Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 12 Oct 2016 13:47:23 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/12/t1476276709dmk4lrlxuif4i7o.htm/, Retrieved Sun, 05 May 2024 22:34:04 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 05 May 2024 22:34:04 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
180
215
264
197
262
191
200
221
211
212
304
191
255
273
248
196
261
230
278
245
244
276
281
215
269
231
290
248
294
250
272
196
204
293
243
228
238
219
185
211
171
129
145
142
169
152
141
146
119
141
150
111
83
107
104
81
106
113
86
131





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Gertrude Mary Cox' @ cox.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean200.87.9990394903614325.1030139608583
Geometric Mean189.934243250759
Harmonic Mean177.714079515765
Quadratic Mean209.989841024116
Winsorized Mean ( 1 / 20 )200.6666666666677.955833828208825.2225814414534
Winsorized Mean ( 2 / 20 )200.7333333333337.9244264675700425.330960436672
Winsorized Mean ( 3 / 20 )201.4833333333337.6876337585778926.208758073122
Winsorized Mean ( 4 / 20 )201.0166666666677.5465969307632226.6367302389286
Winsorized Mean ( 5 / 20 )200.857.4845537741230826.8352671463747
Winsorized Mean ( 6 / 20 )201.057.3658789235490527.2947739280962
Winsorized Mean ( 7 / 20 )200.9333333333337.2581093033333227.683977319142
Winsorized Mean ( 8 / 20 )201.67.074310970420728.4974749969199
Winsorized Mean ( 9 / 20 )202.656.7104701478003630.1990762996579
Winsorized Mean ( 10 / 20 )202.156.5116507926329831.0443551777537
Winsorized Mean ( 11 / 20 )203.6166666666676.1235440638629833.2514414109102
Winsorized Mean ( 12 / 20 )203.4166666666676.0913614699374733.3942859360068
Winsorized Mean ( 13 / 20 )202.3333333333335.8501855041652334.5857978673113
Winsorized Mean ( 14 / 20 )201.8666666666675.5534621291214136.3496971750491
Winsorized Mean ( 15 / 20 )201.6166666666675.4372169926567637.0808571625816
Winsorized Mean ( 16 / 20 )202.6833333333335.2540805592929938.5763657496351
Winsorized Mean ( 17 / 20 )202.45.0347493050768440.2006113384648
Winsorized Mean ( 18 / 20 )207.24.1576829705517349.8354495683216
Winsorized Mean ( 19 / 20 )207.5166666666674.0120223049626651.7237071214633
Winsorized Mean ( 20 / 20 )208.853.3085939287423563.1234912769689
Trimmed Mean ( 1 / 20 )201.0862068965527.8070068146484725.7571450455569
Trimmed Mean ( 2 / 20 )201.5357142857147.6215247258385126.4429653560616
Trimmed Mean ( 3 / 20 )201.9814814814817.4108958417533527.2546647253505
Trimmed Mean ( 4 / 20 )202.1730769230777.2614252386231527.8420654732805
Trimmed Mean ( 5 / 20 )202.527.1247335789788428.4249225258787
Trimmed Mean ( 6 / 20 )202.93756.968037861555529.1240524279668
Trimmed Mean ( 7 / 20 )203.3478260869576.800768455535129.90071304684
Trimmed Mean ( 8 / 20 )203.8181818181826.6119624379162330.8256714601687
Trimmed Mean ( 9 / 20 )204.2142857142866.415042545801531.8336603781279
Trimmed Mean ( 10 / 20 )204.4756.2536130582289232.6970981568708
Trimmed Mean ( 11 / 20 )204.8421052631586.0850452502948433.6632016422939
Trimmed Mean ( 12 / 20 )205.0277777777785.9573199086356934.4161100834237
Trimmed Mean ( 13 / 20 )205.2647058823535.7798760886263135.5136862339099
Trimmed Mean ( 14 / 20 )205.68755.5902488367202136.793979303554
Trimmed Mean ( 15 / 20 )206.2333333333335.3974628636040438.2093102898397
Trimmed Mean ( 16 / 20 )206.8928571428575.1383863209543840.2641693753438
Trimmed Mean ( 17 / 20 )207.54.8077661532790343.1593370776737
Trimmed Mean ( 18 / 20 )208.254.3664772057581847.6929089943205
Trimmed Mean ( 19 / 20 )208.4090909090914.0838924915726351.0319728884039
Trimmed Mean ( 20 / 20 )208.553.6666885964256556.8769325552484
Median211
Midrange192.5
Midmean - Weighted Average at Xnp204.258064516129
Midmean - Weighted Average at X(n+1)p206.233333333333
Midmean - Empirical Distribution Function204.258064516129
Midmean - Empirical Distribution Function - Averaging206.233333333333
Midmean - Empirical Distribution Function - Interpolation206.233333333333
Midmean - Closest Observation204.258064516129
Midmean - True Basic - Statistics Graphics Toolkit206.233333333333
Midmean - MS Excel (old versions)205.6875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 200.8 & 7.99903949036143 & 25.1030139608583 \tabularnewline
Geometric Mean & 189.934243250759 &  &  \tabularnewline
Harmonic Mean & 177.714079515765 &  &  \tabularnewline
Quadratic Mean & 209.989841024116 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 200.666666666667 & 7.9558338282088 & 25.2225814414534 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 200.733333333333 & 7.92442646757004 & 25.330960436672 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 201.483333333333 & 7.68763375857789 & 26.208758073122 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 201.016666666667 & 7.54659693076322 & 26.6367302389286 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 200.85 & 7.48455377412308 & 26.8352671463747 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 201.05 & 7.36587892354905 & 27.2947739280962 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 200.933333333333 & 7.25810930333332 & 27.683977319142 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 201.6 & 7.0743109704207 & 28.4974749969199 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 202.65 & 6.71047014780036 & 30.1990762996579 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 202.15 & 6.51165079263298 & 31.0443551777537 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 203.616666666667 & 6.12354406386298 & 33.2514414109102 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 203.416666666667 & 6.09136146993747 & 33.3942859360068 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 202.333333333333 & 5.85018550416523 & 34.5857978673113 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 201.866666666667 & 5.55346212912141 & 36.3496971750491 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 201.616666666667 & 5.43721699265676 & 37.0808571625816 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 202.683333333333 & 5.25408055929299 & 38.5763657496351 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 202.4 & 5.03474930507684 & 40.2006113384648 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 207.2 & 4.15768297055173 & 49.8354495683216 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 207.516666666667 & 4.01202230496266 & 51.7237071214633 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 208.85 & 3.30859392874235 & 63.1234912769689 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 201.086206896552 & 7.80700681464847 & 25.7571450455569 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 201.535714285714 & 7.62152472583851 & 26.4429653560616 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 201.981481481481 & 7.41089584175335 & 27.2546647253505 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 202.173076923077 & 7.26142523862315 & 27.8420654732805 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 202.52 & 7.12473357897884 & 28.4249225258787 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 202.9375 & 6.9680378615555 & 29.1240524279668 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 203.347826086957 & 6.8007684555351 & 29.90071304684 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 203.818181818182 & 6.61196243791623 & 30.8256714601687 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 204.214285714286 & 6.4150425458015 & 31.8336603781279 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 204.475 & 6.25361305822892 & 32.6970981568708 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 204.842105263158 & 6.08504525029484 & 33.6632016422939 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 205.027777777778 & 5.95731990863569 & 34.4161100834237 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 205.264705882353 & 5.77987608862631 & 35.5136862339099 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 205.6875 & 5.59024883672021 & 36.793979303554 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 206.233333333333 & 5.39746286360404 & 38.2093102898397 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 206.892857142857 & 5.13838632095438 & 40.2641693753438 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 207.5 & 4.80776615327903 & 43.1593370776737 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 208.25 & 4.36647720575818 & 47.6929089943205 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 208.409090909091 & 4.08389249157263 & 51.0319728884039 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 208.55 & 3.66668859642565 & 56.8769325552484 \tabularnewline
Median & 211 &  &  \tabularnewline
Midrange & 192.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 204.258064516129 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 206.233333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 204.258064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 206.233333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 206.233333333333 &  &  \tabularnewline
Midmean - Closest Observation & 204.258064516129 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 206.233333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 205.6875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]200.8[/C][C]7.99903949036143[/C][C]25.1030139608583[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]189.934243250759[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]177.714079515765[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]209.989841024116[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]200.666666666667[/C][C]7.9558338282088[/C][C]25.2225814414534[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]200.733333333333[/C][C]7.92442646757004[/C][C]25.330960436672[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]201.483333333333[/C][C]7.68763375857789[/C][C]26.208758073122[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]201.016666666667[/C][C]7.54659693076322[/C][C]26.6367302389286[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]200.85[/C][C]7.48455377412308[/C][C]26.8352671463747[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]201.05[/C][C]7.36587892354905[/C][C]27.2947739280962[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]200.933333333333[/C][C]7.25810930333332[/C][C]27.683977319142[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]201.6[/C][C]7.0743109704207[/C][C]28.4974749969199[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]202.65[/C][C]6.71047014780036[/C][C]30.1990762996579[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]202.15[/C][C]6.51165079263298[/C][C]31.0443551777537[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]203.616666666667[/C][C]6.12354406386298[/C][C]33.2514414109102[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]203.416666666667[/C][C]6.09136146993747[/C][C]33.3942859360068[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]202.333333333333[/C][C]5.85018550416523[/C][C]34.5857978673113[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]201.866666666667[/C][C]5.55346212912141[/C][C]36.3496971750491[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]201.616666666667[/C][C]5.43721699265676[/C][C]37.0808571625816[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]202.683333333333[/C][C]5.25408055929299[/C][C]38.5763657496351[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]202.4[/C][C]5.03474930507684[/C][C]40.2006113384648[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]207.2[/C][C]4.15768297055173[/C][C]49.8354495683216[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]207.516666666667[/C][C]4.01202230496266[/C][C]51.7237071214633[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]208.85[/C][C]3.30859392874235[/C][C]63.1234912769689[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]201.086206896552[/C][C]7.80700681464847[/C][C]25.7571450455569[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]201.535714285714[/C][C]7.62152472583851[/C][C]26.4429653560616[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]201.981481481481[/C][C]7.41089584175335[/C][C]27.2546647253505[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]202.173076923077[/C][C]7.26142523862315[/C][C]27.8420654732805[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]202.52[/C][C]7.12473357897884[/C][C]28.4249225258787[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]202.9375[/C][C]6.9680378615555[/C][C]29.1240524279668[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]203.347826086957[/C][C]6.8007684555351[/C][C]29.90071304684[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]203.818181818182[/C][C]6.61196243791623[/C][C]30.8256714601687[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]204.214285714286[/C][C]6.4150425458015[/C][C]31.8336603781279[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]204.475[/C][C]6.25361305822892[/C][C]32.6970981568708[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]204.842105263158[/C][C]6.08504525029484[/C][C]33.6632016422939[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]205.027777777778[/C][C]5.95731990863569[/C][C]34.4161100834237[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]205.264705882353[/C][C]5.77987608862631[/C][C]35.5136862339099[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]205.6875[/C][C]5.59024883672021[/C][C]36.793979303554[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]206.233333333333[/C][C]5.39746286360404[/C][C]38.2093102898397[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]206.892857142857[/C][C]5.13838632095438[/C][C]40.2641693753438[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]207.5[/C][C]4.80776615327903[/C][C]43.1593370776737[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]208.25[/C][C]4.36647720575818[/C][C]47.6929089943205[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]208.409090909091[/C][C]4.08389249157263[/C][C]51.0319728884039[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]208.55[/C][C]3.66668859642565[/C][C]56.8769325552484[/C][/ROW]
[ROW][C]Median[/C][C]211[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]192.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]204.258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]206.233333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]204.258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]206.233333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]206.233333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]204.258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]206.233333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]205.6875[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean200.87.9990394903614325.1030139608583
Geometric Mean189.934243250759
Harmonic Mean177.714079515765
Quadratic Mean209.989841024116
Winsorized Mean ( 1 / 20 )200.6666666666677.955833828208825.2225814414534
Winsorized Mean ( 2 / 20 )200.7333333333337.9244264675700425.330960436672
Winsorized Mean ( 3 / 20 )201.4833333333337.6876337585778926.208758073122
Winsorized Mean ( 4 / 20 )201.0166666666677.5465969307632226.6367302389286
Winsorized Mean ( 5 / 20 )200.857.4845537741230826.8352671463747
Winsorized Mean ( 6 / 20 )201.057.3658789235490527.2947739280962
Winsorized Mean ( 7 / 20 )200.9333333333337.2581093033333227.683977319142
Winsorized Mean ( 8 / 20 )201.67.074310970420728.4974749969199
Winsorized Mean ( 9 / 20 )202.656.7104701478003630.1990762996579
Winsorized Mean ( 10 / 20 )202.156.5116507926329831.0443551777537
Winsorized Mean ( 11 / 20 )203.6166666666676.1235440638629833.2514414109102
Winsorized Mean ( 12 / 20 )203.4166666666676.0913614699374733.3942859360068
Winsorized Mean ( 13 / 20 )202.3333333333335.8501855041652334.5857978673113
Winsorized Mean ( 14 / 20 )201.8666666666675.5534621291214136.3496971750491
Winsorized Mean ( 15 / 20 )201.6166666666675.4372169926567637.0808571625816
Winsorized Mean ( 16 / 20 )202.6833333333335.2540805592929938.5763657496351
Winsorized Mean ( 17 / 20 )202.45.0347493050768440.2006113384648
Winsorized Mean ( 18 / 20 )207.24.1576829705517349.8354495683216
Winsorized Mean ( 19 / 20 )207.5166666666674.0120223049626651.7237071214633
Winsorized Mean ( 20 / 20 )208.853.3085939287423563.1234912769689
Trimmed Mean ( 1 / 20 )201.0862068965527.8070068146484725.7571450455569
Trimmed Mean ( 2 / 20 )201.5357142857147.6215247258385126.4429653560616
Trimmed Mean ( 3 / 20 )201.9814814814817.4108958417533527.2546647253505
Trimmed Mean ( 4 / 20 )202.1730769230777.2614252386231527.8420654732805
Trimmed Mean ( 5 / 20 )202.527.1247335789788428.4249225258787
Trimmed Mean ( 6 / 20 )202.93756.968037861555529.1240524279668
Trimmed Mean ( 7 / 20 )203.3478260869576.800768455535129.90071304684
Trimmed Mean ( 8 / 20 )203.8181818181826.6119624379162330.8256714601687
Trimmed Mean ( 9 / 20 )204.2142857142866.415042545801531.8336603781279
Trimmed Mean ( 10 / 20 )204.4756.2536130582289232.6970981568708
Trimmed Mean ( 11 / 20 )204.8421052631586.0850452502948433.6632016422939
Trimmed Mean ( 12 / 20 )205.0277777777785.9573199086356934.4161100834237
Trimmed Mean ( 13 / 20 )205.2647058823535.7798760886263135.5136862339099
Trimmed Mean ( 14 / 20 )205.68755.5902488367202136.793979303554
Trimmed Mean ( 15 / 20 )206.2333333333335.3974628636040438.2093102898397
Trimmed Mean ( 16 / 20 )206.8928571428575.1383863209543840.2641693753438
Trimmed Mean ( 17 / 20 )207.54.8077661532790343.1593370776737
Trimmed Mean ( 18 / 20 )208.254.3664772057581847.6929089943205
Trimmed Mean ( 19 / 20 )208.4090909090914.0838924915726351.0319728884039
Trimmed Mean ( 20 / 20 )208.553.6666885964256556.8769325552484
Median211
Midrange192.5
Midmean - Weighted Average at Xnp204.258064516129
Midmean - Weighted Average at X(n+1)p206.233333333333
Midmean - Empirical Distribution Function204.258064516129
Midmean - Empirical Distribution Function - Averaging206.233333333333
Midmean - Empirical Distribution Function - Interpolation206.233333333333
Midmean - Closest Observation204.258064516129
Midmean - True Basic - Statistics Graphics Toolkit206.233333333333
Midmean - MS Excel (old versions)205.6875
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')