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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 computationThu, 16 Oct 2008 07:45:40 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/16/t12241671224t0trd5yursrczr.htm/, Retrieved Sun, 19 May 2024 13:06:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16346, Retrieved Sun, 19 May 2024 13:06:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordskatrien bourdiaudhy 1e tijdsreeks
Estimated Impact189
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [blog 1e tijdreeks...] [2008-10-13 19:23:31] [7173087adebe3e3a714c80ea2417b3eb]
- RMPD    [Central Tendency] [central tendency] [2008-10-16 13:45:40] [95d95b0e883740fcbc85e18ec42dcafb] [Current]
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Dataseries X:
8.2
8
7.9
7.6
7.6
8.2
8.3
8.4
8.4
8.4
8.6
8.9
8.8
8.3
7.5
7.2
7.5
8.8
9.3
9.3
8.7
8.2
8.3
8.5
8.6
8.6
8.2
8.1
8
8.6
8.7
8.8
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8.1
8.2
8.1
8.1
7.9
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16346&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16346&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16346&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean8.133333333333330.0716104759351136113.577423234876
Geometric Mean8.11437739638333
Harmonic Mean8.09506011383559
Quadratic Mean8.15191184119815
Winsorized Mean ( 1 / 20 )8.133333333333330.0716104759351136113.577423234876
Winsorized Mean ( 2 / 20 )8.120.0684699612473991118.592151245134
Winsorized Mean ( 3 / 20 )8.1250.0649478278234388125.100411704112
Winsorized Mean ( 4 / 20 )8.1250.0649478278234388125.100411704112
Winsorized Mean ( 5 / 20 )8.1250.0649478278234388125.100411704112
Winsorized Mean ( 6 / 20 )8.1250.0609076822963398133.39860742802
Winsorized Mean ( 7 / 20 )8.1250.0609076822963398133.39860742802
Winsorized Mean ( 8 / 20 )8.151666666666670.0551572823875202147.789490595190
Winsorized Mean ( 9 / 20 )8.151666666666670.0551572823875202147.789490595190
Winsorized Mean ( 10 / 20 )8.1350.0524983185095264154.957343986623
Winsorized Mean ( 11 / 20 )8.153333333333330.0488550644846609166.888191006139
Winsorized Mean ( 12 / 20 )8.153333333333330.0488550644846609166.888191006139
Winsorized Mean ( 13 / 20 )8.1750.0448238863884029182.380437277636
Winsorized Mean ( 14 / 20 )8.221666666666670.0371355485245398221.396128327918
Winsorized Mean ( 15 / 20 )8.196666666666670.0330182851812272248.246286010242
Winsorized Mean ( 16 / 20 )8.196666666666670.0330182851812272248.246286010242
Winsorized Mean ( 17 / 20 )8.196666666666670.0330182851812272248.246286010242
Winsorized Mean ( 18 / 20 )8.196666666666670.0330182851812272248.246286010242
Winsorized Mean ( 19 / 20 )8.196666666666670.0235262405085692348.405290836039
Winsorized Mean ( 20 / 20 )8.196666666666670.0235262405085692348.405290836039
Trimmed Mean ( 1 / 20 )8.132758620689660.068489357430723118.744852131456
Trimmed Mean ( 2 / 20 )8.132142857142860.0646221355896203125.841444002805
Trimmed Mean ( 3 / 20 )8.138888888888890.0619628090403395131.351192996919
Trimmed Mean ( 4 / 20 )8.144230769230770.0603792352369701134.884629413856
Trimmed Mean ( 5 / 20 )8.150.05836199490233139.645672044610
Trimmed Mean ( 6 / 20 )8.156250.0557751827485872146.234393112887
Trimmed Mean ( 7 / 20 )8.163043478260870.0537806149775549151.784122990555
Trimmed Mean ( 8 / 20 )8.170454545454540.0511577944287002159.710844392283
Trimmed Mean ( 9 / 20 )8.173809523809520.0495109091569338165.091081197906
Trimmed Mean ( 10 / 20 )8.17750.0472971376593683172.896297845632
Trimmed Mean ( 11 / 20 )8.184210526315790.0450266739009381181.763604043275
Trimmed Mean ( 12 / 20 )8.188888888888890.0430536353898505190.202030902583
Trimmed Mean ( 13 / 20 )8.194117647058820.0402623253060217203.51824155157
Trimmed Mean ( 14 / 20 )8.1968750.0376968957287022217.441644505464
Trimmed Mean ( 15 / 20 )8.193333333333330.0364938455946140224.512741801663
Trimmed Mean ( 16 / 20 )8.192857142857140.0359778633544227227.719391286476
Trimmed Mean ( 17 / 20 )8.192307692307690.035048571538137233.741557295523
Trimmed Mean ( 18 / 20 )8.191666666666670.0334689271134527244.754384832792
Trimmed Mean ( 19 / 20 )8.190909090909090.0307968422715713265.965874640016
Trimmed Mean ( 20 / 20 )8.190.0306937332880492266.829711561638
Median8.2
Midrange8.15
Midmean - Weighted Average at Xnp8.18387096774194
Midmean - Weighted Average at X(n+1)p8.18387096774194
Midmean - Empirical Distribution Function8.18387096774194
Midmean - Empirical Distribution Function - Averaging8.18387096774194
Midmean - Empirical Distribution Function - Interpolation8.18387096774194
Midmean - Closest Observation8.18387096774194
Midmean - True Basic - Statistics Graphics Toolkit8.18387096774194
Midmean - MS Excel (old versions)8.24166666666667
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.13333333333333 & 0.0716104759351136 & 113.577423234876 \tabularnewline
Geometric Mean & 8.11437739638333 &  &  \tabularnewline
Harmonic Mean & 8.09506011383559 &  &  \tabularnewline
Quadratic Mean & 8.15191184119815 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 8.13333333333333 & 0.0716104759351136 & 113.577423234876 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 8.12 & 0.0684699612473991 & 118.592151245134 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 8.125 & 0.0649478278234388 & 125.100411704112 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 8.125 & 0.0649478278234388 & 125.100411704112 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 8.125 & 0.0649478278234388 & 125.100411704112 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 8.125 & 0.0609076822963398 & 133.39860742802 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 8.125 & 0.0609076822963398 & 133.39860742802 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 8.15166666666667 & 0.0551572823875202 & 147.789490595190 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 8.15166666666667 & 0.0551572823875202 & 147.789490595190 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 8.135 & 0.0524983185095264 & 154.957343986623 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 8.15333333333333 & 0.0488550644846609 & 166.888191006139 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 8.15333333333333 & 0.0488550644846609 & 166.888191006139 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 8.175 & 0.0448238863884029 & 182.380437277636 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 8.22166666666667 & 0.0371355485245398 & 221.396128327918 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 8.19666666666667 & 0.0330182851812272 & 248.246286010242 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 8.19666666666667 & 0.0330182851812272 & 248.246286010242 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 8.19666666666667 & 0.0330182851812272 & 248.246286010242 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 8.19666666666667 & 0.0330182851812272 & 248.246286010242 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 8.19666666666667 & 0.0235262405085692 & 348.405290836039 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 8.19666666666667 & 0.0235262405085692 & 348.405290836039 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 8.13275862068966 & 0.068489357430723 & 118.744852131456 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 8.13214285714286 & 0.0646221355896203 & 125.841444002805 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 8.13888888888889 & 0.0619628090403395 & 131.351192996919 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 8.14423076923077 & 0.0603792352369701 & 134.884629413856 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 8.15 & 0.05836199490233 & 139.645672044610 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 8.15625 & 0.0557751827485872 & 146.234393112887 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 8.16304347826087 & 0.0537806149775549 & 151.784122990555 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 8.17045454545454 & 0.0511577944287002 & 159.710844392283 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 8.17380952380952 & 0.0495109091569338 & 165.091081197906 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 8.1775 & 0.0472971376593683 & 172.896297845632 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 8.18421052631579 & 0.0450266739009381 & 181.763604043275 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 8.18888888888889 & 0.0430536353898505 & 190.202030902583 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 8.19411764705882 & 0.0402623253060217 & 203.51824155157 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 8.196875 & 0.0376968957287022 & 217.441644505464 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 8.19333333333333 & 0.0364938455946140 & 224.512741801663 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 8.19285714285714 & 0.0359778633544227 & 227.719391286476 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 8.19230769230769 & 0.035048571538137 & 233.741557295523 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 8.19166666666667 & 0.0334689271134527 & 244.754384832792 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 8.19090909090909 & 0.0307968422715713 & 265.965874640016 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 8.19 & 0.0306937332880492 & 266.829711561638 \tabularnewline
Median & 8.2 &  &  \tabularnewline
Midrange & 8.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.18387096774194 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.18387096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.18387096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.18387096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.18387096774194 &  &  \tabularnewline
Midmean - Closest Observation & 8.18387096774194 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.18387096774194 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.24166666666667 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16346&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]8.13333333333333[/C][C]0.0716104759351136[/C][C]113.577423234876[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8.11437739638333[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8.09506011383559[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.15191184119815[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]8.13333333333333[/C][C]0.0716104759351136[/C][C]113.577423234876[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]8.12[/C][C]0.0684699612473991[/C][C]118.592151245134[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]8.125[/C][C]0.0649478278234388[/C][C]125.100411704112[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]8.125[/C][C]0.0649478278234388[/C][C]125.100411704112[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]8.125[/C][C]0.0649478278234388[/C][C]125.100411704112[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]8.125[/C][C]0.0609076822963398[/C][C]133.39860742802[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]8.125[/C][C]0.0609076822963398[/C][C]133.39860742802[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]8.15166666666667[/C][C]0.0551572823875202[/C][C]147.789490595190[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]8.15166666666667[/C][C]0.0551572823875202[/C][C]147.789490595190[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]8.135[/C][C]0.0524983185095264[/C][C]154.957343986623[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]8.15333333333333[/C][C]0.0488550644846609[/C][C]166.888191006139[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]8.15333333333333[/C][C]0.0488550644846609[/C][C]166.888191006139[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]8.175[/C][C]0.0448238863884029[/C][C]182.380437277636[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]8.22166666666667[/C][C]0.0371355485245398[/C][C]221.396128327918[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]8.19666666666667[/C][C]0.0330182851812272[/C][C]248.246286010242[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]8.19666666666667[/C][C]0.0330182851812272[/C][C]248.246286010242[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]8.19666666666667[/C][C]0.0330182851812272[/C][C]248.246286010242[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]8.19666666666667[/C][C]0.0330182851812272[/C][C]248.246286010242[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]8.19666666666667[/C][C]0.0235262405085692[/C][C]348.405290836039[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]8.19666666666667[/C][C]0.0235262405085692[/C][C]348.405290836039[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]8.13275862068966[/C][C]0.068489357430723[/C][C]118.744852131456[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]8.13214285714286[/C][C]0.0646221355896203[/C][C]125.841444002805[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]8.13888888888889[/C][C]0.0619628090403395[/C][C]131.351192996919[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]8.14423076923077[/C][C]0.0603792352369701[/C][C]134.884629413856[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]8.15[/C][C]0.05836199490233[/C][C]139.645672044610[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]8.15625[/C][C]0.0557751827485872[/C][C]146.234393112887[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]8.16304347826087[/C][C]0.0537806149775549[/C][C]151.784122990555[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]8.17045454545454[/C][C]0.0511577944287002[/C][C]159.710844392283[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]8.17380952380952[/C][C]0.0495109091569338[/C][C]165.091081197906[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]8.1775[/C][C]0.0472971376593683[/C][C]172.896297845632[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]8.18421052631579[/C][C]0.0450266739009381[/C][C]181.763604043275[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]8.18888888888889[/C][C]0.0430536353898505[/C][C]190.202030902583[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]8.19411764705882[/C][C]0.0402623253060217[/C][C]203.51824155157[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]8.196875[/C][C]0.0376968957287022[/C][C]217.441644505464[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]8.19333333333333[/C][C]0.0364938455946140[/C][C]224.512741801663[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]8.19285714285714[/C][C]0.0359778633544227[/C][C]227.719391286476[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]8.19230769230769[/C][C]0.035048571538137[/C][C]233.741557295523[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]8.19166666666667[/C][C]0.0334689271134527[/C][C]244.754384832792[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]8.19090909090909[/C][C]0.0307968422715713[/C][C]265.965874640016[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]8.19[/C][C]0.0306937332880492[/C][C]266.829711561638[/C][/ROW]
[ROW][C]Median[/C][C]8.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.18387096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.18387096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.18387096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.18387096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.18387096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.18387096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.18387096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.24166666666667[/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=16346&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16346&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 Mean8.133333333333330.0716104759351136113.577423234876
Geometric Mean8.11437739638333
Harmonic Mean8.09506011383559
Quadratic Mean8.15191184119815
Winsorized Mean ( 1 / 20 )8.133333333333330.0716104759351136113.577423234876
Winsorized Mean ( 2 / 20 )8.120.0684699612473991118.592151245134
Winsorized Mean ( 3 / 20 )8.1250.0649478278234388125.100411704112
Winsorized Mean ( 4 / 20 )8.1250.0649478278234388125.100411704112
Winsorized Mean ( 5 / 20 )8.1250.0649478278234388125.100411704112
Winsorized Mean ( 6 / 20 )8.1250.0609076822963398133.39860742802
Winsorized Mean ( 7 / 20 )8.1250.0609076822963398133.39860742802
Winsorized Mean ( 8 / 20 )8.151666666666670.0551572823875202147.789490595190
Winsorized Mean ( 9 / 20 )8.151666666666670.0551572823875202147.789490595190
Winsorized Mean ( 10 / 20 )8.1350.0524983185095264154.957343986623
Winsorized Mean ( 11 / 20 )8.153333333333330.0488550644846609166.888191006139
Winsorized Mean ( 12 / 20 )8.153333333333330.0488550644846609166.888191006139
Winsorized Mean ( 13 / 20 )8.1750.0448238863884029182.380437277636
Winsorized Mean ( 14 / 20 )8.221666666666670.0371355485245398221.396128327918
Winsorized Mean ( 15 / 20 )8.196666666666670.0330182851812272248.246286010242
Winsorized Mean ( 16 / 20 )8.196666666666670.0330182851812272248.246286010242
Winsorized Mean ( 17 / 20 )8.196666666666670.0330182851812272248.246286010242
Winsorized Mean ( 18 / 20 )8.196666666666670.0330182851812272248.246286010242
Winsorized Mean ( 19 / 20 )8.196666666666670.0235262405085692348.405290836039
Winsorized Mean ( 20 / 20 )8.196666666666670.0235262405085692348.405290836039
Trimmed Mean ( 1 / 20 )8.132758620689660.068489357430723118.744852131456
Trimmed Mean ( 2 / 20 )8.132142857142860.0646221355896203125.841444002805
Trimmed Mean ( 3 / 20 )8.138888888888890.0619628090403395131.351192996919
Trimmed Mean ( 4 / 20 )8.144230769230770.0603792352369701134.884629413856
Trimmed Mean ( 5 / 20 )8.150.05836199490233139.645672044610
Trimmed Mean ( 6 / 20 )8.156250.0557751827485872146.234393112887
Trimmed Mean ( 7 / 20 )8.163043478260870.0537806149775549151.784122990555
Trimmed Mean ( 8 / 20 )8.170454545454540.0511577944287002159.710844392283
Trimmed Mean ( 9 / 20 )8.173809523809520.0495109091569338165.091081197906
Trimmed Mean ( 10 / 20 )8.17750.0472971376593683172.896297845632
Trimmed Mean ( 11 / 20 )8.184210526315790.0450266739009381181.763604043275
Trimmed Mean ( 12 / 20 )8.188888888888890.0430536353898505190.202030902583
Trimmed Mean ( 13 / 20 )8.194117647058820.0402623253060217203.51824155157
Trimmed Mean ( 14 / 20 )8.1968750.0376968957287022217.441644505464
Trimmed Mean ( 15 / 20 )8.193333333333330.0364938455946140224.512741801663
Trimmed Mean ( 16 / 20 )8.192857142857140.0359778633544227227.719391286476
Trimmed Mean ( 17 / 20 )8.192307692307690.035048571538137233.741557295523
Trimmed Mean ( 18 / 20 )8.191666666666670.0334689271134527244.754384832792
Trimmed Mean ( 19 / 20 )8.190909090909090.0307968422715713265.965874640016
Trimmed Mean ( 20 / 20 )8.190.0306937332880492266.829711561638
Median8.2
Midrange8.15
Midmean - Weighted Average at Xnp8.18387096774194
Midmean - Weighted Average at X(n+1)p8.18387096774194
Midmean - Empirical Distribution Function8.18387096774194
Midmean - Empirical Distribution Function - Averaging8.18387096774194
Midmean - Empirical Distribution Function - Interpolation8.18387096774194
Midmean - Closest Observation8.18387096774194
Midmean - True Basic - Statistics Graphics Toolkit8.18387096774194
Midmean - MS Excel (old versions)8.24166666666667
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')