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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 22 Dec 2010 15:54:42 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/22/t1293033490md2rpcobcgp76vw.htm/, Retrieved Sun, 05 May 2024 21:41:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114337, Retrieved Sun, 05 May 2024 21:41:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact95
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Gemiddelde van de...] [2010-12-22 15:54:42] [27f38de572a508a633f0ad2411de6a3e] [Current]
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Dataseries X:
217,5
205
194
199,3
219,3
211,1
215,2
240,2
242,2
240,7
255,4
253
218,2
203,7
205,6
215,6
188,5
202,9
214
230,3
230
241
259,6
247,8
270,3
289,7
322,7
315
320,2
329,5
360,6
382,2
435,4
464
468,8
403
351,6
252
188
146,5
152,9
148,1
165,1
177
206,1
244,9
228,6
253,4
241,1
261,4
273,7
263,7
272,5
263,2
279,8
298,1
267,6
264,3
264,3
268,7
269,1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114337&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114337&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114337&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean257.5934426229518.9568973541237228.7592268213675
Geometric Mean249.283549342499
Harmonic Mean241.733511417567
Quadratic Mean266.773203855039
Winsorized Mean ( 1 / 20 )257.5409836065578.9208656301074728.8695059745514
Winsorized Mean ( 2 / 20 )256.7606557377058.54423119822930.0507617105357
Winsorized Mean ( 3 / 20 )255.7672131147547.8996391704659532.377075407568
Winsorized Mean ( 4 / 20 )255.1836065573777.3467011221936134.734447789974
Winsorized Mean ( 5 / 20 )254.3147540983616.7021103584758237.9454739620546
Winsorized Mean ( 6 / 20 )253.478688524596.464892205455939.2084941974241
Winsorized Mean ( 7 / 20 )251.5737704918035.7501783776747743.750602845391
Winsorized Mean ( 8 / 20 )251.3770491803285.4383757788248146.222817143145
Winsorized Mean ( 9 / 20 )251.5393442622955.2748259125902947.6867575215904
Winsorized Mean ( 10 / 20 )250.8180327868855.072188988758949.4496623337092
Winsorized Mean ( 11 / 20 )248.0049180327874.4238650029239956.0606885311523
Winsorized Mean ( 12 / 20 )246.4704918032794.103087831142260.0695139725214
Winsorized Mean ( 13 / 20 )244.4672131147543.7325658276097165.4957539680708
Winsorized Mean ( 14 / 20 )244.2147540983613.3245278526403273.458477390829
Winsorized Mean ( 15 / 20 )244.6327868852463.1642959673385877.3103367732702
Winsorized Mean ( 16 / 20 )244.3704918032793.0301250170446280.6469998527062
Winsorized Mean ( 17 / 20 )244.1475409836072.9649312845614982.3450925338107
Winsorized Mean ( 18 / 20 )244.5901639344262.8590922027097785.5481903320957
Winsorized Mean ( 19 / 20 )244.4655737704922.7768213982621388.0379177153741
Winsorized Mean ( 20 / 20 )243.7442622950822.5725606776873994.7477213692765
Trimmed Mean ( 1 / 20 )255.8966101694928.3134698662025430.7809632184763
Trimmed Mean ( 2 / 20 )254.1368421052637.5386163876382733.7113376032760
Trimmed Mean ( 3 / 20 )252.6818181818186.8209925968382237.0447284019844
Trimmed Mean ( 4 / 20 )251.4981132075476.2553793921213340.2050934791117
Trimmed Mean ( 5 / 20 )250.3960784313735.7784847466213743.3324806434381
Trimmed Mean ( 6 / 20 )249.4204081632655.4187701145511246.0289702073709
Trimmed Mean ( 7 / 20 )248.5425531914895.0379574446832149.3339921824445
Trimmed Mean ( 8 / 20 )247.9555555555564.784721639471651.8223575453259
Trimmed Mean ( 9 / 20 )247.3488372093024.5482114967768754.3837588433581
Trimmed Mean ( 10 / 20 )246.6560975609764.2810316866616557.6160410887587
Trimmed Mean ( 11 / 20 )246.0051282051283.984113101139561.7465222397347
Trimmed Mean ( 12 / 20 )245.7054054054053.789248948906164.8427719367282
Trimmed Mean ( 13 / 20 )245.5942857142863.6184632581442967.8725382001632
Trimmed Mean ( 14 / 20 )245.7545454545453.4883900811300870.4492730855754
Trimmed Mean ( 15 / 20 )245.9709677419353.4183225262566671.9566295610185
Trimmed Mean ( 16 / 20 )246.1586206896553.3550253361107973.3701227350513
Trimmed Mean ( 17 / 20 )246.4111111111113.2896857431522274.9041490130291
Trimmed Mean ( 18 / 20 )246.7363.1964348890677.1909982726286
Trimmed Mean ( 19 / 20 )247.0521739130433.0770273985249880.2892343537375
Trimmed Mean ( 20 / 20 )247.4476190476192.9002924240711985.3181620563188
Median247.8
Midrange307.65
Midmean - Weighted Average at Xnp245.086666666667
Midmean - Weighted Average at X(n+1)p245.970967741935
Midmean - Empirical Distribution Function245.970967741935
Midmean - Empirical Distribution Function - Averaging245.970967741935
Midmean - Empirical Distribution Function - Interpolation245.970967741935
Midmean - Closest Observation244.88125
Midmean - True Basic - Statistics Graphics Toolkit245.970967741935
Midmean - MS Excel (old versions)245.970967741935
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 257.593442622951 & 8.95689735412372 & 28.7592268213675 \tabularnewline
Geometric Mean & 249.283549342499 &  &  \tabularnewline
Harmonic Mean & 241.733511417567 &  &  \tabularnewline
Quadratic Mean & 266.773203855039 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 257.540983606557 & 8.92086563010747 & 28.8695059745514 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 256.760655737705 & 8.544231198229 & 30.0507617105357 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 255.767213114754 & 7.89963917046595 & 32.377075407568 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 255.183606557377 & 7.34670112219361 & 34.734447789974 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 254.314754098361 & 6.70211035847582 & 37.9454739620546 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 253.47868852459 & 6.4648922054559 & 39.2084941974241 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 251.573770491803 & 5.75017837767477 & 43.750602845391 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 251.377049180328 & 5.43837577882481 & 46.222817143145 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 251.539344262295 & 5.27482591259029 & 47.6867575215904 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 250.818032786885 & 5.0721889887589 & 49.4496623337092 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 248.004918032787 & 4.42386500292399 & 56.0606885311523 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 246.470491803279 & 4.1030878311422 & 60.0695139725214 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 244.467213114754 & 3.73256582760971 & 65.4957539680708 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 244.214754098361 & 3.32452785264032 & 73.458477390829 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 244.632786885246 & 3.16429596733858 & 77.3103367732702 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 244.370491803279 & 3.03012501704462 & 80.6469998527062 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 244.147540983607 & 2.96493128456149 & 82.3450925338107 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 244.590163934426 & 2.85909220270977 & 85.5481903320957 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 244.465573770492 & 2.77682139826213 & 88.0379177153741 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 243.744262295082 & 2.57256067768739 & 94.7477213692765 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 255.896610169492 & 8.31346986620254 & 30.7809632184763 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 254.136842105263 & 7.53861638763827 & 33.7113376032760 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 252.681818181818 & 6.82099259683822 & 37.0447284019844 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 251.498113207547 & 6.25537939212133 & 40.2050934791117 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 250.396078431373 & 5.77848474662137 & 43.3324806434381 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 249.420408163265 & 5.41877011455112 & 46.0289702073709 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 248.542553191489 & 5.03795744468321 & 49.3339921824445 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 247.955555555556 & 4.7847216394716 & 51.8223575453259 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 247.348837209302 & 4.54821149677687 & 54.3837588433581 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 246.656097560976 & 4.28103168666165 & 57.6160410887587 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 246.005128205128 & 3.9841131011395 & 61.7465222397347 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 245.705405405405 & 3.7892489489061 & 64.8427719367282 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 245.594285714286 & 3.61846325814429 & 67.8725382001632 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 245.754545454545 & 3.48839008113008 & 70.4492730855754 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 245.970967741935 & 3.41832252625666 & 71.9566295610185 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 246.158620689655 & 3.35502533611079 & 73.3701227350513 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 246.411111111111 & 3.28968574315222 & 74.9041490130291 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 246.736 & 3.19643488906 & 77.1909982726286 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 247.052173913043 & 3.07702739852498 & 80.2892343537375 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 247.447619047619 & 2.90029242407119 & 85.3181620563188 \tabularnewline
Median & 247.8 &  &  \tabularnewline
Midrange & 307.65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 245.086666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 245.970967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 245.970967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 245.970967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 245.970967741935 &  &  \tabularnewline
Midmean - Closest Observation & 244.88125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 245.970967741935 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 245.970967741935 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114337&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]257.593442622951[/C][C]8.95689735412372[/C][C]28.7592268213675[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]249.283549342499[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]241.733511417567[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]266.773203855039[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]257.540983606557[/C][C]8.92086563010747[/C][C]28.8695059745514[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]256.760655737705[/C][C]8.544231198229[/C][C]30.0507617105357[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]255.767213114754[/C][C]7.89963917046595[/C][C]32.377075407568[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]255.183606557377[/C][C]7.34670112219361[/C][C]34.734447789974[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]254.314754098361[/C][C]6.70211035847582[/C][C]37.9454739620546[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]253.47868852459[/C][C]6.4648922054559[/C][C]39.2084941974241[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]251.573770491803[/C][C]5.75017837767477[/C][C]43.750602845391[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]251.377049180328[/C][C]5.43837577882481[/C][C]46.222817143145[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]251.539344262295[/C][C]5.27482591259029[/C][C]47.6867575215904[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]250.818032786885[/C][C]5.0721889887589[/C][C]49.4496623337092[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]248.004918032787[/C][C]4.42386500292399[/C][C]56.0606885311523[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]246.470491803279[/C][C]4.1030878311422[/C][C]60.0695139725214[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]244.467213114754[/C][C]3.73256582760971[/C][C]65.4957539680708[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]244.214754098361[/C][C]3.32452785264032[/C][C]73.458477390829[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]244.632786885246[/C][C]3.16429596733858[/C][C]77.3103367732702[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]244.370491803279[/C][C]3.03012501704462[/C][C]80.6469998527062[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]244.147540983607[/C][C]2.96493128456149[/C][C]82.3450925338107[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]244.590163934426[/C][C]2.85909220270977[/C][C]85.5481903320957[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]244.465573770492[/C][C]2.77682139826213[/C][C]88.0379177153741[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]243.744262295082[/C][C]2.57256067768739[/C][C]94.7477213692765[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]255.896610169492[/C][C]8.31346986620254[/C][C]30.7809632184763[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]254.136842105263[/C][C]7.53861638763827[/C][C]33.7113376032760[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]252.681818181818[/C][C]6.82099259683822[/C][C]37.0447284019844[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]251.498113207547[/C][C]6.25537939212133[/C][C]40.2050934791117[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]250.396078431373[/C][C]5.77848474662137[/C][C]43.3324806434381[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]249.420408163265[/C][C]5.41877011455112[/C][C]46.0289702073709[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]248.542553191489[/C][C]5.03795744468321[/C][C]49.3339921824445[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]247.955555555556[/C][C]4.7847216394716[/C][C]51.8223575453259[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]247.348837209302[/C][C]4.54821149677687[/C][C]54.3837588433581[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]246.656097560976[/C][C]4.28103168666165[/C][C]57.6160410887587[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]246.005128205128[/C][C]3.9841131011395[/C][C]61.7465222397347[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]245.705405405405[/C][C]3.7892489489061[/C][C]64.8427719367282[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]245.594285714286[/C][C]3.61846325814429[/C][C]67.8725382001632[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]245.754545454545[/C][C]3.48839008113008[/C][C]70.4492730855754[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]245.970967741935[/C][C]3.41832252625666[/C][C]71.9566295610185[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]246.158620689655[/C][C]3.35502533611079[/C][C]73.3701227350513[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]246.411111111111[/C][C]3.28968574315222[/C][C]74.9041490130291[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]246.736[/C][C]3.19643488906[/C][C]77.1909982726286[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]247.052173913043[/C][C]3.07702739852498[/C][C]80.2892343537375[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]247.447619047619[/C][C]2.90029242407119[/C][C]85.3181620563188[/C][/ROW]
[ROW][C]Median[/C][C]247.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]307.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]245.086666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]245.970967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]245.970967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]245.970967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]245.970967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]244.88125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]245.970967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]245.970967741935[/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=114337&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114337&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 Mean257.5934426229518.9568973541237228.7592268213675
Geometric Mean249.283549342499
Harmonic Mean241.733511417567
Quadratic Mean266.773203855039
Winsorized Mean ( 1 / 20 )257.5409836065578.9208656301074728.8695059745514
Winsorized Mean ( 2 / 20 )256.7606557377058.54423119822930.0507617105357
Winsorized Mean ( 3 / 20 )255.7672131147547.8996391704659532.377075407568
Winsorized Mean ( 4 / 20 )255.1836065573777.3467011221936134.734447789974
Winsorized Mean ( 5 / 20 )254.3147540983616.7021103584758237.9454739620546
Winsorized Mean ( 6 / 20 )253.478688524596.464892205455939.2084941974241
Winsorized Mean ( 7 / 20 )251.5737704918035.7501783776747743.750602845391
Winsorized Mean ( 8 / 20 )251.3770491803285.4383757788248146.222817143145
Winsorized Mean ( 9 / 20 )251.5393442622955.2748259125902947.6867575215904
Winsorized Mean ( 10 / 20 )250.8180327868855.072188988758949.4496623337092
Winsorized Mean ( 11 / 20 )248.0049180327874.4238650029239956.0606885311523
Winsorized Mean ( 12 / 20 )246.4704918032794.103087831142260.0695139725214
Winsorized Mean ( 13 / 20 )244.4672131147543.7325658276097165.4957539680708
Winsorized Mean ( 14 / 20 )244.2147540983613.3245278526403273.458477390829
Winsorized Mean ( 15 / 20 )244.6327868852463.1642959673385877.3103367732702
Winsorized Mean ( 16 / 20 )244.3704918032793.0301250170446280.6469998527062
Winsorized Mean ( 17 / 20 )244.1475409836072.9649312845614982.3450925338107
Winsorized Mean ( 18 / 20 )244.5901639344262.8590922027097785.5481903320957
Winsorized Mean ( 19 / 20 )244.4655737704922.7768213982621388.0379177153741
Winsorized Mean ( 20 / 20 )243.7442622950822.5725606776873994.7477213692765
Trimmed Mean ( 1 / 20 )255.8966101694928.3134698662025430.7809632184763
Trimmed Mean ( 2 / 20 )254.1368421052637.5386163876382733.7113376032760
Trimmed Mean ( 3 / 20 )252.6818181818186.8209925968382237.0447284019844
Trimmed Mean ( 4 / 20 )251.4981132075476.2553793921213340.2050934791117
Trimmed Mean ( 5 / 20 )250.3960784313735.7784847466213743.3324806434381
Trimmed Mean ( 6 / 20 )249.4204081632655.4187701145511246.0289702073709
Trimmed Mean ( 7 / 20 )248.5425531914895.0379574446832149.3339921824445
Trimmed Mean ( 8 / 20 )247.9555555555564.784721639471651.8223575453259
Trimmed Mean ( 9 / 20 )247.3488372093024.5482114967768754.3837588433581
Trimmed Mean ( 10 / 20 )246.6560975609764.2810316866616557.6160410887587
Trimmed Mean ( 11 / 20 )246.0051282051283.984113101139561.7465222397347
Trimmed Mean ( 12 / 20 )245.7054054054053.789248948906164.8427719367282
Trimmed Mean ( 13 / 20 )245.5942857142863.6184632581442967.8725382001632
Trimmed Mean ( 14 / 20 )245.7545454545453.4883900811300870.4492730855754
Trimmed Mean ( 15 / 20 )245.9709677419353.4183225262566671.9566295610185
Trimmed Mean ( 16 / 20 )246.1586206896553.3550253361107973.3701227350513
Trimmed Mean ( 17 / 20 )246.4111111111113.2896857431522274.9041490130291
Trimmed Mean ( 18 / 20 )246.7363.1964348890677.1909982726286
Trimmed Mean ( 19 / 20 )247.0521739130433.0770273985249880.2892343537375
Trimmed Mean ( 20 / 20 )247.4476190476192.9002924240711985.3181620563188
Median247.8
Midrange307.65
Midmean - Weighted Average at Xnp245.086666666667
Midmean - Weighted Average at X(n+1)p245.970967741935
Midmean - Empirical Distribution Function245.970967741935
Midmean - Empirical Distribution Function - Averaging245.970967741935
Midmean - Empirical Distribution Function - Interpolation245.970967741935
Midmean - Closest Observation244.88125
Midmean - True Basic - Statistics Graphics Toolkit245.970967741935
Midmean - MS Excel (old versions)245.970967741935
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')