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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 20 Oct 2007 03:19:05 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Oct/20/o0rmd82ga4zkl121192875496.htm/, Retrieved Thu, 02 May 2024 19:11:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1156, Retrieved Thu, 02 May 2024 19:11:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact174
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [WS2Q9 G6 niet wer...] [2007-10-20 10:19:05] [68cb8c72d4101523a7ee439633ed352d] [Current]
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Dataseries X:
242621
238545
240337
244752
244576
241572
240541
236089
236997
264579
270349
269645
267037
258113
262813
267413
267366
264777
258863
254844
254868
277267
285351
286602
283042
276687
277915
277128
277103
275037
270150
267140
264993
287259
291186
292300
288186
281477
282656
280190
280408
276836
275216
274352
271311
289802
290726
292300
278506
269826
265861
269034
264176
255198
253353
246057
235372
258556
260993
254663




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

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1156&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1156&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1156&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean266848.5333333332086.48308055958127.893935886490
Geometric Mean266358.923447697
Harmonic Mean265861.227536711
Quadratic Mean267329.368063506
Winsorized Mean ( 1 / 20 )266860.4833333332083.45957111209128.085270783964
Winsorized Mean ( 2 / 20 )266853.6166666672068.4236863804129.013034623309
Winsorized Mean ( 3 / 20 )266908.0166666672045.29455084416130.49857124809
Winsorized Mean ( 4 / 20 )266965.8833333332005.78386822720133.098030930565
Winsorized Mean ( 5 / 20 )266848.2166666671976.63599295352135.001192742594
Winsorized Mean ( 6 / 20 )266858.6166666671936.84108009494137.780336966824
Winsorized Mean ( 7 / 20 )266904.351896.42749236543140.740603621543
Winsorized Mean ( 8 / 20 )266998.2166666671811.77130360014147.368608905615
Winsorized Mean ( 9 / 20 )266678.2666666671748.96354115409152.477887841329
Winsorized Mean ( 10 / 20 )266831.4333333331693.03334107526157.605539630936
Winsorized Mean ( 11 / 20 )267952.8833333331398.87938122471191.548239919543
Winsorized Mean ( 12 / 20 )268001.0833333331318.64816291758203.239264930507
Winsorized Mean ( 13 / 20 )267993.0666666671304.42718187181205.448851719040
Winsorized Mean ( 14 / 20 )267605.7333333331243.08023814062215.276315335536
Winsorized Mean ( 15 / 20 )267540.4833333331207.02178035190221.653401527960
Winsorized Mean ( 16 / 20 )268145.0166666671051.19587468009255.085682055469
Winsorized Mean ( 17 / 20 )268231.151025.2121207616261.634782273876
Winsorized Mean ( 18 / 20 )268315.751009.43198762534265.808646138910
Winsorized Mean ( 19 / 20 )268905.7892.451949457446301.311123992141
Winsorized Mean ( 20 / 20 )269462.7796.225814469186338.424973296854
Trimmed Mean ( 1 / 20 )266952.4137931032041.01190400188130.794148368112
Trimmed Mean ( 2 / 20 )267050.9107142861988.30250502242134.311006519239
Trimmed Mean ( 3 / 20 )267160.5185185191932.64639981996138.235591644393
Trimmed Mean ( 4 / 20 )267257.6346153851874.17646188350142.600037963766
Trimmed Mean ( 5 / 20 )267345.161816.24160025531147.196914751
Trimmed Mean ( 6 / 20 )267469.3958333331752.44924040460152.626044547562
Trimmed Mean ( 7 / 20 )267602.1739130431683.28500585078158.976152572445
Trimmed Mean ( 8 / 20 )267738.1136363641605.91083571877166.720410424611
Trimmed Mean ( 9 / 20 )267870.2380952381530.17314416194175.058776268060
Trimmed Mean ( 10 / 20 )268068.91446.86403805450185.275805431209
Trimmed Mean ( 11 / 20 )268264.2894736841351.19416490645198.538667825181
Trimmed Mean ( 12 / 20 )268311.4722222221312.32493223124204.455059591098
Trimmed Mean ( 13 / 20 )268357.1176470591279.65370327038209.710734209752
Trimmed Mean ( 14 / 20 )268409.6251235.63544017976217.223961268829
Trimmed Mean ( 15 / 20 )268524.4666666671188.48523676471225.938411652166
Trimmed Mean ( 16 / 20 )268665.0357142861128.36353559980238.1014870101
Trimmed Mean ( 17 / 20 )268740.0384615381093.37650560900245.789110231386
Trimmed Mean ( 18 / 20 )268814.8751045.04521834159257.227984284344
Trimmed Mean ( 19 / 20 )268890.5970.329657353311277.112523524665
Trimmed Mean ( 20 / 20 )268888.1902.466975339789297.947855542039
Median268223.5
Midrange263836
Midmean - Weighted Average at Xnp268083.935483871
Midmean - Weighted Average at X(n+1)p268524.466666667
Midmean - Empirical Distribution Function268083.935483871
Midmean - Empirical Distribution Function - Averaging268524.466666667
Midmean - Empirical Distribution Function - Interpolation268524.466666667
Midmean - Closest Observation268083.935483871
Midmean - True Basic - Statistics Graphics Toolkit268524.466666667
Midmean - MS Excel (old versions)268409.625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 266848.533333333 & 2086.48308055958 & 127.893935886490 \tabularnewline
Geometric Mean & 266358.923447697 &  &  \tabularnewline
Harmonic Mean & 265861.227536711 &  &  \tabularnewline
Quadratic Mean & 267329.368063506 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 266860.483333333 & 2083.45957111209 & 128.085270783964 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 266853.616666667 & 2068.4236863804 & 129.013034623309 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 266908.016666667 & 2045.29455084416 & 130.49857124809 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 266965.883333333 & 2005.78386822720 & 133.098030930565 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 266848.216666667 & 1976.63599295352 & 135.001192742594 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 266858.616666667 & 1936.84108009494 & 137.780336966824 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 266904.35 & 1896.42749236543 & 140.740603621543 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 266998.216666667 & 1811.77130360014 & 147.368608905615 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 266678.266666667 & 1748.96354115409 & 152.477887841329 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 266831.433333333 & 1693.03334107526 & 157.605539630936 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 267952.883333333 & 1398.87938122471 & 191.548239919543 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 268001.083333333 & 1318.64816291758 & 203.239264930507 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 267993.066666667 & 1304.42718187181 & 205.448851719040 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 267605.733333333 & 1243.08023814062 & 215.276315335536 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 267540.483333333 & 1207.02178035190 & 221.653401527960 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 268145.016666667 & 1051.19587468009 & 255.085682055469 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 268231.15 & 1025.2121207616 & 261.634782273876 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 268315.75 & 1009.43198762534 & 265.808646138910 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 268905.7 & 892.451949457446 & 301.311123992141 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 269462.7 & 796.225814469186 & 338.424973296854 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 266952.413793103 & 2041.01190400188 & 130.794148368112 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 267050.910714286 & 1988.30250502242 & 134.311006519239 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 267160.518518519 & 1932.64639981996 & 138.235591644393 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 267257.634615385 & 1874.17646188350 & 142.600037963766 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 267345.16 & 1816.24160025531 & 147.196914751 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 267469.395833333 & 1752.44924040460 & 152.626044547562 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 267602.173913043 & 1683.28500585078 & 158.976152572445 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 267738.113636364 & 1605.91083571877 & 166.720410424611 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 267870.238095238 & 1530.17314416194 & 175.058776268060 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 268068.9 & 1446.86403805450 & 185.275805431209 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 268264.289473684 & 1351.19416490645 & 198.538667825181 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 268311.472222222 & 1312.32493223124 & 204.455059591098 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 268357.117647059 & 1279.65370327038 & 209.710734209752 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 268409.625 & 1235.63544017976 & 217.223961268829 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 268524.466666667 & 1188.48523676471 & 225.938411652166 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 268665.035714286 & 1128.36353559980 & 238.1014870101 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 268740.038461538 & 1093.37650560900 & 245.789110231386 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 268814.875 & 1045.04521834159 & 257.227984284344 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 268890.5 & 970.329657353311 & 277.112523524665 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 268888.1 & 902.466975339789 & 297.947855542039 \tabularnewline
Median & 268223.5 &  &  \tabularnewline
Midrange & 263836 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 268083.935483871 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 268524.466666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 268083.935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 268524.466666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 268524.466666667 &  &  \tabularnewline
Midmean - Closest Observation & 268083.935483871 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 268524.466666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 268409.625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1156&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]266848.533333333[/C][C]2086.48308055958[/C][C]127.893935886490[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]266358.923447697[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]265861.227536711[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]267329.368063506[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]266860.483333333[/C][C]2083.45957111209[/C][C]128.085270783964[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]266853.616666667[/C][C]2068.4236863804[/C][C]129.013034623309[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]266908.016666667[/C][C]2045.29455084416[/C][C]130.49857124809[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]266965.883333333[/C][C]2005.78386822720[/C][C]133.098030930565[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]266848.216666667[/C][C]1976.63599295352[/C][C]135.001192742594[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]266858.616666667[/C][C]1936.84108009494[/C][C]137.780336966824[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]266904.35[/C][C]1896.42749236543[/C][C]140.740603621543[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]266998.216666667[/C][C]1811.77130360014[/C][C]147.368608905615[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]266678.266666667[/C][C]1748.96354115409[/C][C]152.477887841329[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]266831.433333333[/C][C]1693.03334107526[/C][C]157.605539630936[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]267952.883333333[/C][C]1398.87938122471[/C][C]191.548239919543[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]268001.083333333[/C][C]1318.64816291758[/C][C]203.239264930507[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]267993.066666667[/C][C]1304.42718187181[/C][C]205.448851719040[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]267605.733333333[/C][C]1243.08023814062[/C][C]215.276315335536[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]267540.483333333[/C][C]1207.02178035190[/C][C]221.653401527960[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]268145.016666667[/C][C]1051.19587468009[/C][C]255.085682055469[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]268231.15[/C][C]1025.2121207616[/C][C]261.634782273876[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]268315.75[/C][C]1009.43198762534[/C][C]265.808646138910[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]268905.7[/C][C]892.451949457446[/C][C]301.311123992141[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]269462.7[/C][C]796.225814469186[/C][C]338.424973296854[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]266952.413793103[/C][C]2041.01190400188[/C][C]130.794148368112[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]267050.910714286[/C][C]1988.30250502242[/C][C]134.311006519239[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]267160.518518519[/C][C]1932.64639981996[/C][C]138.235591644393[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]267257.634615385[/C][C]1874.17646188350[/C][C]142.600037963766[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]267345.16[/C][C]1816.24160025531[/C][C]147.196914751[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]267469.395833333[/C][C]1752.44924040460[/C][C]152.626044547562[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]267602.173913043[/C][C]1683.28500585078[/C][C]158.976152572445[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]267738.113636364[/C][C]1605.91083571877[/C][C]166.720410424611[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]267870.238095238[/C][C]1530.17314416194[/C][C]175.058776268060[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]268068.9[/C][C]1446.86403805450[/C][C]185.275805431209[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]268264.289473684[/C][C]1351.19416490645[/C][C]198.538667825181[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]268311.472222222[/C][C]1312.32493223124[/C][C]204.455059591098[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]268357.117647059[/C][C]1279.65370327038[/C][C]209.710734209752[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]268409.625[/C][C]1235.63544017976[/C][C]217.223961268829[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]268524.466666667[/C][C]1188.48523676471[/C][C]225.938411652166[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]268665.035714286[/C][C]1128.36353559980[/C][C]238.1014870101[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]268740.038461538[/C][C]1093.37650560900[/C][C]245.789110231386[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]268814.875[/C][C]1045.04521834159[/C][C]257.227984284344[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]268890.5[/C][C]970.329657353311[/C][C]277.112523524665[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]268888.1[/C][C]902.466975339789[/C][C]297.947855542039[/C][/ROW]
[ROW][C]Median[/C][C]268223.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]263836[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]268083.935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]268524.466666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]268083.935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]268524.466666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]268524.466666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]268083.935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]268524.466666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]268409.625[/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=1156&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1156&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 Mean266848.5333333332086.48308055958127.893935886490
Geometric Mean266358.923447697
Harmonic Mean265861.227536711
Quadratic Mean267329.368063506
Winsorized Mean ( 1 / 20 )266860.4833333332083.45957111209128.085270783964
Winsorized Mean ( 2 / 20 )266853.6166666672068.4236863804129.013034623309
Winsorized Mean ( 3 / 20 )266908.0166666672045.29455084416130.49857124809
Winsorized Mean ( 4 / 20 )266965.8833333332005.78386822720133.098030930565
Winsorized Mean ( 5 / 20 )266848.2166666671976.63599295352135.001192742594
Winsorized Mean ( 6 / 20 )266858.6166666671936.84108009494137.780336966824
Winsorized Mean ( 7 / 20 )266904.351896.42749236543140.740603621543
Winsorized Mean ( 8 / 20 )266998.2166666671811.77130360014147.368608905615
Winsorized Mean ( 9 / 20 )266678.2666666671748.96354115409152.477887841329
Winsorized Mean ( 10 / 20 )266831.4333333331693.03334107526157.605539630936
Winsorized Mean ( 11 / 20 )267952.8833333331398.87938122471191.548239919543
Winsorized Mean ( 12 / 20 )268001.0833333331318.64816291758203.239264930507
Winsorized Mean ( 13 / 20 )267993.0666666671304.42718187181205.448851719040
Winsorized Mean ( 14 / 20 )267605.7333333331243.08023814062215.276315335536
Winsorized Mean ( 15 / 20 )267540.4833333331207.02178035190221.653401527960
Winsorized Mean ( 16 / 20 )268145.0166666671051.19587468009255.085682055469
Winsorized Mean ( 17 / 20 )268231.151025.2121207616261.634782273876
Winsorized Mean ( 18 / 20 )268315.751009.43198762534265.808646138910
Winsorized Mean ( 19 / 20 )268905.7892.451949457446301.311123992141
Winsorized Mean ( 20 / 20 )269462.7796.225814469186338.424973296854
Trimmed Mean ( 1 / 20 )266952.4137931032041.01190400188130.794148368112
Trimmed Mean ( 2 / 20 )267050.9107142861988.30250502242134.311006519239
Trimmed Mean ( 3 / 20 )267160.5185185191932.64639981996138.235591644393
Trimmed Mean ( 4 / 20 )267257.6346153851874.17646188350142.600037963766
Trimmed Mean ( 5 / 20 )267345.161816.24160025531147.196914751
Trimmed Mean ( 6 / 20 )267469.3958333331752.44924040460152.626044547562
Trimmed Mean ( 7 / 20 )267602.1739130431683.28500585078158.976152572445
Trimmed Mean ( 8 / 20 )267738.1136363641605.91083571877166.720410424611
Trimmed Mean ( 9 / 20 )267870.2380952381530.17314416194175.058776268060
Trimmed Mean ( 10 / 20 )268068.91446.86403805450185.275805431209
Trimmed Mean ( 11 / 20 )268264.2894736841351.19416490645198.538667825181
Trimmed Mean ( 12 / 20 )268311.4722222221312.32493223124204.455059591098
Trimmed Mean ( 13 / 20 )268357.1176470591279.65370327038209.710734209752
Trimmed Mean ( 14 / 20 )268409.6251235.63544017976217.223961268829
Trimmed Mean ( 15 / 20 )268524.4666666671188.48523676471225.938411652166
Trimmed Mean ( 16 / 20 )268665.0357142861128.36353559980238.1014870101
Trimmed Mean ( 17 / 20 )268740.0384615381093.37650560900245.789110231386
Trimmed Mean ( 18 / 20 )268814.8751045.04521834159257.227984284344
Trimmed Mean ( 19 / 20 )268890.5970.329657353311277.112523524665
Trimmed Mean ( 20 / 20 )268888.1902.466975339789297.947855542039
Median268223.5
Midrange263836
Midmean - Weighted Average at Xnp268083.935483871
Midmean - Weighted Average at X(n+1)p268524.466666667
Midmean - Empirical Distribution Function268083.935483871
Midmean - Empirical Distribution Function - Averaging268524.466666667
Midmean - Empirical Distribution Function - Interpolation268524.466666667
Midmean - Closest Observation268083.935483871
Midmean - True Basic - Statistics Graphics Toolkit268524.466666667
Midmean - MS Excel (old versions)268409.625
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')