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 11:53:30 +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/t1476270050df8unl0w3727g6k.htm/, Retrieved Sun, 05 May 2024 21:37:35 +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 21:37:35 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
182 414
182 510
186 424
187 827
188 222
189 422
191 395
191 568
191 987
192 684
195 978
198 480
200 140
201 920
203 089
203 583
205 491
206 996
207 221
210 027
210 176
210 506
211 451
211 524
211 701
214 419
215 177
215 191
216 222
217 811
219 576
220 189
221 270
224 325
224 790
225 436
225 939
227 755
228 987
229 127
229 570
229 697
229 827
230 079
230 703
233 164
235 572
235 980
236 168
236 675
237 201
237 736
239 567
239 973
241 292
242 084
245 413
245 472
247 826
248 511




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean217524.3333333332402.2244227408990.551212149089
Geometric Mean216727.761786897
Harmonic Mean215918.682635494
Quadratic Mean218305.533233967
Winsorized Mean ( 1 / 20 )217514.5166666672399.3581209082190.6552943352752
Winsorized Mean ( 2 / 20 )217566.5166666672352.2804293614592.491742885319
Winsorized Mean ( 3 / 20 )217633.7166666672336.2301630250593.1559399031408
Winsorized Mean ( 4 / 20 )217438.1166666672287.8868614973695.0388414418182
Winsorized Mean ( 5 / 20 )217472.1166666672254.5839829578396.4577581986373
Winsorized Mean ( 6 / 20 )217537.5166666672190.5517369243399.3071804695666
Winsorized Mean ( 7 / 20 )217510.3333333332178.2974501127399.8533663628341
Winsorized Mean ( 8 / 20 )217322.0666666672126.19107409012102.211917505894
Winsorized Mean ( 9 / 20 )217346.3666666672092.20440229871103.883906576177
Winsorized Mean ( 10 / 20 )217807.71971.5908958558110.47307048223
Winsorized Mean ( 11 / 20 )218173.451872.50440072876116.514252204208
Winsorized Mean ( 12 / 20 )218467.851808.22962203444120.81864346089
Winsorized Mean ( 13 / 20 )218765.1166666671728.68679578022126.549885844376
Winsorized Mean ( 14 / 20 )218476.0166666671593.55352250602137.099892523906
Winsorized Mean ( 15 / 20 )217984.2666666671480.29155107899147.257657795707
Winsorized Mean ( 16 / 20 )218326.6666666671373.81310451581158.920209706119
Winsorized Mean ( 17 / 20 )218681.6833333331297.08395101628168.594857073048
Winsorized Mean ( 18 / 20 )218710.1833333331281.1258494331170.717173047529
Winsorized Mean ( 19 / 20 )219558.5333333331144.72211106586191.800727190374
Winsorized Mean ( 20 / 20 )219460.5333333331115.92955740934196.661636817665
Trimmed Mean ( 1 / 20 )217595.4310344832348.5597333258292.6505840779037
Trimmed Mean ( 2 / 20 )217682.1252285.5927254290395.2409948535949
Trimmed Mean ( 3 / 20 )217746.3518518522238.4220915475997.276716788167
Trimmed Mean ( 4 / 20 )217789.6730769232186.5692924142199.6033712869258
Trimmed Mean ( 5 / 20 )217895.142139.46592248569101.84557637022
Trimmed Mean ( 6 / 20 )218000.8958333332090.13967139928104.299678541286
Trimmed Mean ( 7 / 20 )218101.6304347832045.92642501593106.602870840326
Trimmed Mean ( 8 / 20 )218216.8181818181990.89596552191109.607343608541
Trimmed Mean ( 9 / 20 )218376.5952380951932.24118939806113.017255007448
Trimmed Mean ( 10 / 20 )218548.31862.85149675822117.319228280044
Trimmed Mean ( 11 / 20 )218665.2368421051803.86442586603121.22043857987
Trimmed Mean ( 12 / 20 )218739.751750.51710971041124.957219090641
Trimmed Mean ( 13 / 20 )218779.7352941181693.49165995378129.188551953122
Trimmed Mean ( 14 / 20 )218781.843751634.91655979092133.818354484084
Trimmed Mean ( 15 / 20 )218825.5333333331589.62133619627137.658905520827
Trimmed Mean ( 16 / 20 )218945.7142857141553.53584572764140.933802646289
Trimmed Mean ( 17 / 20 )2190351528.90076248868143.26305890741
Trimmed Mean ( 18 / 20 )219086.9583333331509.58881108324145.130221372085
Trimmed Mean ( 19 / 20 )219144.0454545451474.51964219752148.620634939762
Trimmed Mean ( 20 / 20 )219078.61462.31383772431149.816403529994
Median218693.5
Midrange215462.5
Midmean - Weighted Average at Xnp218317.903225806
Midmean - Weighted Average at X(n+1)p218825.533333333
Midmean - Empirical Distribution Function218317.903225806
Midmean - Empirical Distribution Function - Averaging218825.533333333
Midmean - Empirical Distribution Function - Interpolation218825.533333333
Midmean - Closest Observation218317.903225806
Midmean - True Basic - Statistics Graphics Toolkit218825.533333333
Midmean - MS Excel (old versions)218781.84375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 217524.333333333 & 2402.22442274089 & 90.551212149089 \tabularnewline
Geometric Mean & 216727.761786897 &  &  \tabularnewline
Harmonic Mean & 215918.682635494 &  &  \tabularnewline
Quadratic Mean & 218305.533233967 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 217514.516666667 & 2399.35812090821 & 90.6552943352752 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 217566.516666667 & 2352.28042936145 & 92.491742885319 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 217633.716666667 & 2336.23016302505 & 93.1559399031408 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 217438.116666667 & 2287.88686149736 & 95.0388414418182 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 217472.116666667 & 2254.58398295783 & 96.4577581986373 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 217537.516666667 & 2190.55173692433 & 99.3071804695666 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 217510.333333333 & 2178.29745011273 & 99.8533663628341 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 217322.066666667 & 2126.19107409012 & 102.211917505894 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 217346.366666667 & 2092.20440229871 & 103.883906576177 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 217807.7 & 1971.5908958558 & 110.47307048223 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 218173.45 & 1872.50440072876 & 116.514252204208 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 218467.85 & 1808.22962203444 & 120.81864346089 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 218765.116666667 & 1728.68679578022 & 126.549885844376 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 218476.016666667 & 1593.55352250602 & 137.099892523906 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 217984.266666667 & 1480.29155107899 & 147.257657795707 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 218326.666666667 & 1373.81310451581 & 158.920209706119 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 218681.683333333 & 1297.08395101628 & 168.594857073048 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 218710.183333333 & 1281.1258494331 & 170.717173047529 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 219558.533333333 & 1144.72211106586 & 191.800727190374 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 219460.533333333 & 1115.92955740934 & 196.661636817665 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 217595.431034483 & 2348.55973332582 & 92.6505840779037 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 217682.125 & 2285.59272542903 & 95.2409948535949 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 217746.351851852 & 2238.42209154759 & 97.276716788167 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 217789.673076923 & 2186.56929241421 & 99.6033712869258 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 217895.14 & 2139.46592248569 & 101.84557637022 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 218000.895833333 & 2090.13967139928 & 104.299678541286 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 218101.630434783 & 2045.92642501593 & 106.602870840326 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 218216.818181818 & 1990.89596552191 & 109.607343608541 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 218376.595238095 & 1932.24118939806 & 113.017255007448 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 218548.3 & 1862.85149675822 & 117.319228280044 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 218665.236842105 & 1803.86442586603 & 121.22043857987 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 218739.75 & 1750.51710971041 & 124.957219090641 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 218779.735294118 & 1693.49165995378 & 129.188551953122 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 218781.84375 & 1634.91655979092 & 133.818354484084 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 218825.533333333 & 1589.62133619627 & 137.658905520827 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 218945.714285714 & 1553.53584572764 & 140.933802646289 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 219035 & 1528.90076248868 & 143.26305890741 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 219086.958333333 & 1509.58881108324 & 145.130221372085 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 219144.045454545 & 1474.51964219752 & 148.620634939762 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 219078.6 & 1462.31383772431 & 149.816403529994 \tabularnewline
Median & 218693.5 &  &  \tabularnewline
Midrange & 215462.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 218317.903225806 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 218825.533333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 218317.903225806 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 218825.533333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 218825.533333333 &  &  \tabularnewline
Midmean - Closest Observation & 218317.903225806 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 218825.533333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 218781.84375 &  &  \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]217524.333333333[/C][C]2402.22442274089[/C][C]90.551212149089[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]216727.761786897[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]215918.682635494[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]218305.533233967[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]217514.516666667[/C][C]2399.35812090821[/C][C]90.6552943352752[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]217566.516666667[/C][C]2352.28042936145[/C][C]92.491742885319[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]217633.716666667[/C][C]2336.23016302505[/C][C]93.1559399031408[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]217438.116666667[/C][C]2287.88686149736[/C][C]95.0388414418182[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]217472.116666667[/C][C]2254.58398295783[/C][C]96.4577581986373[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]217537.516666667[/C][C]2190.55173692433[/C][C]99.3071804695666[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]217510.333333333[/C][C]2178.29745011273[/C][C]99.8533663628341[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]217322.066666667[/C][C]2126.19107409012[/C][C]102.211917505894[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]217346.366666667[/C][C]2092.20440229871[/C][C]103.883906576177[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]217807.7[/C][C]1971.5908958558[/C][C]110.47307048223[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]218173.45[/C][C]1872.50440072876[/C][C]116.514252204208[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]218467.85[/C][C]1808.22962203444[/C][C]120.81864346089[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]218765.116666667[/C][C]1728.68679578022[/C][C]126.549885844376[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]218476.016666667[/C][C]1593.55352250602[/C][C]137.099892523906[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]217984.266666667[/C][C]1480.29155107899[/C][C]147.257657795707[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]218326.666666667[/C][C]1373.81310451581[/C][C]158.920209706119[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]218681.683333333[/C][C]1297.08395101628[/C][C]168.594857073048[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]218710.183333333[/C][C]1281.1258494331[/C][C]170.717173047529[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]219558.533333333[/C][C]1144.72211106586[/C][C]191.800727190374[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]219460.533333333[/C][C]1115.92955740934[/C][C]196.661636817665[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]217595.431034483[/C][C]2348.55973332582[/C][C]92.6505840779037[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]217682.125[/C][C]2285.59272542903[/C][C]95.2409948535949[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]217746.351851852[/C][C]2238.42209154759[/C][C]97.276716788167[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]217789.673076923[/C][C]2186.56929241421[/C][C]99.6033712869258[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]217895.14[/C][C]2139.46592248569[/C][C]101.84557637022[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]218000.895833333[/C][C]2090.13967139928[/C][C]104.299678541286[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]218101.630434783[/C][C]2045.92642501593[/C][C]106.602870840326[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]218216.818181818[/C][C]1990.89596552191[/C][C]109.607343608541[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]218376.595238095[/C][C]1932.24118939806[/C][C]113.017255007448[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]218548.3[/C][C]1862.85149675822[/C][C]117.319228280044[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]218665.236842105[/C][C]1803.86442586603[/C][C]121.22043857987[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]218739.75[/C][C]1750.51710971041[/C][C]124.957219090641[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]218779.735294118[/C][C]1693.49165995378[/C][C]129.188551953122[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]218781.84375[/C][C]1634.91655979092[/C][C]133.818354484084[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]218825.533333333[/C][C]1589.62133619627[/C][C]137.658905520827[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]218945.714285714[/C][C]1553.53584572764[/C][C]140.933802646289[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]219035[/C][C]1528.90076248868[/C][C]143.26305890741[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]219086.958333333[/C][C]1509.58881108324[/C][C]145.130221372085[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]219144.045454545[/C][C]1474.51964219752[/C][C]148.620634939762[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]219078.6[/C][C]1462.31383772431[/C][C]149.816403529994[/C][/ROW]
[ROW][C]Median[/C][C]218693.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]215462.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]218317.903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]218825.533333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]218317.903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]218825.533333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]218825.533333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]218317.903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]218825.533333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]218781.84375[/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 Mean217524.3333333332402.2244227408990.551212149089
Geometric Mean216727.761786897
Harmonic Mean215918.682635494
Quadratic Mean218305.533233967
Winsorized Mean ( 1 / 20 )217514.5166666672399.3581209082190.6552943352752
Winsorized Mean ( 2 / 20 )217566.5166666672352.2804293614592.491742885319
Winsorized Mean ( 3 / 20 )217633.7166666672336.2301630250593.1559399031408
Winsorized Mean ( 4 / 20 )217438.1166666672287.8868614973695.0388414418182
Winsorized Mean ( 5 / 20 )217472.1166666672254.5839829578396.4577581986373
Winsorized Mean ( 6 / 20 )217537.5166666672190.5517369243399.3071804695666
Winsorized Mean ( 7 / 20 )217510.3333333332178.2974501127399.8533663628341
Winsorized Mean ( 8 / 20 )217322.0666666672126.19107409012102.211917505894
Winsorized Mean ( 9 / 20 )217346.3666666672092.20440229871103.883906576177
Winsorized Mean ( 10 / 20 )217807.71971.5908958558110.47307048223
Winsorized Mean ( 11 / 20 )218173.451872.50440072876116.514252204208
Winsorized Mean ( 12 / 20 )218467.851808.22962203444120.81864346089
Winsorized Mean ( 13 / 20 )218765.1166666671728.68679578022126.549885844376
Winsorized Mean ( 14 / 20 )218476.0166666671593.55352250602137.099892523906
Winsorized Mean ( 15 / 20 )217984.2666666671480.29155107899147.257657795707
Winsorized Mean ( 16 / 20 )218326.6666666671373.81310451581158.920209706119
Winsorized Mean ( 17 / 20 )218681.6833333331297.08395101628168.594857073048
Winsorized Mean ( 18 / 20 )218710.1833333331281.1258494331170.717173047529
Winsorized Mean ( 19 / 20 )219558.5333333331144.72211106586191.800727190374
Winsorized Mean ( 20 / 20 )219460.5333333331115.92955740934196.661636817665
Trimmed Mean ( 1 / 20 )217595.4310344832348.5597333258292.6505840779037
Trimmed Mean ( 2 / 20 )217682.1252285.5927254290395.2409948535949
Trimmed Mean ( 3 / 20 )217746.3518518522238.4220915475997.276716788167
Trimmed Mean ( 4 / 20 )217789.6730769232186.5692924142199.6033712869258
Trimmed Mean ( 5 / 20 )217895.142139.46592248569101.84557637022
Trimmed Mean ( 6 / 20 )218000.8958333332090.13967139928104.299678541286
Trimmed Mean ( 7 / 20 )218101.6304347832045.92642501593106.602870840326
Trimmed Mean ( 8 / 20 )218216.8181818181990.89596552191109.607343608541
Trimmed Mean ( 9 / 20 )218376.5952380951932.24118939806113.017255007448
Trimmed Mean ( 10 / 20 )218548.31862.85149675822117.319228280044
Trimmed Mean ( 11 / 20 )218665.2368421051803.86442586603121.22043857987
Trimmed Mean ( 12 / 20 )218739.751750.51710971041124.957219090641
Trimmed Mean ( 13 / 20 )218779.7352941181693.49165995378129.188551953122
Trimmed Mean ( 14 / 20 )218781.843751634.91655979092133.818354484084
Trimmed Mean ( 15 / 20 )218825.5333333331589.62133619627137.658905520827
Trimmed Mean ( 16 / 20 )218945.7142857141553.53584572764140.933802646289
Trimmed Mean ( 17 / 20 )2190351528.90076248868143.26305890741
Trimmed Mean ( 18 / 20 )219086.9583333331509.58881108324145.130221372085
Trimmed Mean ( 19 / 20 )219144.0454545451474.51964219752148.620634939762
Trimmed Mean ( 20 / 20 )219078.61462.31383772431149.816403529994
Median218693.5
Midrange215462.5
Midmean - Weighted Average at Xnp218317.903225806
Midmean - Weighted Average at X(n+1)p218825.533333333
Midmean - Empirical Distribution Function218317.903225806
Midmean - Empirical Distribution Function - Averaging218825.533333333
Midmean - Empirical Distribution Function - Interpolation218825.533333333
Midmean - Closest Observation218317.903225806
Midmean - True Basic - Statistics Graphics Toolkit218825.533333333
Midmean - MS Excel (old versions)218781.84375
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')