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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 computationTue, 15 Dec 2015 19:47:19 +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/2015/Dec/15/t1450208845ctwcz29wbeatxwe.htm/, Retrieved Sat, 18 May 2024 14:49:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286581, Retrieved Sat, 18 May 2024 14:49:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact72
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2015-12-15 19:47:19] [9d441e5437781f0cd4d5053adc3d2c6c] [Current]
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Dataseries X:
64281
64023
63935
64387
64161
64011
63685
63522
63541
65070
65357
64281
64152
64043
63966
65040
64640
64179
63633
63327
63237
64793
64622
63615
63319
63261
62699
61956
62069
62179
62327
62526
63055
65277
65783
65353
65583
65950
66634
67836
67700
67463
67412
67308
67881
69652
69733
68891
68994
69021
69072
70283
70795
71111
70274
69220
69841
71275
71295
69073
68752




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=286581&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=286581&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286581&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 Mean65907.4426229508354.341153051234185.999966572952
Geometric Mean65851.0152758407
Harmonic Mean65795.3414240191
Quadratic Mean65964.5696738961
Winsorized Mean ( 1 / 20 )65908.9672131148353.918543596135186.226374417739
Winsorized Mean ( 2 / 20 )65907.1967213115351.932062199784187.272498871948
Winsorized Mean ( 3 / 20 )65898.9344262295346.921540293467189.953423965789
Winsorized Mean ( 4 / 20 )65878.4098360656337.1117077242195.420118395777
Winsorized Mean ( 5 / 20 )65891.8524590164334.648129237594196.898911728965
Winsorized Mean ( 6 / 20 )65884.2786885246320.243009787204205.732136767961
Winsorized Mean ( 7 / 20 )65892.7704918033314.699524825473209.383126740805
Winsorized Mean ( 8 / 20 )65885.2950819672312.108959137532211.097096552536
Winsorized Mean ( 9 / 20 )65830.1147540984298.457977837121220.567448828673
Winsorized Mean ( 10 / 20 )65807.3278688525293.759984107795224.01733193417
Winsorized Mean ( 11 / 20 )65842.3114754098288.897762600388227.908692967224
Winsorized Mean ( 12 / 20 )65836.0163934426286.534095179682229.76677994344
Winsorized Mean ( 13 / 20 )65846.0327868852283.381039667946232.358639321956
Winsorized Mean ( 14 / 20 )65826.5245901639278.482562272617236.375750255141
Winsorized Mean ( 15 / 20 )65805.131147541270.571133920736243.208246918234
Winsorized Mean ( 16 / 20 )65642.2459016393221.992734405472295.695469842464
Winsorized Mean ( 17 / 20 )65638.3442622951218.784980510216300.013026987609
Winsorized Mean ( 18 / 20 )65611.4918032787210.418013086144311.814995498592
Winsorized Mean ( 19 / 20 )65541.4098360656197.857808104446331.255109232118
Winsorized Mean ( 20 / 20 )65531.2459016393194.317899998857337.237310108974
Trimmed Mean ( 1 / 20 )65883.1016949153348.188255386814189.216898260177
Trimmed Mean ( 2 / 20 )65855.4210526316341.015532381472193.115605593482
Trimmed Mean ( 3 / 20 )65826.7090909091333.343557088391197.474070493146
Trimmed Mean ( 4 / 20 )65799326.084031126315201.785410259822
Trimmed Mean ( 5 / 20 )65775.2549019608320.661162371499205.123858516291
Trimmed Mean ( 6 / 20 )65746.2244897959314.378222674961209.130975836617
Trimmed Mean ( 7 / 20 )65716.3617021277310.47470059426211.664143894315
Trimmed Mean ( 8 / 20 )65682.2306.554542414148214.259425036557
Trimmed Mean ( 9 / 20 )65646.1860465116301.706633774568217.582839413341
Trimmed Mean ( 10 / 20 )65615.7804878049298.541906835244219.78750381606
Trimmed Mean ( 11 / 20 )65585.8205128205294.967728219006222.349139374748
Trimmed Mean ( 12 / 20 )65547.3783783784290.587259669982225.568658628806
Trimmed Mean ( 13 / 20 )65505.4571428571284.504940344508230.243654340541
Trimmed Mean ( 14 / 20 )65457.0303030303276.101603789698237.075878606224
Trimmed Mean ( 15 / 20 )65405.0967741935264.977679542197246.832476181368
Trimmed Mean ( 16 / 20 )65349250.729222184298260.635754503181
Trimmed Mean ( 17 / 20 )65307.5925925926246.311197201498265.142605511217
Trimmed Mean ( 18 / 20 )65260.12239.237422657911272.783911793417
Trimmed Mean ( 19 / 20 )65208.347826087229.992967831109283.523224388197
Trimmed Mean ( 20 / 20 )65157.4285714286219.430047118054296.939409288709
Median65040
Midrange66625.5
Midmean - Weighted Average at Xnp65293.5333333333
Midmean - Weighted Average at X(n+1)p65405.0967741935
Midmean - Empirical Distribution Function65405.0967741935
Midmean - Empirical Distribution Function - Averaging65405.0967741935
Midmean - Empirical Distribution Function - Interpolation65405.0967741935
Midmean - Closest Observation65349.71875
Midmean - True Basic - Statistics Graphics Toolkit65405.0967741935
Midmean - MS Excel (old versions)65405.0967741935
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 65907.4426229508 & 354.341153051234 & 185.999966572952 \tabularnewline
Geometric Mean & 65851.0152758407 &  &  \tabularnewline
Harmonic Mean & 65795.3414240191 &  &  \tabularnewline
Quadratic Mean & 65964.5696738961 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 65908.9672131148 & 353.918543596135 & 186.226374417739 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 65907.1967213115 & 351.932062199784 & 187.272498871948 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 65898.9344262295 & 346.921540293467 & 189.953423965789 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 65878.4098360656 & 337.1117077242 & 195.420118395777 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 65891.8524590164 & 334.648129237594 & 196.898911728965 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 65884.2786885246 & 320.243009787204 & 205.732136767961 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 65892.7704918033 & 314.699524825473 & 209.383126740805 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 65885.2950819672 & 312.108959137532 & 211.097096552536 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 65830.1147540984 & 298.457977837121 & 220.567448828673 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 65807.3278688525 & 293.759984107795 & 224.01733193417 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 65842.3114754098 & 288.897762600388 & 227.908692967224 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 65836.0163934426 & 286.534095179682 & 229.76677994344 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 65846.0327868852 & 283.381039667946 & 232.358639321956 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 65826.5245901639 & 278.482562272617 & 236.375750255141 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 65805.131147541 & 270.571133920736 & 243.208246918234 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 65642.2459016393 & 221.992734405472 & 295.695469842464 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 65638.3442622951 & 218.784980510216 & 300.013026987609 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 65611.4918032787 & 210.418013086144 & 311.814995498592 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 65541.4098360656 & 197.857808104446 & 331.255109232118 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 65531.2459016393 & 194.317899998857 & 337.237310108974 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 65883.1016949153 & 348.188255386814 & 189.216898260177 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 65855.4210526316 & 341.015532381472 & 193.115605593482 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 65826.7090909091 & 333.343557088391 & 197.474070493146 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 65799 & 326.084031126315 & 201.785410259822 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 65775.2549019608 & 320.661162371499 & 205.123858516291 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 65746.2244897959 & 314.378222674961 & 209.130975836617 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 65716.3617021277 & 310.47470059426 & 211.664143894315 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 65682.2 & 306.554542414148 & 214.259425036557 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 65646.1860465116 & 301.706633774568 & 217.582839413341 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 65615.7804878049 & 298.541906835244 & 219.78750381606 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 65585.8205128205 & 294.967728219006 & 222.349139374748 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 65547.3783783784 & 290.587259669982 & 225.568658628806 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 65505.4571428571 & 284.504940344508 & 230.243654340541 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 65457.0303030303 & 276.101603789698 & 237.075878606224 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 65405.0967741935 & 264.977679542197 & 246.832476181368 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 65349 & 250.729222184298 & 260.635754503181 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 65307.5925925926 & 246.311197201498 & 265.142605511217 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 65260.12 & 239.237422657911 & 272.783911793417 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 65208.347826087 & 229.992967831109 & 283.523224388197 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 65157.4285714286 & 219.430047118054 & 296.939409288709 \tabularnewline
Median & 65040 &  &  \tabularnewline
Midrange & 66625.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 65293.5333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 65405.0967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 65405.0967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 65405.0967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 65405.0967741935 &  &  \tabularnewline
Midmean - Closest Observation & 65349.71875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 65405.0967741935 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 65405.0967741935 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286581&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]65907.4426229508[/C][C]354.341153051234[/C][C]185.999966572952[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]65851.0152758407[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]65795.3414240191[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]65964.5696738961[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]65908.9672131148[/C][C]353.918543596135[/C][C]186.226374417739[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]65907.1967213115[/C][C]351.932062199784[/C][C]187.272498871948[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]65898.9344262295[/C][C]346.921540293467[/C][C]189.953423965789[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]65878.4098360656[/C][C]337.1117077242[/C][C]195.420118395777[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]65891.8524590164[/C][C]334.648129237594[/C][C]196.898911728965[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]65884.2786885246[/C][C]320.243009787204[/C][C]205.732136767961[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]65892.7704918033[/C][C]314.699524825473[/C][C]209.383126740805[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]65885.2950819672[/C][C]312.108959137532[/C][C]211.097096552536[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]65830.1147540984[/C][C]298.457977837121[/C][C]220.567448828673[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]65807.3278688525[/C][C]293.759984107795[/C][C]224.01733193417[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]65842.3114754098[/C][C]288.897762600388[/C][C]227.908692967224[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]65836.0163934426[/C][C]286.534095179682[/C][C]229.76677994344[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]65846.0327868852[/C][C]283.381039667946[/C][C]232.358639321956[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]65826.5245901639[/C][C]278.482562272617[/C][C]236.375750255141[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]65805.131147541[/C][C]270.571133920736[/C][C]243.208246918234[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]65642.2459016393[/C][C]221.992734405472[/C][C]295.695469842464[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]65638.3442622951[/C][C]218.784980510216[/C][C]300.013026987609[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]65611.4918032787[/C][C]210.418013086144[/C][C]311.814995498592[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]65541.4098360656[/C][C]197.857808104446[/C][C]331.255109232118[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]65531.2459016393[/C][C]194.317899998857[/C][C]337.237310108974[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]65883.1016949153[/C][C]348.188255386814[/C][C]189.216898260177[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]65855.4210526316[/C][C]341.015532381472[/C][C]193.115605593482[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]65826.7090909091[/C][C]333.343557088391[/C][C]197.474070493146[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]65799[/C][C]326.084031126315[/C][C]201.785410259822[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]65775.2549019608[/C][C]320.661162371499[/C][C]205.123858516291[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]65746.2244897959[/C][C]314.378222674961[/C][C]209.130975836617[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]65716.3617021277[/C][C]310.47470059426[/C][C]211.664143894315[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]65682.2[/C][C]306.554542414148[/C][C]214.259425036557[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]65646.1860465116[/C][C]301.706633774568[/C][C]217.582839413341[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]65615.7804878049[/C][C]298.541906835244[/C][C]219.78750381606[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]65585.8205128205[/C][C]294.967728219006[/C][C]222.349139374748[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]65547.3783783784[/C][C]290.587259669982[/C][C]225.568658628806[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]65505.4571428571[/C][C]284.504940344508[/C][C]230.243654340541[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]65457.0303030303[/C][C]276.101603789698[/C][C]237.075878606224[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]65405.0967741935[/C][C]264.977679542197[/C][C]246.832476181368[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]65349[/C][C]250.729222184298[/C][C]260.635754503181[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]65307.5925925926[/C][C]246.311197201498[/C][C]265.142605511217[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]65260.12[/C][C]239.237422657911[/C][C]272.783911793417[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]65208.347826087[/C][C]229.992967831109[/C][C]283.523224388197[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]65157.4285714286[/C][C]219.430047118054[/C][C]296.939409288709[/C][/ROW]
[ROW][C]Median[/C][C]65040[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]66625.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]65293.5333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]65405.0967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]65405.0967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]65405.0967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]65405.0967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]65349.71875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]65405.0967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]65405.0967741935[/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=286581&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286581&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 Mean65907.4426229508354.341153051234185.999966572952
Geometric Mean65851.0152758407
Harmonic Mean65795.3414240191
Quadratic Mean65964.5696738961
Winsorized Mean ( 1 / 20 )65908.9672131148353.918543596135186.226374417739
Winsorized Mean ( 2 / 20 )65907.1967213115351.932062199784187.272498871948
Winsorized Mean ( 3 / 20 )65898.9344262295346.921540293467189.953423965789
Winsorized Mean ( 4 / 20 )65878.4098360656337.1117077242195.420118395777
Winsorized Mean ( 5 / 20 )65891.8524590164334.648129237594196.898911728965
Winsorized Mean ( 6 / 20 )65884.2786885246320.243009787204205.732136767961
Winsorized Mean ( 7 / 20 )65892.7704918033314.699524825473209.383126740805
Winsorized Mean ( 8 / 20 )65885.2950819672312.108959137532211.097096552536
Winsorized Mean ( 9 / 20 )65830.1147540984298.457977837121220.567448828673
Winsorized Mean ( 10 / 20 )65807.3278688525293.759984107795224.01733193417
Winsorized Mean ( 11 / 20 )65842.3114754098288.897762600388227.908692967224
Winsorized Mean ( 12 / 20 )65836.0163934426286.534095179682229.76677994344
Winsorized Mean ( 13 / 20 )65846.0327868852283.381039667946232.358639321956
Winsorized Mean ( 14 / 20 )65826.5245901639278.482562272617236.375750255141
Winsorized Mean ( 15 / 20 )65805.131147541270.571133920736243.208246918234
Winsorized Mean ( 16 / 20 )65642.2459016393221.992734405472295.695469842464
Winsorized Mean ( 17 / 20 )65638.3442622951218.784980510216300.013026987609
Winsorized Mean ( 18 / 20 )65611.4918032787210.418013086144311.814995498592
Winsorized Mean ( 19 / 20 )65541.4098360656197.857808104446331.255109232118
Winsorized Mean ( 20 / 20 )65531.2459016393194.317899998857337.237310108974
Trimmed Mean ( 1 / 20 )65883.1016949153348.188255386814189.216898260177
Trimmed Mean ( 2 / 20 )65855.4210526316341.015532381472193.115605593482
Trimmed Mean ( 3 / 20 )65826.7090909091333.343557088391197.474070493146
Trimmed Mean ( 4 / 20 )65799326.084031126315201.785410259822
Trimmed Mean ( 5 / 20 )65775.2549019608320.661162371499205.123858516291
Trimmed Mean ( 6 / 20 )65746.2244897959314.378222674961209.130975836617
Trimmed Mean ( 7 / 20 )65716.3617021277310.47470059426211.664143894315
Trimmed Mean ( 8 / 20 )65682.2306.554542414148214.259425036557
Trimmed Mean ( 9 / 20 )65646.1860465116301.706633774568217.582839413341
Trimmed Mean ( 10 / 20 )65615.7804878049298.541906835244219.78750381606
Trimmed Mean ( 11 / 20 )65585.8205128205294.967728219006222.349139374748
Trimmed Mean ( 12 / 20 )65547.3783783784290.587259669982225.568658628806
Trimmed Mean ( 13 / 20 )65505.4571428571284.504940344508230.243654340541
Trimmed Mean ( 14 / 20 )65457.0303030303276.101603789698237.075878606224
Trimmed Mean ( 15 / 20 )65405.0967741935264.977679542197246.832476181368
Trimmed Mean ( 16 / 20 )65349250.729222184298260.635754503181
Trimmed Mean ( 17 / 20 )65307.5925925926246.311197201498265.142605511217
Trimmed Mean ( 18 / 20 )65260.12239.237422657911272.783911793417
Trimmed Mean ( 19 / 20 )65208.347826087229.992967831109283.523224388197
Trimmed Mean ( 20 / 20 )65157.4285714286219.430047118054296.939409288709
Median65040
Midrange66625.5
Midmean - Weighted Average at Xnp65293.5333333333
Midmean - Weighted Average at X(n+1)p65405.0967741935
Midmean - Empirical Distribution Function65405.0967741935
Midmean - Empirical Distribution Function - Averaging65405.0967741935
Midmean - Empirical Distribution Function - Interpolation65405.0967741935
Midmean - Closest Observation65349.71875
Midmean - True Basic - Statistics Graphics Toolkit65405.0967741935
Midmean - MS Excel (old versions)65405.0967741935
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')