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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, 11 Dec 2008 15:56:40 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/11/t1229036272bef2plyzob8ergh.htm/, Retrieved Fri, 17 May 2024 03:41:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32467, Retrieved Fri, 17 May 2024 03:41:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact171
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Paper central ten...] [2007-11-09 08:56:17] [74be16979710d4c4e7c6647856088456]
-    D    [Central Tendency] [central tendency ...] [2008-12-11 22:56:40] [e8f764b122b426f433a1e1038b457077] [Current]
-    D      [Central Tendency] [central tendency ...] [2008-12-11 22:59:27] [4ddbf81f78ea7c738951638c7e93f6ee]
-    D        [Central Tendency] [central tendency ...] [2008-12-11 23:02:29] [4ddbf81f78ea7c738951638c7e93f6ee]
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Dataseries X:
7,5
7,6
7,9
7,9
8,1
8,2
8
7,5
6,8
6,5
6,6
7,6
8
8
7,7
7,5
7,6
7,7
7,9
7,8
7,5
7,5
7,1
7,5
7,5
7,6
7,7
7,7
7,9
8,1
8,2
8,2
8,1
7,9
7,3
6,9
6,6
6,7
6,9
7
7,1
7,2
7,1
6,9
7
6,8
6,4
6,7
6,7
6,4
6,3
6,2
6,5
6,8
6,8
6,5
6,3
5,9
5,9
6,4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32467&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32467&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32467&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.236666666666670.082748228399171887.4540374660045
Geometric Mean7.20820319418317
Harmonic Mean7.1792435737109
Quadratic Mean7.26452567848262
Winsorized Mean ( 1 / 20 )7.236666666666670.082748228399171887.4540374660045
Winsorized Mean ( 2 / 20 )7.246666666666670.080270259130898690.2783514732319
Winsorized Mean ( 3 / 20 )7.246666666666670.078238613245868192.622636905561
Winsorized Mean ( 4 / 20 )7.246666666666670.078238613245868192.622636905561
Winsorized Mean ( 5 / 20 )7.2550.076595090636440494.718864351711
Winsorized Mean ( 6 / 20 )7.2450.074803886723395396.853256125448
Winsorized Mean ( 7 / 20 )7.2450.074803886723395396.853256125448
Winsorized Mean ( 8 / 20 )7.258333333333330.0723414559734185100.334355117215
Winsorized Mean ( 9 / 20 )7.243333333333330.0698410894658566103.711631486997
Winsorized Mean ( 10 / 20 )7.243333333333330.0698410894658566103.711631486997
Winsorized Mean ( 11 / 20 )7.261666666666670.0666422978060768108.964830231357
Winsorized Mean ( 12 / 20 )7.261666666666670.0666422978060768108.964830231357
Winsorized Mean ( 13 / 20 )7.283333333333330.0631188756794932115.390733040253
Winsorized Mean ( 14 / 20 )7.260.059384793275016122.253519792152
Winsorized Mean ( 15 / 20 )7.2350.055683985262275129.929637146528
Winsorized Mean ( 16 / 20 )7.261666666666670.0514804371086379141.056818366607
Winsorized Mean ( 17 / 20 )7.261666666666670.0514804371086379141.056818366607
Winsorized Mean ( 18 / 20 )7.261666666666670.0514804371086379141.056818366607
Winsorized Mean ( 19 / 20 )7.230.0470784895763549153.573321171953
Winsorized Mean ( 20 / 20 )7.263333333333330.0420496522934942172.732304244454
Trimmed Mean ( 1 / 20 )7.243103448275860.080684911003701689.7702353286796
Trimmed Mean ( 2 / 20 )7.250.078127435026987292.7971076676928
Trimmed Mean ( 3 / 20 )7.251851851851850.076604237673219194.666458046186
Trimmed Mean ( 4 / 20 )7.253846153846150.075630160019244295.9120825871636
Trimmed Mean ( 5 / 20 )7.2560.07434942323040597.593225135238
Trimmed Mean ( 6 / 20 )7.256250.073230076200176799.0883852170905
Trimmed Mean ( 7 / 20 )7.258695652173910.0722700308696403100.438529841879
Trimmed Mean ( 8 / 20 )7.261363636363640.0709506505303943102.343862700074
Trimmed Mean ( 9 / 20 )7.261904761904760.0698390701093066103.980547715469
Trimmed Mean ( 10 / 20 )7.2650.0689248940923454105.404587060611
Trimmed Mean ( 11 / 20 )7.268421052631580.0675843357197394107.545942047466
Trimmed Mean ( 12 / 20 )7.269444444444440.0665259758844027109.272270685304
Trimmed Mean ( 13 / 20 )7.270588235294120.0649323536335353111.971734096192
Trimmed Mean ( 14 / 20 )7.268750.0635694787538191114.343394699667
Trimmed Mean ( 15 / 20 )7.270.0625419399513124116.241997060845
Trimmed Mean ( 16 / 20 )7.2750.0618551388411521117.613510151237
Trimmed Mean ( 17 / 20 )7.276923076923080.061845388437667117.663147742331
Trimmed Mean ( 18 / 20 )7.279166666666670.0613788327610676118.594087557882
Trimmed Mean ( 19 / 20 )7.281818181818180.0601716029572088121.017520291036
Trimmed Mean ( 20 / 20 )7.290.0593384582844798122.85455690558
Median7.4
Midrange7.05
Midmean - Weighted Average at Xnp7.234375
Midmean - Weighted Average at X(n+1)p7.234375
Midmean - Empirical Distribution Function7.234375
Midmean - Empirical Distribution Function - Averaging7.234375
Midmean - Empirical Distribution Function - Interpolation7.234375
Midmean - Closest Observation7.234375
Midmean - True Basic - Statistics Graphics Toolkit7.234375
Midmean - MS Excel (old versions)7.25151515151515
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.23666666666667 & 0.0827482283991718 & 87.4540374660045 \tabularnewline
Geometric Mean & 7.20820319418317 &  &  \tabularnewline
Harmonic Mean & 7.1792435737109 &  &  \tabularnewline
Quadratic Mean & 7.26452567848262 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 7.23666666666667 & 0.0827482283991718 & 87.4540374660045 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 7.24666666666667 & 0.0802702591308986 & 90.2783514732319 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 7.24666666666667 & 0.0782386132458681 & 92.622636905561 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 7.24666666666667 & 0.0782386132458681 & 92.622636905561 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 7.255 & 0.0765950906364404 & 94.718864351711 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 7.245 & 0.0748038867233953 & 96.853256125448 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 7.245 & 0.0748038867233953 & 96.853256125448 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 7.25833333333333 & 0.0723414559734185 & 100.334355117215 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 7.24333333333333 & 0.0698410894658566 & 103.711631486997 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 7.24333333333333 & 0.0698410894658566 & 103.711631486997 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 7.26166666666667 & 0.0666422978060768 & 108.964830231357 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 7.26166666666667 & 0.0666422978060768 & 108.964830231357 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 7.28333333333333 & 0.0631188756794932 & 115.390733040253 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 7.26 & 0.059384793275016 & 122.253519792152 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 7.235 & 0.055683985262275 & 129.929637146528 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 7.26166666666667 & 0.0514804371086379 & 141.056818366607 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 7.26166666666667 & 0.0514804371086379 & 141.056818366607 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 7.26166666666667 & 0.0514804371086379 & 141.056818366607 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 7.23 & 0.0470784895763549 & 153.573321171953 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 7.26333333333333 & 0.0420496522934942 & 172.732304244454 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 7.24310344827586 & 0.0806849110037016 & 89.7702353286796 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 7.25 & 0.0781274350269872 & 92.7971076676928 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 7.25185185185185 & 0.0766042376732191 & 94.666458046186 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 7.25384615384615 & 0.0756301600192442 & 95.9120825871636 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 7.256 & 0.074349423230405 & 97.593225135238 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 7.25625 & 0.0732300762001767 & 99.0883852170905 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 7.25869565217391 & 0.0722700308696403 & 100.438529841879 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 7.26136363636364 & 0.0709506505303943 & 102.343862700074 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 7.26190476190476 & 0.0698390701093066 & 103.980547715469 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 7.265 & 0.0689248940923454 & 105.404587060611 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 7.26842105263158 & 0.0675843357197394 & 107.545942047466 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 7.26944444444444 & 0.0665259758844027 & 109.272270685304 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 7.27058823529412 & 0.0649323536335353 & 111.971734096192 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 7.26875 & 0.0635694787538191 & 114.343394699667 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 7.27 & 0.0625419399513124 & 116.241997060845 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 7.275 & 0.0618551388411521 & 117.613510151237 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 7.27692307692308 & 0.061845388437667 & 117.663147742331 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 7.27916666666667 & 0.0613788327610676 & 118.594087557882 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 7.28181818181818 & 0.0601716029572088 & 121.017520291036 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 7.29 & 0.0593384582844798 & 122.85455690558 \tabularnewline
Median & 7.4 &  &  \tabularnewline
Midrange & 7.05 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.234375 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.234375 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.234375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.234375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.234375 &  &  \tabularnewline
Midmean - Closest Observation & 7.234375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.234375 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.25151515151515 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32467&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]7.23666666666667[/C][C]0.0827482283991718[/C][C]87.4540374660045[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.20820319418317[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.1792435737109[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.26452567848262[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]7.23666666666667[/C][C]0.0827482283991718[/C][C]87.4540374660045[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]7.24666666666667[/C][C]0.0802702591308986[/C][C]90.2783514732319[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]7.24666666666667[/C][C]0.0782386132458681[/C][C]92.622636905561[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]7.24666666666667[/C][C]0.0782386132458681[/C][C]92.622636905561[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]7.255[/C][C]0.0765950906364404[/C][C]94.718864351711[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]7.245[/C][C]0.0748038867233953[/C][C]96.853256125448[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]7.245[/C][C]0.0748038867233953[/C][C]96.853256125448[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]7.25833333333333[/C][C]0.0723414559734185[/C][C]100.334355117215[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]7.24333333333333[/C][C]0.0698410894658566[/C][C]103.711631486997[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]7.24333333333333[/C][C]0.0698410894658566[/C][C]103.711631486997[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]7.26166666666667[/C][C]0.0666422978060768[/C][C]108.964830231357[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]7.26166666666667[/C][C]0.0666422978060768[/C][C]108.964830231357[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]7.28333333333333[/C][C]0.0631188756794932[/C][C]115.390733040253[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]7.26[/C][C]0.059384793275016[/C][C]122.253519792152[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]7.235[/C][C]0.055683985262275[/C][C]129.929637146528[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]7.26166666666667[/C][C]0.0514804371086379[/C][C]141.056818366607[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]7.26166666666667[/C][C]0.0514804371086379[/C][C]141.056818366607[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]7.26166666666667[/C][C]0.0514804371086379[/C][C]141.056818366607[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]7.23[/C][C]0.0470784895763549[/C][C]153.573321171953[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]7.26333333333333[/C][C]0.0420496522934942[/C][C]172.732304244454[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]7.24310344827586[/C][C]0.0806849110037016[/C][C]89.7702353286796[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]7.25[/C][C]0.0781274350269872[/C][C]92.7971076676928[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]7.25185185185185[/C][C]0.0766042376732191[/C][C]94.666458046186[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]7.25384615384615[/C][C]0.0756301600192442[/C][C]95.9120825871636[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]7.256[/C][C]0.074349423230405[/C][C]97.593225135238[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]7.25625[/C][C]0.0732300762001767[/C][C]99.0883852170905[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]7.25869565217391[/C][C]0.0722700308696403[/C][C]100.438529841879[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]7.26136363636364[/C][C]0.0709506505303943[/C][C]102.343862700074[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]7.26190476190476[/C][C]0.0698390701093066[/C][C]103.980547715469[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]7.265[/C][C]0.0689248940923454[/C][C]105.404587060611[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]7.26842105263158[/C][C]0.0675843357197394[/C][C]107.545942047466[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]7.26944444444444[/C][C]0.0665259758844027[/C][C]109.272270685304[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]7.27058823529412[/C][C]0.0649323536335353[/C][C]111.971734096192[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]7.26875[/C][C]0.0635694787538191[/C][C]114.343394699667[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]7.27[/C][C]0.0625419399513124[/C][C]116.241997060845[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]7.275[/C][C]0.0618551388411521[/C][C]117.613510151237[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]7.27692307692308[/C][C]0.061845388437667[/C][C]117.663147742331[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]7.27916666666667[/C][C]0.0613788327610676[/C][C]118.594087557882[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]7.28181818181818[/C][C]0.0601716029572088[/C][C]121.017520291036[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]7.29[/C][C]0.0593384582844798[/C][C]122.85455690558[/C][/ROW]
[ROW][C]Median[/C][C]7.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.234375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.234375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.234375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.234375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.234375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.234375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.234375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.25151515151515[/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=32467&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32467&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 Mean7.236666666666670.082748228399171887.4540374660045
Geometric Mean7.20820319418317
Harmonic Mean7.1792435737109
Quadratic Mean7.26452567848262
Winsorized Mean ( 1 / 20 )7.236666666666670.082748228399171887.4540374660045
Winsorized Mean ( 2 / 20 )7.246666666666670.080270259130898690.2783514732319
Winsorized Mean ( 3 / 20 )7.246666666666670.078238613245868192.622636905561
Winsorized Mean ( 4 / 20 )7.246666666666670.078238613245868192.622636905561
Winsorized Mean ( 5 / 20 )7.2550.076595090636440494.718864351711
Winsorized Mean ( 6 / 20 )7.2450.074803886723395396.853256125448
Winsorized Mean ( 7 / 20 )7.2450.074803886723395396.853256125448
Winsorized Mean ( 8 / 20 )7.258333333333330.0723414559734185100.334355117215
Winsorized Mean ( 9 / 20 )7.243333333333330.0698410894658566103.711631486997
Winsorized Mean ( 10 / 20 )7.243333333333330.0698410894658566103.711631486997
Winsorized Mean ( 11 / 20 )7.261666666666670.0666422978060768108.964830231357
Winsorized Mean ( 12 / 20 )7.261666666666670.0666422978060768108.964830231357
Winsorized Mean ( 13 / 20 )7.283333333333330.0631188756794932115.390733040253
Winsorized Mean ( 14 / 20 )7.260.059384793275016122.253519792152
Winsorized Mean ( 15 / 20 )7.2350.055683985262275129.929637146528
Winsorized Mean ( 16 / 20 )7.261666666666670.0514804371086379141.056818366607
Winsorized Mean ( 17 / 20 )7.261666666666670.0514804371086379141.056818366607
Winsorized Mean ( 18 / 20 )7.261666666666670.0514804371086379141.056818366607
Winsorized Mean ( 19 / 20 )7.230.0470784895763549153.573321171953
Winsorized Mean ( 20 / 20 )7.263333333333330.0420496522934942172.732304244454
Trimmed Mean ( 1 / 20 )7.243103448275860.080684911003701689.7702353286796
Trimmed Mean ( 2 / 20 )7.250.078127435026987292.7971076676928
Trimmed Mean ( 3 / 20 )7.251851851851850.076604237673219194.666458046186
Trimmed Mean ( 4 / 20 )7.253846153846150.075630160019244295.9120825871636
Trimmed Mean ( 5 / 20 )7.2560.07434942323040597.593225135238
Trimmed Mean ( 6 / 20 )7.256250.073230076200176799.0883852170905
Trimmed Mean ( 7 / 20 )7.258695652173910.0722700308696403100.438529841879
Trimmed Mean ( 8 / 20 )7.261363636363640.0709506505303943102.343862700074
Trimmed Mean ( 9 / 20 )7.261904761904760.0698390701093066103.980547715469
Trimmed Mean ( 10 / 20 )7.2650.0689248940923454105.404587060611
Trimmed Mean ( 11 / 20 )7.268421052631580.0675843357197394107.545942047466
Trimmed Mean ( 12 / 20 )7.269444444444440.0665259758844027109.272270685304
Trimmed Mean ( 13 / 20 )7.270588235294120.0649323536335353111.971734096192
Trimmed Mean ( 14 / 20 )7.268750.0635694787538191114.343394699667
Trimmed Mean ( 15 / 20 )7.270.0625419399513124116.241997060845
Trimmed Mean ( 16 / 20 )7.2750.0618551388411521117.613510151237
Trimmed Mean ( 17 / 20 )7.276923076923080.061845388437667117.663147742331
Trimmed Mean ( 18 / 20 )7.279166666666670.0613788327610676118.594087557882
Trimmed Mean ( 19 / 20 )7.281818181818180.0601716029572088121.017520291036
Trimmed Mean ( 20 / 20 )7.290.0593384582844798122.85455690558
Median7.4
Midrange7.05
Midmean - Weighted Average at Xnp7.234375
Midmean - Weighted Average at X(n+1)p7.234375
Midmean - Empirical Distribution Function7.234375
Midmean - Empirical Distribution Function - Averaging7.234375
Midmean - Empirical Distribution Function - Interpolation7.234375
Midmean - Closest Observation7.234375
Midmean - True Basic - Statistics Graphics Toolkit7.234375
Midmean - MS Excel (old versions)7.25151515151515
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')