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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 07 Mar 2012 11:03:38 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/07/t1331136326dvtppgc671ahoyo.htm/, Retrieved Mon, 29 Apr 2024 07:46:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163647, Retrieved Mon, 29 Apr 2024 07:46:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact73
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-03-07 16:03:38] [606e5654d317e57bd58e5a48c9e4e9a9] [Current]
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Dataseries X:
163.93			
164.28			
164.58			
165.97			
166.30			
166.27			
166.27			
166.44			
166.26			
166.64			
166.07			
166.19			
166.19			
166.19			
166.35			
166.52			
167.17			
167.16			
167.16			
167.16			
167.39			
168.46			
168.55			
168.58			
168.58			
169.21			
169.29			
169.24			
169.53			
169.57			
169.57			
169.67			
170.04			
170.39			
170.57			
170.48			
170.48			
170.48			
170.49			
170.72			
171.11			
171.07			
171.07			
171.07			
171.05			
172.28			
172.74			
172.86			
172.86			
173.24			
173.20			
173.38			
172.89			
172.98			
172.98			
172.69			
172.77			
172.65			
172.30			
172.17




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=163647&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=163647&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163647&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 Mean169.36250.349166531828514485.047920008493
Geometric Mean169.341226861453
Harmonic Mean169.319918258684
Quadratic Mean169.383734534931
Winsorized Mean ( 1 / 20 )169.3660.347225012116852487.770160817226
Winsorized Mean ( 2 / 20 )169.3746666666670.344552642625898491.578486746849
Winsorized Mean ( 3 / 20 )169.4331666666670.328046649196367516.49107552763
Winsorized Mean ( 4 / 20 )169.4398333333330.326867731129098518.374306169771
Winsorized Mean ( 5 / 20 )169.4423333333330.323777436868654523.329651911694
Winsorized Mean ( 6 / 20 )169.4393333333330.323237670046516524.194266432344
Winsorized Mean ( 7 / 20 )169.4393333333330.323237670046516524.194266432344
Winsorized Mean ( 8 / 20 )169.4366666666670.319518941612175530.286767387722
Winsorized Mean ( 9 / 20 )169.4336666666670.318472516678398532.019743599305
Winsorized Mean ( 10 / 20 )169.4253333333330.317012044778806534.444467091303
Winsorized Mean ( 11 / 20 )169.42350.314808687756557538.179238976454
Winsorized Mean ( 12 / 20 )169.36350.301251234847553562.200185123576
Winsorized Mean ( 13 / 20 )169.3786666666670.297247872240979569.822974306613
Winsorized Mean ( 14 / 20 )169.3716666666670.289904832101989584.231954461116
Winsorized Mean ( 15 / 20 )169.1366666666670.244730991097913691.112580012384
Winsorized Mean ( 16 / 20 )169.2646666666670.219990172696106769.419218105205
Winsorized Mean ( 17 / 20 )169.2646666666670.219990172696106769.419218105205
Winsorized Mean ( 18 / 20 )169.2646666666670.219990172696106769.419218105205
Winsorized Mean ( 19 / 20 )169.26150.218597070837035774.308179665341
Winsorized Mean ( 20 / 20 )169.2248333333330.191787383993666882.356439769375
Trimmed Mean ( 1 / 20 )169.3868965517240.34165367808194495.785373957249
Trimmed Mean ( 2 / 20 )169.4092857142860.334656914561498506.217796026307
Trimmed Mean ( 3 / 20 )169.4285185185190.327642128852046517.11456982697
Trimmed Mean ( 4 / 20 )169.4267307692310.326471228646223518.963742905591
Trimmed Mean ( 5 / 20 )169.42280.324989926374492521.317081701698
Trimmed Mean ( 6 / 20 )169.4179166666670.323634331774782523.485613338961
Trimmed Mean ( 7 / 20 )169.4132608695650.321547594443721526.868382152418
Trimmed Mean ( 8 / 20 )169.4081818181820.318353864690786532.137977915632
Trimmed Mean ( 9 / 20 )169.4030952380950.314698662734644538.302558282357
Trimmed Mean ( 10 / 20 )169.3980.309659076388443547.046777945897
Trimmed Mean ( 11 / 20 )169.3936842105260.302859868128796559.313735613492
Trimmed Mean ( 12 / 20 )169.3891666666670.2938373308212576.472588398716
Trimmed Mean ( 13 / 20 )169.3929411764710.284913136655397594.542403923451
Trimmed Mean ( 14 / 20 )169.3950.273168018129927620.112856401186
Trimmed Mean ( 15 / 20 )169.3983333333330.258326214214105655.753555049327
Trimmed Mean ( 16 / 20 )169.4357142857140.250607425334233676.100135739153
Trimmed Mean ( 17 / 20 )169.4603846153850.246870555161844686.434169940961
Trimmed Mean ( 18 / 20 )169.4891666666670.239684965841084707.13307391604
Trimmed Mean ( 19 / 20 )169.5231818181820.226789551325273747.49114686965
Trimmed Mean ( 20 / 20 )169.56450.204292714402385830.00757269306
Median169.57
Midrange168.655
Midmean - Weighted Average at Xnp169.305483870968
Midmean - Weighted Average at X(n+1)p169.398333333333
Midmean - Empirical Distribution Function169.305483870968
Midmean - Empirical Distribution Function - Averaging169.398333333333
Midmean - Empirical Distribution Function - Interpolation169.398333333333
Midmean - Closest Observation169.305483870968
Midmean - True Basic - Statistics Graphics Toolkit169.398333333333
Midmean - MS Excel (old versions)169.395
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 169.3625 & 0.349166531828514 & 485.047920008493 \tabularnewline
Geometric Mean & 169.341226861453 &  &  \tabularnewline
Harmonic Mean & 169.319918258684 &  &  \tabularnewline
Quadratic Mean & 169.383734534931 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 169.366 & 0.347225012116852 & 487.770160817226 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 169.374666666667 & 0.344552642625898 & 491.578486746849 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 169.433166666667 & 0.328046649196367 & 516.49107552763 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 169.439833333333 & 0.326867731129098 & 518.374306169771 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 169.442333333333 & 0.323777436868654 & 523.329651911694 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 169.439333333333 & 0.323237670046516 & 524.194266432344 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 169.439333333333 & 0.323237670046516 & 524.194266432344 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 169.436666666667 & 0.319518941612175 & 530.286767387722 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 169.433666666667 & 0.318472516678398 & 532.019743599305 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 169.425333333333 & 0.317012044778806 & 534.444467091303 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 169.4235 & 0.314808687756557 & 538.179238976454 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 169.3635 & 0.301251234847553 & 562.200185123576 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 169.378666666667 & 0.297247872240979 & 569.822974306613 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 169.371666666667 & 0.289904832101989 & 584.231954461116 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 169.136666666667 & 0.244730991097913 & 691.112580012384 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 169.264666666667 & 0.219990172696106 & 769.419218105205 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 169.264666666667 & 0.219990172696106 & 769.419218105205 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 169.264666666667 & 0.219990172696106 & 769.419218105205 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 169.2615 & 0.218597070837035 & 774.308179665341 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 169.224833333333 & 0.191787383993666 & 882.356439769375 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 169.386896551724 & 0.34165367808194 & 495.785373957249 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 169.409285714286 & 0.334656914561498 & 506.217796026307 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 169.428518518519 & 0.327642128852046 & 517.11456982697 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 169.426730769231 & 0.326471228646223 & 518.963742905591 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 169.4228 & 0.324989926374492 & 521.317081701698 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 169.417916666667 & 0.323634331774782 & 523.485613338961 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 169.413260869565 & 0.321547594443721 & 526.868382152418 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 169.408181818182 & 0.318353864690786 & 532.137977915632 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 169.403095238095 & 0.314698662734644 & 538.302558282357 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 169.398 & 0.309659076388443 & 547.046777945897 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 169.393684210526 & 0.302859868128796 & 559.313735613492 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 169.389166666667 & 0.2938373308212 & 576.472588398716 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 169.392941176471 & 0.284913136655397 & 594.542403923451 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 169.395 & 0.273168018129927 & 620.112856401186 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 169.398333333333 & 0.258326214214105 & 655.753555049327 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 169.435714285714 & 0.250607425334233 & 676.100135739153 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 169.460384615385 & 0.246870555161844 & 686.434169940961 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 169.489166666667 & 0.239684965841084 & 707.13307391604 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 169.523181818182 & 0.226789551325273 & 747.49114686965 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 169.5645 & 0.204292714402385 & 830.00757269306 \tabularnewline
Median & 169.57 &  &  \tabularnewline
Midrange & 168.655 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 169.305483870968 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 169.398333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 169.305483870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 169.398333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 169.398333333333 &  &  \tabularnewline
Midmean - Closest Observation & 169.305483870968 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 169.398333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 169.395 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163647&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]169.3625[/C][C]0.349166531828514[/C][C]485.047920008493[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]169.341226861453[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]169.319918258684[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]169.383734534931[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]169.366[/C][C]0.347225012116852[/C][C]487.770160817226[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]169.374666666667[/C][C]0.344552642625898[/C][C]491.578486746849[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]169.433166666667[/C][C]0.328046649196367[/C][C]516.49107552763[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]169.439833333333[/C][C]0.326867731129098[/C][C]518.374306169771[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]169.442333333333[/C][C]0.323777436868654[/C][C]523.329651911694[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]169.439333333333[/C][C]0.323237670046516[/C][C]524.194266432344[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]169.439333333333[/C][C]0.323237670046516[/C][C]524.194266432344[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]169.436666666667[/C][C]0.319518941612175[/C][C]530.286767387722[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]169.433666666667[/C][C]0.318472516678398[/C][C]532.019743599305[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]169.425333333333[/C][C]0.317012044778806[/C][C]534.444467091303[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]169.4235[/C][C]0.314808687756557[/C][C]538.179238976454[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]169.3635[/C][C]0.301251234847553[/C][C]562.200185123576[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]169.378666666667[/C][C]0.297247872240979[/C][C]569.822974306613[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]169.371666666667[/C][C]0.289904832101989[/C][C]584.231954461116[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]169.136666666667[/C][C]0.244730991097913[/C][C]691.112580012384[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]169.264666666667[/C][C]0.219990172696106[/C][C]769.419218105205[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]169.264666666667[/C][C]0.219990172696106[/C][C]769.419218105205[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]169.264666666667[/C][C]0.219990172696106[/C][C]769.419218105205[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]169.2615[/C][C]0.218597070837035[/C][C]774.308179665341[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]169.224833333333[/C][C]0.191787383993666[/C][C]882.356439769375[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]169.386896551724[/C][C]0.34165367808194[/C][C]495.785373957249[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]169.409285714286[/C][C]0.334656914561498[/C][C]506.217796026307[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]169.428518518519[/C][C]0.327642128852046[/C][C]517.11456982697[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]169.426730769231[/C][C]0.326471228646223[/C][C]518.963742905591[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]169.4228[/C][C]0.324989926374492[/C][C]521.317081701698[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]169.417916666667[/C][C]0.323634331774782[/C][C]523.485613338961[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]169.413260869565[/C][C]0.321547594443721[/C][C]526.868382152418[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]169.408181818182[/C][C]0.318353864690786[/C][C]532.137977915632[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]169.403095238095[/C][C]0.314698662734644[/C][C]538.302558282357[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]169.398[/C][C]0.309659076388443[/C][C]547.046777945897[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]169.393684210526[/C][C]0.302859868128796[/C][C]559.313735613492[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]169.389166666667[/C][C]0.2938373308212[/C][C]576.472588398716[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]169.392941176471[/C][C]0.284913136655397[/C][C]594.542403923451[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]169.395[/C][C]0.273168018129927[/C][C]620.112856401186[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]169.398333333333[/C][C]0.258326214214105[/C][C]655.753555049327[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]169.435714285714[/C][C]0.250607425334233[/C][C]676.100135739153[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]169.460384615385[/C][C]0.246870555161844[/C][C]686.434169940961[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]169.489166666667[/C][C]0.239684965841084[/C][C]707.13307391604[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]169.523181818182[/C][C]0.226789551325273[/C][C]747.49114686965[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]169.5645[/C][C]0.204292714402385[/C][C]830.00757269306[/C][/ROW]
[ROW][C]Median[/C][C]169.57[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]168.655[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]169.305483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]169.398333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]169.305483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]169.398333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]169.398333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]169.305483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]169.398333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]169.395[/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=163647&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163647&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 Mean169.36250.349166531828514485.047920008493
Geometric Mean169.341226861453
Harmonic Mean169.319918258684
Quadratic Mean169.383734534931
Winsorized Mean ( 1 / 20 )169.3660.347225012116852487.770160817226
Winsorized Mean ( 2 / 20 )169.3746666666670.344552642625898491.578486746849
Winsorized Mean ( 3 / 20 )169.4331666666670.328046649196367516.49107552763
Winsorized Mean ( 4 / 20 )169.4398333333330.326867731129098518.374306169771
Winsorized Mean ( 5 / 20 )169.4423333333330.323777436868654523.329651911694
Winsorized Mean ( 6 / 20 )169.4393333333330.323237670046516524.194266432344
Winsorized Mean ( 7 / 20 )169.4393333333330.323237670046516524.194266432344
Winsorized Mean ( 8 / 20 )169.4366666666670.319518941612175530.286767387722
Winsorized Mean ( 9 / 20 )169.4336666666670.318472516678398532.019743599305
Winsorized Mean ( 10 / 20 )169.4253333333330.317012044778806534.444467091303
Winsorized Mean ( 11 / 20 )169.42350.314808687756557538.179238976454
Winsorized Mean ( 12 / 20 )169.36350.301251234847553562.200185123576
Winsorized Mean ( 13 / 20 )169.3786666666670.297247872240979569.822974306613
Winsorized Mean ( 14 / 20 )169.3716666666670.289904832101989584.231954461116
Winsorized Mean ( 15 / 20 )169.1366666666670.244730991097913691.112580012384
Winsorized Mean ( 16 / 20 )169.2646666666670.219990172696106769.419218105205
Winsorized Mean ( 17 / 20 )169.2646666666670.219990172696106769.419218105205
Winsorized Mean ( 18 / 20 )169.2646666666670.219990172696106769.419218105205
Winsorized Mean ( 19 / 20 )169.26150.218597070837035774.308179665341
Winsorized Mean ( 20 / 20 )169.2248333333330.191787383993666882.356439769375
Trimmed Mean ( 1 / 20 )169.3868965517240.34165367808194495.785373957249
Trimmed Mean ( 2 / 20 )169.4092857142860.334656914561498506.217796026307
Trimmed Mean ( 3 / 20 )169.4285185185190.327642128852046517.11456982697
Trimmed Mean ( 4 / 20 )169.4267307692310.326471228646223518.963742905591
Trimmed Mean ( 5 / 20 )169.42280.324989926374492521.317081701698
Trimmed Mean ( 6 / 20 )169.4179166666670.323634331774782523.485613338961
Trimmed Mean ( 7 / 20 )169.4132608695650.321547594443721526.868382152418
Trimmed Mean ( 8 / 20 )169.4081818181820.318353864690786532.137977915632
Trimmed Mean ( 9 / 20 )169.4030952380950.314698662734644538.302558282357
Trimmed Mean ( 10 / 20 )169.3980.309659076388443547.046777945897
Trimmed Mean ( 11 / 20 )169.3936842105260.302859868128796559.313735613492
Trimmed Mean ( 12 / 20 )169.3891666666670.2938373308212576.472588398716
Trimmed Mean ( 13 / 20 )169.3929411764710.284913136655397594.542403923451
Trimmed Mean ( 14 / 20 )169.3950.273168018129927620.112856401186
Trimmed Mean ( 15 / 20 )169.3983333333330.258326214214105655.753555049327
Trimmed Mean ( 16 / 20 )169.4357142857140.250607425334233676.100135739153
Trimmed Mean ( 17 / 20 )169.4603846153850.246870555161844686.434169940961
Trimmed Mean ( 18 / 20 )169.4891666666670.239684965841084707.13307391604
Trimmed Mean ( 19 / 20 )169.5231818181820.226789551325273747.49114686965
Trimmed Mean ( 20 / 20 )169.56450.204292714402385830.00757269306
Median169.57
Midrange168.655
Midmean - Weighted Average at Xnp169.305483870968
Midmean - Weighted Average at X(n+1)p169.398333333333
Midmean - Empirical Distribution Function169.305483870968
Midmean - Empirical Distribution Function - Averaging169.398333333333
Midmean - Empirical Distribution Function - Interpolation169.398333333333
Midmean - Closest Observation169.305483870968
Midmean - True Basic - Statistics Graphics Toolkit169.398333333333
Midmean - MS Excel (old versions)169.395
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')