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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 30 Nov 2008 12:24:23 -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/Nov/30/t1228073125lcba3fyam9wy19k.htm/, Retrieved Tue, 14 May 2024 01:04:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26703, Retrieved Tue, 14 May 2024 01:04:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact174

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Q1 central tenden...] [2007-10-18 09:40:43] [b731da8b544846036771bbf9bf2f34ce]
F    D  [Central Tendency] [task 3 Q1 Reprodu...] [2008-10-19 12:06:44] [86761fc994bdf34e4f4ab5b8e1d9e1c3]
-    D    [Central Tendency] [CT Bouwproductie] [2008-11-30 18:25:17] [aa5573c1db401b164e448aef050955a1]
- R         [Central Tendency] [Central Tendancy ...] [2008-11-30 18:59:06] [aa5573c1db401b164e448aef050955a1]
- R  D          [Central Tendency] [Central Tendancy ...] [2008-11-30 19:24:23] [8a1195ff8db4df756ce44b463a631c76] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
97.4
97
105.4
102.7
98.1
104.5
87.4
89.9
109.8
111.7
98.6
96.9
95.1
97
112.7
102.9
97.4
111.4
87.4
96.8
114.1
110.3
103.9
101.6
94.6
95.9
104.7
102.8
98.1
113.9
80.9
95.7
113.2
105.9
108.8
102.3
99
100.7
115.5
100.7
109.9
114.6
85.4
100.5
114.8
116.5
112.9
102
106
105.3
118.8
106.1
109.3
117.2
92.5
104.2
112.5
122.4
113.3
100
110.7
112.8
109.8
117.3
109.1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26703&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26703&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26703&T=0

As an alternative you can also use a QR Code:  
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'George Udny Yule' @ 72.249.76.132






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-2.31747180206704e-131.09932173817480-2.10809240060579e-13
Geometric MeanNaN
Harmonic Mean7.49707855614652
Quadratic Mean8.79457390539842
Winsorized Mean ( 1 / 21 )0.01384615384592201.065124065612980.0129995690576698
Winsorized Mean ( 2 / 21 )0.02923076923053741.039313041211900.0281250865441393
Winsorized Mean ( 3 / 21 )0.0246153846151531.038423539190810.0237045710985467
Winsorized Mean ( 4 / 21 )0.1353846153843840.9927405510883230.136374619970912
Winsorized Mean ( 5 / 21 )0.2584615384613060.935070204306740.276408698802385
Winsorized Mean ( 6 / 21 )0.3876923076920750.886330402750710.437412850206738
Winsorized Mean ( 7 / 21 )0.4199999999997670.8730189746950030.481089199861317
Winsorized Mean ( 8 / 21 )0.432307692307460.8497592767380460.508741362573823
Winsorized Mean ( 9 / 21 )0.4323076923074620.840440853601470.51438205372208
Winsorized Mean ( 10 / 21 )0.4784615384613060.80268332345420.596077586864935
Winsorized Mean ( 11 / 21 )0.4784615384613080.7972624667124390.600130519669732
Winsorized Mean ( 12 / 21 )0.4415384615382310.7854295832075050.562161740502686
Winsorized Mean ( 13 / 21 )0.4215384615382290.782236448234640.538888800808964
Winsorized Mean ( 14 / 21 )0.4861538461536160.7654763184337190.635099786167599
Winsorized Mean ( 15 / 21 )0.4399999999997690.7581611200949760.580351574800683
Winsorized Mean ( 16 / 21 )0.4153846153843820.7013929504963090.592228101366651
Winsorized Mean ( 17 / 21 )0.3369230769228450.689467732702460.488671276322432
Winsorized Mean ( 18 / 21 )0.2815384615382280.6398870208156160.43998151607978
Winsorized Mean ( 19 / 21 )0.2815384615382280.605562052483710.464920911710864
Winsorized Mean ( 20 / 21 )0.4661538461536160.5435594527723950.857594958152276
Winsorized Mean ( 21 / 21 )0.5953846153843820.5165502747947511.15261697541630
Trimmed Mean ( 1 / 21 )0.08759462759439571.030830347136430.0849748242644652
Trimmed Mean ( 2 / 21 )0.1661790668345730.9891367758850260.168004133387806
Trimmed Mean ( 3 / 21 )0.2416166883961170.9554157447737180.252891675396601
Trimmed Mean ( 4 / 21 )0.3241025641023320.9142780453416880.354490152917548
Trimmed Mean ( 5 / 21 )0.3798601398599080.8818318579938470.430762550044499
Trimmed Mean ( 6 / 21 )0.40963715529730.8611433677862510.475689845176835
Trimmed Mean ( 7 / 21 )0.4142986425337050.849385421350230.48776283665796
Trimmed Mean ( 8 / 21 )0.4132182103608360.8374689826022030.493413151943699
Trimmed Mean ( 9 / 21 )0.4099181669392120.8274580084584360.495394524856789
Trimmed Mean ( 10 / 21 )0.4063247863245540.8159641725371260.497968905989027
Trimmed Mean ( 11 / 21 )0.3954203935596970.8090158732368560.488767163464454
Trimmed Mean ( 12 / 21 )0.3834521575982670.7997971560210120.479436760573069
Trimmed Mean ( 13 / 21 )0.3753846153843830.789014815259020.475763709533326
Trimmed Mean ( 14 / 21 )0.3691476091473770.7738998307113150.476996627338815
Trimmed Mean ( 15 / 21 )0.3536263736261410.7562410992799160.467610625715609
Trimmed Mean ( 16 / 21 )0.342284382284150.7324217976163110.467332325987737
Trimmed Mean ( 17 / 21 )0.3327047146399660.7138834306449670.466049077983754
Trimmed Mean ( 18 / 21 )0.3321485411138260.6890329705585440.482050286860119
Trimmed Mean ( 19 / 21 )0.3389173789171470.6669736551811540.508142077703346
Trimmed Mean ( 20 / 21 )0.3467692307689990.6434562922219350.538916527759114
Trimmed Mean ( 21 / 21 )0.3298996655516070.6276481961417170.525612385376981
Median0.0907692307689985
Midrange-2.75923076923100
Midmean - Weighted Average at Xnp0.125144230768998
Midmean - Weighted Average at X(n+1)p0.34228438228415
Midmean - Empirical Distribution Function0.34228438228415
Midmean - Empirical Distribution Function - Averaging0.34228438228415
Midmean - Empirical Distribution Function - Interpolation0.34228438228415
Midmean - Closest Observation-0.0778021978024299
Midmean - True Basic - Statistics Graphics Toolkit0.34228438228415
Midmean - MS Excel (old versions)0.34228438228415
Number of observations65

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -2.31747180206704e-13 & 1.09932173817480 & -2.10809240060579e-13 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 7.49707855614652 &  &  \tabularnewline
Quadratic Mean & 8.79457390539842 &  &  \tabularnewline
Winsorized Mean ( 1 / 21 ) & 0.0138461538459220 & 1.06512406561298 & 0.0129995690576698 \tabularnewline
Winsorized Mean ( 2 / 21 ) & 0.0292307692305374 & 1.03931304121190 & 0.0281250865441393 \tabularnewline
Winsorized Mean ( 3 / 21 ) & 0.024615384615153 & 1.03842353919081 & 0.0237045710985467 \tabularnewline
Winsorized Mean ( 4 / 21 ) & 0.135384615384384 & 0.992740551088323 & 0.136374619970912 \tabularnewline
Winsorized Mean ( 5 / 21 ) & 0.258461538461306 & 0.93507020430674 & 0.276408698802385 \tabularnewline
Winsorized Mean ( 6 / 21 ) & 0.387692307692075 & 0.88633040275071 & 0.437412850206738 \tabularnewline
Winsorized Mean ( 7 / 21 ) & 0.419999999999767 & 0.873018974695003 & 0.481089199861317 \tabularnewline
Winsorized Mean ( 8 / 21 ) & 0.43230769230746 & 0.849759276738046 & 0.508741362573823 \tabularnewline
Winsorized Mean ( 9 / 21 ) & 0.432307692307462 & 0.84044085360147 & 0.51438205372208 \tabularnewline
Winsorized Mean ( 10 / 21 ) & 0.478461538461306 & 0.8026833234542 & 0.596077586864935 \tabularnewline
Winsorized Mean ( 11 / 21 ) & 0.478461538461308 & 0.797262466712439 & 0.600130519669732 \tabularnewline
Winsorized Mean ( 12 / 21 ) & 0.441538461538231 & 0.785429583207505 & 0.562161740502686 \tabularnewline
Winsorized Mean ( 13 / 21 ) & 0.421538461538229 & 0.78223644823464 & 0.538888800808964 \tabularnewline
Winsorized Mean ( 14 / 21 ) & 0.486153846153616 & 0.765476318433719 & 0.635099786167599 \tabularnewline
Winsorized Mean ( 15 / 21 ) & 0.439999999999769 & 0.758161120094976 & 0.580351574800683 \tabularnewline
Winsorized Mean ( 16 / 21 ) & 0.415384615384382 & 0.701392950496309 & 0.592228101366651 \tabularnewline
Winsorized Mean ( 17 / 21 ) & 0.336923076922845 & 0.68946773270246 & 0.488671276322432 \tabularnewline
Winsorized Mean ( 18 / 21 ) & 0.281538461538228 & 0.639887020815616 & 0.43998151607978 \tabularnewline
Winsorized Mean ( 19 / 21 ) & 0.281538461538228 & 0.60556205248371 & 0.464920911710864 \tabularnewline
Winsorized Mean ( 20 / 21 ) & 0.466153846153616 & 0.543559452772395 & 0.857594958152276 \tabularnewline
Winsorized Mean ( 21 / 21 ) & 0.595384615384382 & 0.516550274794751 & 1.15261697541630 \tabularnewline
Trimmed Mean ( 1 / 21 ) & 0.0875946275943957 & 1.03083034713643 & 0.0849748242644652 \tabularnewline
Trimmed Mean ( 2 / 21 ) & 0.166179066834573 & 0.989136775885026 & 0.168004133387806 \tabularnewline
Trimmed Mean ( 3 / 21 ) & 0.241616688396117 & 0.955415744773718 & 0.252891675396601 \tabularnewline
Trimmed Mean ( 4 / 21 ) & 0.324102564102332 & 0.914278045341688 & 0.354490152917548 \tabularnewline
Trimmed Mean ( 5 / 21 ) & 0.379860139859908 & 0.881831857993847 & 0.430762550044499 \tabularnewline
Trimmed Mean ( 6 / 21 ) & 0.4096371552973 & 0.861143367786251 & 0.475689845176835 \tabularnewline
Trimmed Mean ( 7 / 21 ) & 0.414298642533705 & 0.84938542135023 & 0.48776283665796 \tabularnewline
Trimmed Mean ( 8 / 21 ) & 0.413218210360836 & 0.837468982602203 & 0.493413151943699 \tabularnewline
Trimmed Mean ( 9 / 21 ) & 0.409918166939212 & 0.827458008458436 & 0.495394524856789 \tabularnewline
Trimmed Mean ( 10 / 21 ) & 0.406324786324554 & 0.815964172537126 & 0.497968905989027 \tabularnewline
Trimmed Mean ( 11 / 21 ) & 0.395420393559697 & 0.809015873236856 & 0.488767163464454 \tabularnewline
Trimmed Mean ( 12 / 21 ) & 0.383452157598267 & 0.799797156021012 & 0.479436760573069 \tabularnewline
Trimmed Mean ( 13 / 21 ) & 0.375384615384383 & 0.78901481525902 & 0.475763709533326 \tabularnewline
Trimmed Mean ( 14 / 21 ) & 0.369147609147377 & 0.773899830711315 & 0.476996627338815 \tabularnewline
Trimmed Mean ( 15 / 21 ) & 0.353626373626141 & 0.756241099279916 & 0.467610625715609 \tabularnewline
Trimmed Mean ( 16 / 21 ) & 0.34228438228415 & 0.732421797616311 & 0.467332325987737 \tabularnewline
Trimmed Mean ( 17 / 21 ) & 0.332704714639966 & 0.713883430644967 & 0.466049077983754 \tabularnewline
Trimmed Mean ( 18 / 21 ) & 0.332148541113826 & 0.689032970558544 & 0.482050286860119 \tabularnewline
Trimmed Mean ( 19 / 21 ) & 0.338917378917147 & 0.666973655181154 & 0.508142077703346 \tabularnewline
Trimmed Mean ( 20 / 21 ) & 0.346769230768999 & 0.643456292221935 & 0.538916527759114 \tabularnewline
Trimmed Mean ( 21 / 21 ) & 0.329899665551607 & 0.627648196141717 & 0.525612385376981 \tabularnewline
Median & 0.0907692307689985 &  &  \tabularnewline
Midrange & -2.75923076923100 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.125144230768998 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.34228438228415 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.34228438228415 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.34228438228415 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.34228438228415 &  &  \tabularnewline
Midmean - Closest Observation & -0.0778021978024299 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.34228438228415 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.34228438228415 &  &  \tabularnewline
Number of observations & 65 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26703&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]-2.31747180206704e-13[/C][C]1.09932173817480[/C][C]-2.10809240060579e-13[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.49707855614652[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.79457390539842[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 21 )[/C][C]0.0138461538459220[/C][C]1.06512406561298[/C][C]0.0129995690576698[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 21 )[/C][C]0.0292307692305374[/C][C]1.03931304121190[/C][C]0.0281250865441393[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 21 )[/C][C]0.024615384615153[/C][C]1.03842353919081[/C][C]0.0237045710985467[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 21 )[/C][C]0.135384615384384[/C][C]0.992740551088323[/C][C]0.136374619970912[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 21 )[/C][C]0.258461538461306[/C][C]0.93507020430674[/C][C]0.276408698802385[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 21 )[/C][C]0.387692307692075[/C][C]0.88633040275071[/C][C]0.437412850206738[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 21 )[/C][C]0.419999999999767[/C][C]0.873018974695003[/C][C]0.481089199861317[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 21 )[/C][C]0.43230769230746[/C][C]0.849759276738046[/C][C]0.508741362573823[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 21 )[/C][C]0.432307692307462[/C][C]0.84044085360147[/C][C]0.51438205372208[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 21 )[/C][C]0.478461538461306[/C][C]0.8026833234542[/C][C]0.596077586864935[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 21 )[/C][C]0.478461538461308[/C][C]0.797262466712439[/C][C]0.600130519669732[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 21 )[/C][C]0.441538461538231[/C][C]0.785429583207505[/C][C]0.562161740502686[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 21 )[/C][C]0.421538461538229[/C][C]0.78223644823464[/C][C]0.538888800808964[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 21 )[/C][C]0.486153846153616[/C][C]0.765476318433719[/C][C]0.635099786167599[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 21 )[/C][C]0.439999999999769[/C][C]0.758161120094976[/C][C]0.580351574800683[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 21 )[/C][C]0.415384615384382[/C][C]0.701392950496309[/C][C]0.592228101366651[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 21 )[/C][C]0.336923076922845[/C][C]0.68946773270246[/C][C]0.488671276322432[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 21 )[/C][C]0.281538461538228[/C][C]0.639887020815616[/C][C]0.43998151607978[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 21 )[/C][C]0.281538461538228[/C][C]0.60556205248371[/C][C]0.464920911710864[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 21 )[/C][C]0.466153846153616[/C][C]0.543559452772395[/C][C]0.857594958152276[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 21 )[/C][C]0.595384615384382[/C][C]0.516550274794751[/C][C]1.15261697541630[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 21 )[/C][C]0.0875946275943957[/C][C]1.03083034713643[/C][C]0.0849748242644652[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 21 )[/C][C]0.166179066834573[/C][C]0.989136775885026[/C][C]0.168004133387806[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 21 )[/C][C]0.241616688396117[/C][C]0.955415744773718[/C][C]0.252891675396601[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 21 )[/C][C]0.324102564102332[/C][C]0.914278045341688[/C][C]0.354490152917548[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 21 )[/C][C]0.379860139859908[/C][C]0.881831857993847[/C][C]0.430762550044499[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 21 )[/C][C]0.4096371552973[/C][C]0.861143367786251[/C][C]0.475689845176835[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 21 )[/C][C]0.414298642533705[/C][C]0.84938542135023[/C][C]0.48776283665796[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 21 )[/C][C]0.413218210360836[/C][C]0.837468982602203[/C][C]0.493413151943699[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 21 )[/C][C]0.409918166939212[/C][C]0.827458008458436[/C][C]0.495394524856789[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 21 )[/C][C]0.406324786324554[/C][C]0.815964172537126[/C][C]0.497968905989027[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 21 )[/C][C]0.395420393559697[/C][C]0.809015873236856[/C][C]0.488767163464454[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 21 )[/C][C]0.383452157598267[/C][C]0.799797156021012[/C][C]0.479436760573069[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 21 )[/C][C]0.375384615384383[/C][C]0.78901481525902[/C][C]0.475763709533326[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 21 )[/C][C]0.369147609147377[/C][C]0.773899830711315[/C][C]0.476996627338815[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 21 )[/C][C]0.353626373626141[/C][C]0.756241099279916[/C][C]0.467610625715609[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 21 )[/C][C]0.34228438228415[/C][C]0.732421797616311[/C][C]0.467332325987737[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 21 )[/C][C]0.332704714639966[/C][C]0.713883430644967[/C][C]0.466049077983754[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 21 )[/C][C]0.332148541113826[/C][C]0.689032970558544[/C][C]0.482050286860119[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 21 )[/C][C]0.338917378917147[/C][C]0.666973655181154[/C][C]0.508142077703346[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 21 )[/C][C]0.346769230768999[/C][C]0.643456292221935[/C][C]0.538916527759114[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 21 )[/C][C]0.329899665551607[/C][C]0.627648196141717[/C][C]0.525612385376981[/C][/ROW]
[ROW][C]Median[/C][C]0.0907692307689985[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-2.75923076923100[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.125144230768998[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.34228438228415[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.34228438228415[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.34228438228415[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.34228438228415[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-0.0778021978024299[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.34228438228415[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.34228438228415[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]65[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26703&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26703&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-2.31747180206704e-131.09932173817480-2.10809240060579e-13
Geometric MeanNaN
Harmonic Mean7.49707855614652
Quadratic Mean8.79457390539842
Winsorized Mean ( 1 / 21 )0.01384615384592201.065124065612980.0129995690576698
Winsorized Mean ( 2 / 21 )0.02923076923053741.039313041211900.0281250865441393
Winsorized Mean ( 3 / 21 )0.0246153846151531.038423539190810.0237045710985467
Winsorized Mean ( 4 / 21 )0.1353846153843840.9927405510883230.136374619970912
Winsorized Mean ( 5 / 21 )0.2584615384613060.935070204306740.276408698802385
Winsorized Mean ( 6 / 21 )0.3876923076920750.886330402750710.437412850206738
Winsorized Mean ( 7 / 21 )0.4199999999997670.8730189746950030.481089199861317
Winsorized Mean ( 8 / 21 )0.432307692307460.8497592767380460.508741362573823
Winsorized Mean ( 9 / 21 )0.4323076923074620.840440853601470.51438205372208
Winsorized Mean ( 10 / 21 )0.4784615384613060.80268332345420.596077586864935
Winsorized Mean ( 11 / 21 )0.4784615384613080.7972624667124390.600130519669732
Winsorized Mean ( 12 / 21 )0.4415384615382310.7854295832075050.562161740502686
Winsorized Mean ( 13 / 21 )0.4215384615382290.782236448234640.538888800808964
Winsorized Mean ( 14 / 21 )0.4861538461536160.7654763184337190.635099786167599
Winsorized Mean ( 15 / 21 )0.4399999999997690.7581611200949760.580351574800683
Winsorized Mean ( 16 / 21 )0.4153846153843820.7013929504963090.592228101366651
Winsorized Mean ( 17 / 21 )0.3369230769228450.689467732702460.488671276322432
Winsorized Mean ( 18 / 21 )0.2815384615382280.6398870208156160.43998151607978
Winsorized Mean ( 19 / 21 )0.2815384615382280.605562052483710.464920911710864
Winsorized Mean ( 20 / 21 )0.4661538461536160.5435594527723950.857594958152276
Winsorized Mean ( 21 / 21 )0.5953846153843820.5165502747947511.15261697541630
Trimmed Mean ( 1 / 21 )0.08759462759439571.030830347136430.0849748242644652
Trimmed Mean ( 2 / 21 )0.1661790668345730.9891367758850260.168004133387806
Trimmed Mean ( 3 / 21 )0.2416166883961170.9554157447737180.252891675396601
Trimmed Mean ( 4 / 21 )0.3241025641023320.9142780453416880.354490152917548
Trimmed Mean ( 5 / 21 )0.3798601398599080.8818318579938470.430762550044499
Trimmed Mean ( 6 / 21 )0.40963715529730.8611433677862510.475689845176835
Trimmed Mean ( 7 / 21 )0.4142986425337050.849385421350230.48776283665796
Trimmed Mean ( 8 / 21 )0.4132182103608360.8374689826022030.493413151943699
Trimmed Mean ( 9 / 21 )0.4099181669392120.8274580084584360.495394524856789
Trimmed Mean ( 10 / 21 )0.4063247863245540.8159641725371260.497968905989027
Trimmed Mean ( 11 / 21 )0.3954203935596970.8090158732368560.488767163464454
Trimmed Mean ( 12 / 21 )0.3834521575982670.7997971560210120.479436760573069
Trimmed Mean ( 13 / 21 )0.3753846153843830.789014815259020.475763709533326
Trimmed Mean ( 14 / 21 )0.3691476091473770.7738998307113150.476996627338815
Trimmed Mean ( 15 / 21 )0.3536263736261410.7562410992799160.467610625715609
Trimmed Mean ( 16 / 21 )0.342284382284150.7324217976163110.467332325987737
Trimmed Mean ( 17 / 21 )0.3327047146399660.7138834306449670.466049077983754
Trimmed Mean ( 18 / 21 )0.3321485411138260.6890329705585440.482050286860119
Trimmed Mean ( 19 / 21 )0.3389173789171470.6669736551811540.508142077703346
Trimmed Mean ( 20 / 21 )0.3467692307689990.6434562922219350.538916527759114
Trimmed Mean ( 21 / 21 )0.3298996655516070.6276481961417170.525612385376981
Median0.0907692307689985
Midrange-2.75923076923100
Midmean - Weighted Average at Xnp0.125144230768998
Midmean - Weighted Average at X(n+1)p0.34228438228415
Midmean - Empirical Distribution Function0.34228438228415
Midmean - Empirical Distribution Function - Averaging0.34228438228415
Midmean - Empirical Distribution Function - Interpolation0.34228438228415
Midmean - Closest Observation-0.0778021978024299
Midmean - True Basic - Statistics Graphics Toolkit0.34228438228415
Midmean - MS Excel (old versions)0.34228438228415
Number of observations65


Figures (Output of Computation)

Input Parameters & R Code

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')