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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 08 Jan 2016 09:18:00 +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/2016/Jan/08/t14522447478opltgcax76doep.htm/, Retrieved Sat, 27 Apr 2024 19:03:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=287403, Retrieved Sat, 27 Apr 2024 19:03:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact142
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [] [2015-10-10 11:56:53] [a642a7d7b5f7c65c232df2d499025a08]
- R  D    [Central Tendency] [] [2016-01-08 09:18:00] [c6ba03d4d421ca9ab835e2907c34aa87] [Current]
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Dataseries X:
99,2
99,1
99,1
99,1
99,1
99,1
99,9
100
100
101,3
102
102
102,4
103
103
103,6
103,6
103,6
103,6
103,6
103,9
104
104
104
104,9
105,1
105,2
105,5
105,7
105,7
105,7
105,7
105,7
105,8
105,8
105,8
106,6
107
107,2
107,3
107,3
107,3
107,4
107,4
107,4
107,4
107,5
107,5
105
105,2
105,2
105,3
105,3
105,3
105,3
105,3
105,3
105,3
106,1
106,1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287403&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287403&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287403&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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean104.3466666666670.331564231974244314.710263062308
Geometric Mean104.315142924778
Harmonic Mean104.283173369786
Quadratic Mean104.377741880154
Winsorized Mean ( 1 / 20 )104.3466666666670.331564231974244314.710263062308
Winsorized Mean ( 2 / 20 )104.3433333333330.331034730001315315.203584025516
Winsorized Mean ( 3 / 20 )104.3433333333330.331034730001315315.203584025516
Winsorized Mean ( 4 / 20 )104.3433333333330.331034730001315315.203584025516
Winsorized Mean ( 5 / 20 )104.3516666666670.328809629007516317.361954945308
Winsorized Mean ( 6 / 20 )104.4116666666670.30926458847948337.612745060835
Winsorized Mean ( 7 / 20 )104.4233333333330.306394807034613340.812999880696
Winsorized Mean ( 8 / 20 )104.4233333333330.306394807034613340.812999880696
Winsorized Mean ( 9 / 20 )104.6033333333330.258744979117385404.271934822271
Winsorized Mean ( 10 / 20 )104.6866666666670.228758213296614457.630198968756
Winsorized Mean ( 11 / 20 )104.6133333333330.216761821782106482.618813927912
Winsorized Mean ( 12 / 20 )104.5933333333330.18586895734146562.726206836061
Winsorized Mean ( 13 / 20 )104.7233333333330.160988589037784650.501591195104
Winsorized Mean ( 14 / 20 )104.6533333333330.151405219492731691.213510894567
Winsorized Mean ( 15 / 20 )104.8033333333330.125143232438816837.467047086011
Winsorized Mean ( 16 / 20 )104.8033333333330.125143232438816837.467047086011
Winsorized Mean ( 17 / 20 )104.7750.121400141475546863.055007403802
Winsorized Mean ( 18 / 20 )104.7750.121400141475546863.055007403802
Winsorized Mean ( 19 / 20 )104.7750.121400141475546863.055007403802
Winsorized Mean ( 20 / 20 )104.8750.10532771028401995.701888109131
Trimmed Mean ( 1 / 20 )104.382758620690.326127231536457320.067594873692
Trimmed Mean ( 2 / 20 )104.4214285714290.319249467712177327.084111744145
Trimmed Mean ( 3 / 20 )104.4648148148150.310891927216128336.016492130374
Trimmed Mean ( 4 / 20 )104.5115384615380.300272046663011348.056169806674
Trimmed Mean ( 5 / 20 )104.5620.286682502331163364.731014797738
Trimmed Mean ( 6 / 20 )104.6145833333330.269965022414799387.511620570585
Trimmed Mean ( 7 / 20 )104.6586956521740.255274335465605409.985185002178
Trimmed Mean ( 8 / 20 )104.7045454545450.236829716112612442.10898519491
Trimmed Mean ( 9 / 20 )104.7547619047620.211657975283685494.924709377755
Trimmed Mean ( 10 / 20 )104.780.194810887917698537.854948047187
Trimmed Mean ( 11 / 20 )104.7947368421050.181934732971651576.001817412371
Trimmed Mean ( 12 / 20 )104.8222222222220.167716271707352624.99733123764
Trimmed Mean ( 13 / 20 )104.8558823529410.157701356812972664.901586593808
Trimmed Mean ( 14 / 20 )104.8750.15193642558437690.255806641725
Trimmed Mean ( 15 / 20 )104.9066666666670.145817815266319719.436554957756
Trimmed Mean ( 16 / 20 )104.9214285714290.14542013052291721.50553155293
Trimmed Mean ( 17 / 20 )104.9384615384620.143909899491306729.195572433857
Trimmed Mean ( 18 / 20 )104.96250.14165334549475740.981440525807
Trimmed Mean ( 19 / 20 )104.9909090909090.136896505748349766.93636931763
Trimmed Mean ( 20 / 20 )105.0250.127707519458784822.386970204173
Median105.25
Midrange103.3
Midmean - Weighted Average at Xnp104.818181818182
Midmean - Weighted Average at X(n+1)p104.935483870968
Midmean - Empirical Distribution Function104.818181818182
Midmean - Empirical Distribution Function - Averaging104.935483870968
Midmean - Empirical Distribution Function - Interpolation104.935483870968
Midmean - Closest Observation104.818181818182
Midmean - True Basic - Statistics Graphics Toolkit104.935483870968
Midmean - MS Excel (old versions)104.818181818182
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 104.346666666667 & 0.331564231974244 & 314.710263062308 \tabularnewline
Geometric Mean & 104.315142924778 &  &  \tabularnewline
Harmonic Mean & 104.283173369786 &  &  \tabularnewline
Quadratic Mean & 104.377741880154 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 104.346666666667 & 0.331564231974244 & 314.710263062308 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 104.343333333333 & 0.331034730001315 & 315.203584025516 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 104.343333333333 & 0.331034730001315 & 315.203584025516 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 104.343333333333 & 0.331034730001315 & 315.203584025516 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 104.351666666667 & 0.328809629007516 & 317.361954945308 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 104.411666666667 & 0.30926458847948 & 337.612745060835 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 104.423333333333 & 0.306394807034613 & 340.812999880696 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 104.423333333333 & 0.306394807034613 & 340.812999880696 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 104.603333333333 & 0.258744979117385 & 404.271934822271 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 104.686666666667 & 0.228758213296614 & 457.630198968756 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 104.613333333333 & 0.216761821782106 & 482.618813927912 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 104.593333333333 & 0.18586895734146 & 562.726206836061 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 104.723333333333 & 0.160988589037784 & 650.501591195104 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 104.653333333333 & 0.151405219492731 & 691.213510894567 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 104.803333333333 & 0.125143232438816 & 837.467047086011 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 104.803333333333 & 0.125143232438816 & 837.467047086011 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 104.775 & 0.121400141475546 & 863.055007403802 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 104.775 & 0.121400141475546 & 863.055007403802 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 104.775 & 0.121400141475546 & 863.055007403802 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 104.875 & 0.10532771028401 & 995.701888109131 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 104.38275862069 & 0.326127231536457 & 320.067594873692 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 104.421428571429 & 0.319249467712177 & 327.084111744145 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 104.464814814815 & 0.310891927216128 & 336.016492130374 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 104.511538461538 & 0.300272046663011 & 348.056169806674 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 104.562 & 0.286682502331163 & 364.731014797738 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 104.614583333333 & 0.269965022414799 & 387.511620570585 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 104.658695652174 & 0.255274335465605 & 409.985185002178 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 104.704545454545 & 0.236829716112612 & 442.10898519491 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 104.754761904762 & 0.211657975283685 & 494.924709377755 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 104.78 & 0.194810887917698 & 537.854948047187 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 104.794736842105 & 0.181934732971651 & 576.001817412371 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 104.822222222222 & 0.167716271707352 & 624.99733123764 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 104.855882352941 & 0.157701356812972 & 664.901586593808 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 104.875 & 0.15193642558437 & 690.255806641725 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 104.906666666667 & 0.145817815266319 & 719.436554957756 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 104.921428571429 & 0.14542013052291 & 721.50553155293 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 104.938461538462 & 0.143909899491306 & 729.195572433857 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 104.9625 & 0.14165334549475 & 740.981440525807 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 104.990909090909 & 0.136896505748349 & 766.93636931763 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 105.025 & 0.127707519458784 & 822.386970204173 \tabularnewline
Median & 105.25 &  &  \tabularnewline
Midrange & 103.3 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 104.818181818182 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 104.935483870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 104.818181818182 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 104.935483870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 104.935483870968 &  &  \tabularnewline
Midmean - Closest Observation & 104.818181818182 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 104.935483870968 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 104.818181818182 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287403&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]104.346666666667[/C][C]0.331564231974244[/C][C]314.710263062308[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]104.315142924778[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]104.283173369786[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]104.377741880154[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]104.346666666667[/C][C]0.331564231974244[/C][C]314.710263062308[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]104.343333333333[/C][C]0.331034730001315[/C][C]315.203584025516[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]104.343333333333[/C][C]0.331034730001315[/C][C]315.203584025516[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]104.343333333333[/C][C]0.331034730001315[/C][C]315.203584025516[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]104.351666666667[/C][C]0.328809629007516[/C][C]317.361954945308[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]104.411666666667[/C][C]0.30926458847948[/C][C]337.612745060835[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]104.423333333333[/C][C]0.306394807034613[/C][C]340.812999880696[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]104.423333333333[/C][C]0.306394807034613[/C][C]340.812999880696[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]104.603333333333[/C][C]0.258744979117385[/C][C]404.271934822271[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]104.686666666667[/C][C]0.228758213296614[/C][C]457.630198968756[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]104.613333333333[/C][C]0.216761821782106[/C][C]482.618813927912[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]104.593333333333[/C][C]0.18586895734146[/C][C]562.726206836061[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]104.723333333333[/C][C]0.160988589037784[/C][C]650.501591195104[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]104.653333333333[/C][C]0.151405219492731[/C][C]691.213510894567[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]104.803333333333[/C][C]0.125143232438816[/C][C]837.467047086011[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]104.803333333333[/C][C]0.125143232438816[/C][C]837.467047086011[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]104.775[/C][C]0.121400141475546[/C][C]863.055007403802[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]104.775[/C][C]0.121400141475546[/C][C]863.055007403802[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]104.775[/C][C]0.121400141475546[/C][C]863.055007403802[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]104.875[/C][C]0.10532771028401[/C][C]995.701888109131[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]104.38275862069[/C][C]0.326127231536457[/C][C]320.067594873692[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]104.421428571429[/C][C]0.319249467712177[/C][C]327.084111744145[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]104.464814814815[/C][C]0.310891927216128[/C][C]336.016492130374[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]104.511538461538[/C][C]0.300272046663011[/C][C]348.056169806674[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]104.562[/C][C]0.286682502331163[/C][C]364.731014797738[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]104.614583333333[/C][C]0.269965022414799[/C][C]387.511620570585[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]104.658695652174[/C][C]0.255274335465605[/C][C]409.985185002178[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]104.704545454545[/C][C]0.236829716112612[/C][C]442.10898519491[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]104.754761904762[/C][C]0.211657975283685[/C][C]494.924709377755[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]104.78[/C][C]0.194810887917698[/C][C]537.854948047187[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]104.794736842105[/C][C]0.181934732971651[/C][C]576.001817412371[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]104.822222222222[/C][C]0.167716271707352[/C][C]624.99733123764[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]104.855882352941[/C][C]0.157701356812972[/C][C]664.901586593808[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]104.875[/C][C]0.15193642558437[/C][C]690.255806641725[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]104.906666666667[/C][C]0.145817815266319[/C][C]719.436554957756[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]104.921428571429[/C][C]0.14542013052291[/C][C]721.50553155293[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]104.938461538462[/C][C]0.143909899491306[/C][C]729.195572433857[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]104.9625[/C][C]0.14165334549475[/C][C]740.981440525807[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]104.990909090909[/C][C]0.136896505748349[/C][C]766.93636931763[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]105.025[/C][C]0.127707519458784[/C][C]822.386970204173[/C][/ROW]
[ROW][C]Median[/C][C]105.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]103.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]104.818181818182[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]104.935483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]104.818181818182[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]104.935483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]104.935483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]104.818181818182[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]104.935483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]104.818181818182[/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=287403&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287403&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 Mean104.3466666666670.331564231974244314.710263062308
Geometric Mean104.315142924778
Harmonic Mean104.283173369786
Quadratic Mean104.377741880154
Winsorized Mean ( 1 / 20 )104.3466666666670.331564231974244314.710263062308
Winsorized Mean ( 2 / 20 )104.3433333333330.331034730001315315.203584025516
Winsorized Mean ( 3 / 20 )104.3433333333330.331034730001315315.203584025516
Winsorized Mean ( 4 / 20 )104.3433333333330.331034730001315315.203584025516
Winsorized Mean ( 5 / 20 )104.3516666666670.328809629007516317.361954945308
Winsorized Mean ( 6 / 20 )104.4116666666670.30926458847948337.612745060835
Winsorized Mean ( 7 / 20 )104.4233333333330.306394807034613340.812999880696
Winsorized Mean ( 8 / 20 )104.4233333333330.306394807034613340.812999880696
Winsorized Mean ( 9 / 20 )104.6033333333330.258744979117385404.271934822271
Winsorized Mean ( 10 / 20 )104.6866666666670.228758213296614457.630198968756
Winsorized Mean ( 11 / 20 )104.6133333333330.216761821782106482.618813927912
Winsorized Mean ( 12 / 20 )104.5933333333330.18586895734146562.726206836061
Winsorized Mean ( 13 / 20 )104.7233333333330.160988589037784650.501591195104
Winsorized Mean ( 14 / 20 )104.6533333333330.151405219492731691.213510894567
Winsorized Mean ( 15 / 20 )104.8033333333330.125143232438816837.467047086011
Winsorized Mean ( 16 / 20 )104.8033333333330.125143232438816837.467047086011
Winsorized Mean ( 17 / 20 )104.7750.121400141475546863.055007403802
Winsorized Mean ( 18 / 20 )104.7750.121400141475546863.055007403802
Winsorized Mean ( 19 / 20 )104.7750.121400141475546863.055007403802
Winsorized Mean ( 20 / 20 )104.8750.10532771028401995.701888109131
Trimmed Mean ( 1 / 20 )104.382758620690.326127231536457320.067594873692
Trimmed Mean ( 2 / 20 )104.4214285714290.319249467712177327.084111744145
Trimmed Mean ( 3 / 20 )104.4648148148150.310891927216128336.016492130374
Trimmed Mean ( 4 / 20 )104.5115384615380.300272046663011348.056169806674
Trimmed Mean ( 5 / 20 )104.5620.286682502331163364.731014797738
Trimmed Mean ( 6 / 20 )104.6145833333330.269965022414799387.511620570585
Trimmed Mean ( 7 / 20 )104.6586956521740.255274335465605409.985185002178
Trimmed Mean ( 8 / 20 )104.7045454545450.236829716112612442.10898519491
Trimmed Mean ( 9 / 20 )104.7547619047620.211657975283685494.924709377755
Trimmed Mean ( 10 / 20 )104.780.194810887917698537.854948047187
Trimmed Mean ( 11 / 20 )104.7947368421050.181934732971651576.001817412371
Trimmed Mean ( 12 / 20 )104.8222222222220.167716271707352624.99733123764
Trimmed Mean ( 13 / 20 )104.8558823529410.157701356812972664.901586593808
Trimmed Mean ( 14 / 20 )104.8750.15193642558437690.255806641725
Trimmed Mean ( 15 / 20 )104.9066666666670.145817815266319719.436554957756
Trimmed Mean ( 16 / 20 )104.9214285714290.14542013052291721.50553155293
Trimmed Mean ( 17 / 20 )104.9384615384620.143909899491306729.195572433857
Trimmed Mean ( 18 / 20 )104.96250.14165334549475740.981440525807
Trimmed Mean ( 19 / 20 )104.9909090909090.136896505748349766.93636931763
Trimmed Mean ( 20 / 20 )105.0250.127707519458784822.386970204173
Median105.25
Midrange103.3
Midmean - Weighted Average at Xnp104.818181818182
Midmean - Weighted Average at X(n+1)p104.935483870968
Midmean - Empirical Distribution Function104.818181818182
Midmean - Empirical Distribution Function - Averaging104.935483870968
Midmean - Empirical Distribution Function - Interpolation104.935483870968
Midmean - Closest Observation104.818181818182
Midmean - True Basic - Statistics Graphics Toolkit104.935483870968
Midmean - MS Excel (old versions)104.818181818182
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')