918918924.9950882456927642.2398727537655
Trimmed Mean ( 13 / 20 )210.984.7195744716316644.7031827272045
Trimmed Mean ( 14 / 20 )211.1181818181824.4165783036017547.8012994009443
Trimmed Mean ( 15 / 20 )211.2774193548394.0897845716523051.6597917697854
Trimmed Mean ( 16 / 20 )211.4068965517243.8447614255722754.9856995405787
Trimmed Mean ( 17 / 20 )211.4666666666673.5970983874668858.7881241734909
Trimmed Mean ( 18 / 20 )211.2083.3605055175275862.8500679134107
Trimmed Mean ( 19 / 20 )211.2173913043483.1433765748727967.1944281168079
Trimmed Mean ( 20 / 20 )210.9571428571432.9794260507414470.804624536543
Median213.3
Midrange293.95
Midmean - Weighted Average at Xnp209.936666666667
Midmean - Weighted Average at X(n+1)p211.277419354839
Midmean - Empirical Distribution Function211.277419354839
Midmean - Empirical Distribution Function - Averaging211.277419354839
Midmean - Empirical Distribution Function - Interpolation211.277419354839
Midmean - Closest Observation209.628125
Midmean - True Basic - Statistics Graphics Toolkit211.277419354839
Midmean - MS Excel (old versions)211.277419354839
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 227.619672131148 & 11.4511909848228 & 19.8773797793462 \tabularnewline
Geometric Mean & 212.475434306261 &  &  \tabularnewline
Harmonic Mean & 199.102572198468 &  &  \tabularnewline
Quadratic Mean & 244.291837029697 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 227.526229508197 & 11.3820513247255 & 19.9899142093953 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 226.634426229508 & 10.9752988645083 & 20.6494993008703 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 225.488524590164 & 10.6152998403919 & 21.2418422447349 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 224.170491803279 & 9.95287018060792 & 22.5232006180539 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 222.670491803279 & 9.4828163095097 & 23.4814726485819 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 223.319672131148 & 9.27958680411143 & 24.0656913767112 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 220.863934426230 & 8.50680056877251 & 25.9632199721474 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 218.922950819672 & 7.92605352961556 & 27.6206752833135 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 219.085245901639 & 7.86538269926027 & 27.8543656778765 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 219.577049180328 & 7.43986580812153 & 29.5135765675548 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 214.870491803279 & 6.3608868613296 & 33.7799581233811 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 211.073770491803 & 5.58029412509944 & 37.8248468198873 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 210.008196721311 & 5.31121110116174 & 39.5405478564721 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 209.985245901639 & 4.98937167439713 & 42.0865110088260 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 210.354098360656 & 4.33506264806868 & 48.5238889118178 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 210.983606557377 & 4.00507613725128 & 52.6790501171788 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 213.268852459016 & 3.62458027793112 & 58.839599651728 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 211.144262295082 & 3.25364068852123 & 64.894769431669 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 212.919672131148 & 2.81252936321977 & 75.7039819443514 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 213.050819672131 & 2.67765559205747 & 79.5661773321738 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 225.371186440678 & 10.7936825503326 & 20.8799161351779 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 223.064912280702 & 10.0532269196971 & 22.1883892666995 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 221.085454545455 & 9.40788780674968 & 23.5000096819646 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 219.396226415094 & 8.7803473166194 & 24.9871922491975 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 217.968627450980 & 8.27231266248149 & 26.3491766262127 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 216.797959183673 & 7.80388469993177 & 27.7807742579242 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 215.387234042553 & 7.26331092779797 & 29.6541393014346 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 214.326666666667 & 6.82400945562834 & 31.4077329552780 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 213.511627906977 & 6.43552932984428 & 33.1770110838952 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 212.590243902439 & 5.93176114685941 & 35.8393129188952 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 211.497435897436 & 5.37852791942368 & 39.3225505316514 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 210.991891891892 & 4.99508824569276 & 42.2398727537655 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 210.98 & 4.71957447163166 & 44.7031827272045 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 211.118181818182 & 4.41657830360175 & 47.8012994009443 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 211.277419354839 & 4.08978457165230 & 51.6597917697854 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 211.406896551724 & 3.84476142557227 & 54.9856995405787 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 211.466666666667 & 3.59709838746688 & 58.7881241734909 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 211.208 & 3.36050551752758 & 62.8500679134107 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 211.217391304348 & 3.14337657487279 & 67.1944281168079 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 210.957142857143 & 2.97942605074144 & 70.804624536543 \tabularnewline
Median & 213.3 &  &  \tabularnewline
Midrange & 293.95 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 209.936666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 211.277419354839 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 211.277419354839 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 211.277419354839 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 211.277419354839 &  &  \tabularnewline
Midmean - Closest Observation & 209.628125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 211.277419354839 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 211.277419354839 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35532&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]227.619672131148[/C][C]11.4511909848228[/C][C]19.8773797793462[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]212.475434306261[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]199.102572198468[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]244.291837029697[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]227.526229508197[/C][C]11.3820513247255[/C][C]19.9899142093953[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]226.634426229508[/C][C]10.9752988645083[/C][C]20.6494993008703[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]225.488524590164[/C][C]10.6152998403919[/C][C]21.2418422447349[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]224.170491803279[/C][C]9.95287018060792[/C][C]22.5232006180539[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]222.670491803279[/C][C]9.4828163095097[/C][C]23.4814726485819[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]223.319672131148[/C][C]9.27958680411143[/C][C]24.0656913767112[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]220.863934426230[/C][C]8.50680056877251[/C][C]25.9632199721474[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]218.922950819672[/C][C]7.92605352961556[/C][C]27.6206752833135[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]219.085245901639[/C][C]7.86538269926027[/C][C]27.8543656778765[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]219.577049180328[/C][C]7.43986580812153[/C][C]29.5135765675548[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]214.870491803279[/C][C]6.3608868613296[/C][C]33.7799581233811[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]211.073770491803[/C][C]5.58029412509944[/C][C]37.8248468198873[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]210.008196721311[/C][C]5.31121110116174[/C][C]39.5405478564721[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]209.985245901639[/C][C]4.98937167439713[/C][C]42.0865110088260[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]210.354098360656[/C][C]4.33506264806868[/C][C]48.5238889118178[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]210.983606557377[/C][C]4.00507613725128[/C][C]52.6790501171788[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]213.268852459016[/C][C]3.62458027793112[/C][C]58.839599651728[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]211.144262295082[/C][C]3.25364068852123[/C][C]64.894769431669[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]212.919672131148[/C][C]2.81252936321977[/C][C]75.7039819443514[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]213.050819672131[/C][C]2.67765559205747[/C][C]79.5661773321738[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]225.371186440678[/C][C]10.7936825503326[/C][C]20.8799161351779[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]223.064912280702[/C][C]10.0532269196971[/C][C]22.1883892666995[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]221.085454545455[/C][C]9.40788780674968[/C][C]23.5000096819646[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]219.396226415094[/C][C]8.7803473166194[/C][C]24.9871922491975[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]217.968627450980[/C][C]8.27231266248149[/C][C]26.3491766262127[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]216.797959183673[/C][C]7.80388469993177[/C][C]27.7807742579242[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]215.387234042553[/C][C]7.26331092779797[/C][C]29.6541393014346[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]214.326666666667[/C][C]6.82400945562834[/C][C]31.4077329552780[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]213.511627906977[/C][C]6.43552932984428[/C][C]33.1770110838952[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]212.590243902439[/C][C]5.93176114685941[/C][C]35.8393129188952[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]211.497435897436[/C][C]5.37852791942368[/C][C]39.3225505316514[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]210.991891891892[/C][C]4.99508824569276[/C][C]42.2398727537655[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]210.98[/C][C]4.71957447163166[/C][C]44.7031827272045[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]211.118181818182[/C][C]4.41657830360175[/C][C]47.8012994009443[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]211.277419354839[/C][C]4.08978457165230[/C][C]51.6597917697854[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]211.406896551724[/C][C]3.84476142557227[/C][C]54.9856995405787[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]211.466666666667[/C][C]3.59709838746688[/C][C]58.7881241734909[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]211.208[/C][C]3.36050551752758[/C][C]62.8500679134107[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]211.217391304348[/C][C]3.14337657487279[/C][C]67.1944281168079[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]210.957142857143[/C][C]2.97942605074144[/C][C]70.804624536543[/C][/ROW]
[ROW][C]Median[/C][C]213.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]293.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]209.936666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]211.277419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]211.277419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]211.277419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]211.277419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]209.628125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]211.277419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]211.277419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35532&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35532&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 Mean227.61967213114811.451190984822819.8773797793462
Geometric Mean212.475434306261
Harmonic Mean199.102572198468
Quadratic Mean244.291837029697
Winsorized Mean ( 1 / 20 )227.52622950819711.382051324725519.9899142093953
Winsorized Mean ( 2 / 20 )226.63442622950810.975298864508320.6494993008703
Winsorized Mean ( 3 / 20 )225.48852459016410.615299840391921.2418422447349
Winsorized Mean ( 4 / 20 )224.1704918032799.9528701806079222.5232006180539
Winsorized Mean ( 5 / 20 )222.6704918032799.482816309509723.4814726485819
Winsorized Mean ( 6 / 20 )223.3196721311489.2795868041114324.0656913767112
Winsorized Mean ( 7 / 20 )220.8639344262308.5068005687725125.9632199721474
Winsorized Mean ( 8 / 20 )218.9229508196727.9260535296155627.6206752833135
Winsorized Mean ( 9 / 20 )219.0852459016397.8653826992602727.8543656778765
Winsorized Mean ( 10 / 20 )219.5770491803287.4398658081215329.5135765675548
Winsorized Mean ( 11 / 20 )214.8704918032796.360886861329633.7799581233811
Winsorized Mean ( 12 / 20 )211.0737704918035.5802941250994437.8248468198873
Winsorized Mean ( 13 / 20 )210.0081967213115.3112111011617439.5405478564721
Winsorized Mean ( 14 / 20 )209.9852459016394.9893716743971342.0865110088260
Winsorized Mean ( 15 / 20 )210.3540983606564.3350626480686848.5238889118178
Winsorized Mean ( 16 / 20 )210.9836065573774.0050761372512852.6790501171788
Winsorized Mean ( 17 / 20 )213.2688524590163.6245802779311258.839599651728
Winsorized Mean ( 18 / 20 )211.1442622950823.2536406885212364.894769431669
Winsorized Mean ( 19 / 20 )212.9196721311482.8125293632197775.7039819443514
Winsorized Mean ( 20 / 20 )213.0508196721312.6776555920574779.5661773321738
Trimmed Mean ( 1 / 20 )225.37118644067810.793682550332620.8799161351779
Trimmed Mean ( 2 / 20 )223.06491228070210.053226919697122.1883892666995
Trimmed Mean ( 3 / 20 )221.0854545454559.4078878067496823.5000096819646
Trimmed Mean ( 4 / 20 )219.3962264150948.780347316619424.9871922491975
Trimmed Mean ( 5 / 20 )217.9686274509808.2723126624814926.3491766262127
Trimmed Mean ( 6 / 20 )216.7979591836737.8038846999317727.7807742579242
Trimmed Mean ( 7 / 20 )215.3872340425537.2633109277979729.6541393014346
Trimmed Mean ( 8 / 20 )214.3266666666676.8240094556283431.4077329552780
Trimmed Mean ( 9 / 20 )213.5116279069776.4355293298442833.1770110838952
Trimmed Mean ( 10 / 20 )212.5902439024395.9317611468594135.8393129188952
Trimmed Mean ( 11 / 20 )211.4974358974365.3785279194236839.3225505316514
Trimmed Mean ( 12 / 20 )210.9918918918924.9950882456927642.2398727537655
Trimmed Mean ( 13 / 20 )210.984.7195744716316644.7031827272045
Trimmed Mean ( 14 / 20 )211.1181818181824.4165783036017547.8012994009443
Trimmed Mean ( 15 / 20 )211.2774193548394.0897845716523051.6597917697854
Trimmed Mean ( 16 / 20 )211.4068965517243.8447614255722754.9856995405787
Trimmed Mean ( 17 / 20 )211.4666666666673.5970983874668858.7881241734909
Trimmed Mean ( 18 / 20 )211.2083.3605055175275862.8500679134107
Trimmed Mean ( 19 / 20 )211.2173913043483.1433765748727967.1944281168079
Trimmed Mean ( 20 / 20 )210.9571428571432.9794260507414470.804624536543
Median213.3
Midrange293.95
Midmean - Weighted Average at Xnp209.936666666667
Midmean - Weighted Average at X(n+1)p211.277419354839
Midmean - Empirical Distribution Function211.277419354839
Midmean - Empirical Distribution Function - Averaging211.277419354839
Midmean - Empirical Distribution Function - Interpolation211.277419354839
Midmean - Closest Observation209.628125
Midmean - True Basic - Statistics Graphics Toolkit211.277419354839
Midmean - MS Excel (old versions)211.277419354839
Number of observations61



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