Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 17 Dec 2011 12:04:51 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/17/t1324141500qxo7w76gtv7tjcc.htm/, Retrieved Tue, 30 Apr 2024 01:25:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=156488, Retrieved Tue, 30 Apr 2024 01:25:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact100
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Factor Analysis] [Sleep in Mammals ...] [2010-03-21 11:39:53] [b98453cac15ba1066b407e146608df68]
- RMPD  [Testing Mean with unknown Variance - Critical Value] [Hypothesis Test a...] [2010-10-19 11:45:26] [b98453cac15ba1066b407e146608df68]
- R PD    [Testing Mean with unknown Variance - Critical Value] [Q4] [2011-10-20 17:39:37] [0f81819b439c6e991d1a2004e9982756]
- RMP       [Variability] [Var Q4] [2011-10-23 12:56:17] [0f81819b439c6e991d1a2004e9982756]
- R PD        [Variability] [D1 H1] [2011-12-17 17:03:19] [0f81819b439c6e991d1a2004e9982756]
- RM D            [Central Tendency] [D1 H2] [2011-12-17 17:04:51] [cdf03f2f7d2bbe3f2da091606ae8e03f] [Current]
Feedback Forum

Post a new message
Dataseries X:
8,0
8,0
8,0
8,0
7,9
7,9
7,9
8,0
7,9
7,5
7,2
7,0
6,9
7,1
7,1
7,2
7,1
6,9
6,8
6,7
6,7
6,9
7,3
7,4
7,3
7,1
7,0
7,1
7,5
7,7
7,8
7,7
7,7
7,8
8,0
8,1
8,1
8,0
8,1
8,2
8,3
8,4
8,5
8,5
8,5
8,5
8,5
8,3
8,2
8,1
7,9
7,6
7,3
7,1
7,0
7,0
7,0
7,0
6,9
6,8
6,7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156488&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156488&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156488&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.585245901639340.072119969327593105.175390011394
Geometric Mean7.56464537144303
Harmonic Mean7.54406341822116
Quadratic Mean7.6057894256208
Winsorized Mean ( 1 / 20 )7.585245901639340.072119969327593105.175390011394
Winsorized Mean ( 2 / 20 )7.585245901639340.072119969327593105.175390011394
Winsorized Mean ( 3 / 20 )7.590163934426230.0711615155876097106.661077574742
Winsorized Mean ( 4 / 20 )7.590163934426230.0711615155876097106.661077574742
Winsorized Mean ( 5 / 20 )7.590163934426230.0680206059277647111.586244063846
Winsorized Mean ( 6 / 20 )7.580327868852460.0661518237249542114.589854701057
Winsorized Mean ( 7 / 20 )7.580327868852460.0661518237249542114.589854701057
Winsorized Mean ( 8 / 20 )7.56721311475410.0638783556848659118.462866390703
Winsorized Mean ( 9 / 20 )7.581967213114750.0614269389970124123.430653340605
Winsorized Mean ( 10 / 20 )7.56557377049180.058808071910809128.648560047439
Winsorized Mean ( 11 / 20 )7.56557377049180.058808071910809128.648560047439
Winsorized Mean ( 12 / 20 )7.56557377049180.058808071910809128.648560047439
Winsorized Mean ( 13 / 20 )7.56557377049180.058808071910809128.648560047439
Winsorized Mean ( 14 / 20 )7.542622950819670.0554888368822361135.930456910232
Winsorized Mean ( 15 / 20 )7.56721311475410.0516250305428883146.58031259599
Winsorized Mean ( 16 / 20 )7.56721311475410.0516250305428883146.58031259599
Winsorized Mean ( 17 / 20 )7.56721311475410.0516250305428883146.58031259599
Winsorized Mean ( 18 / 20 )7.56721311475410.0516250305428883146.58031259599
Winsorized Mean ( 19 / 20 )7.56721311475410.0516250305428883146.58031259599
Winsorized Mean ( 20 / 20 )7.56721311475410.0516250305428883146.58031259599
Trimmed Mean ( 1 / 20 )7.584745762711860.0713407361816269106.317178216409
Trimmed Mean ( 2 / 20 )7.584210526315790.0703459707412239107.813005441566
Trimmed Mean ( 3 / 20 )7.583636363636360.0690855925652507109.771604788273
Trimmed Mean ( 4 / 20 )7.58113207547170.067939645149002111.586277185362
Trimmed Mean ( 5 / 20 )7.578431372549020.0664691422134344114.014279712147
Trimmed Mean ( 6 / 20 )7.575510204081630.0656295139195816115.428406392956
Trimmed Mean ( 7 / 20 )7.574468085106380.0650530335920048116.435278523849
Trimmed Mean ( 8 / 20 )7.573333333333330.0642281287696639117.913030916609
Trimmed Mean ( 9 / 20 )7.574418604651160.0636724925226828118.959040310113
Trimmed Mean ( 10 / 20 )7.573170731707320.0634404262745865119.374524674987
Trimmed Mean ( 11 / 20 )7.574358974358970.0635985584417584119.096394005461
Trimmed Mean ( 12 / 20 )7.575675675675680.0636013066476497119.111950288141
Trimmed Mean ( 13 / 20 )7.577142857142860.0633896466224538119.532814282307
Trimmed Mean ( 14 / 20 )7.578787878787880.0628787878787879120.530120481928
Trimmed Mean ( 15 / 20 )7.583870967741940.0627500202105179120.85846255187
Trimmed Mean ( 16 / 20 )7.586206896551720.0633086383748902119.828937903056
Trimmed Mean ( 17 / 20 )7.588888888888890.0636795157153962119.17315644808
Trimmed Mean ( 18 / 20 )7.5920.0637495098020369119.091111815222
Trimmed Mean ( 19 / 20 )7.595652173913040.0633324439236518119.933034371289
Trimmed Mean ( 20 / 20 )7.60.0621059003408119122.371625856711
Median7.7
Midrange7.6
Midmean - Weighted Average at Xnp7.596875
Midmean - Weighted Average at X(n+1)p7.596875
Midmean - Empirical Distribution Function7.596875
Midmean - Empirical Distribution Function - Averaging7.596875
Midmean - Empirical Distribution Function - Interpolation7.596875
Midmean - Closest Observation7.50263157894737
Midmean - True Basic - Statistics Graphics Toolkit7.596875
Midmean - MS Excel (old versions)7.596875
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.58524590163934 & 0.072119969327593 & 105.175390011394 \tabularnewline
Geometric Mean & 7.56464537144303 &  &  \tabularnewline
Harmonic Mean & 7.54406341822116 &  &  \tabularnewline
Quadratic Mean & 7.6057894256208 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 7.58524590163934 & 0.072119969327593 & 105.175390011394 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 7.58524590163934 & 0.072119969327593 & 105.175390011394 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 7.59016393442623 & 0.0711615155876097 & 106.661077574742 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 7.59016393442623 & 0.0711615155876097 & 106.661077574742 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 7.59016393442623 & 0.0680206059277647 & 111.586244063846 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 7.58032786885246 & 0.0661518237249542 & 114.589854701057 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 7.58032786885246 & 0.0661518237249542 & 114.589854701057 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 7.5672131147541 & 0.0638783556848659 & 118.462866390703 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 7.58196721311475 & 0.0614269389970124 & 123.430653340605 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 7.5655737704918 & 0.058808071910809 & 128.648560047439 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 7.5655737704918 & 0.058808071910809 & 128.648560047439 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 7.5655737704918 & 0.058808071910809 & 128.648560047439 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 7.5655737704918 & 0.058808071910809 & 128.648560047439 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 7.54262295081967 & 0.0554888368822361 & 135.930456910232 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 7.5672131147541 & 0.0516250305428883 & 146.58031259599 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 7.5672131147541 & 0.0516250305428883 & 146.58031259599 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 7.5672131147541 & 0.0516250305428883 & 146.58031259599 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 7.5672131147541 & 0.0516250305428883 & 146.58031259599 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 7.5672131147541 & 0.0516250305428883 & 146.58031259599 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 7.5672131147541 & 0.0516250305428883 & 146.58031259599 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 7.58474576271186 & 0.0713407361816269 & 106.317178216409 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 7.58421052631579 & 0.0703459707412239 & 107.813005441566 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 7.58363636363636 & 0.0690855925652507 & 109.771604788273 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 7.5811320754717 & 0.067939645149002 & 111.586277185362 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 7.57843137254902 & 0.0664691422134344 & 114.014279712147 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 7.57551020408163 & 0.0656295139195816 & 115.428406392956 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 7.57446808510638 & 0.0650530335920048 & 116.435278523849 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 7.57333333333333 & 0.0642281287696639 & 117.913030916609 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 7.57441860465116 & 0.0636724925226828 & 118.959040310113 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 7.57317073170732 & 0.0634404262745865 & 119.374524674987 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 7.57435897435897 & 0.0635985584417584 & 119.096394005461 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 7.57567567567568 & 0.0636013066476497 & 119.111950288141 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 7.57714285714286 & 0.0633896466224538 & 119.532814282307 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 7.57878787878788 & 0.0628787878787879 & 120.530120481928 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 7.58387096774194 & 0.0627500202105179 & 120.85846255187 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 7.58620689655172 & 0.0633086383748902 & 119.828937903056 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 7.58888888888889 & 0.0636795157153962 & 119.17315644808 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 7.592 & 0.0637495098020369 & 119.091111815222 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 7.59565217391304 & 0.0633324439236518 & 119.933034371289 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 7.6 & 0.0621059003408119 & 122.371625856711 \tabularnewline
Median & 7.7 &  &  \tabularnewline
Midrange & 7.6 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.596875 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.596875 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.596875 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.596875 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.596875 &  &  \tabularnewline
Midmean - Closest Observation & 7.50263157894737 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.596875 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.596875 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156488&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]7.58524590163934[/C][C]0.072119969327593[/C][C]105.175390011394[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.56464537144303[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.54406341822116[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.6057894256208[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]7.58524590163934[/C][C]0.072119969327593[/C][C]105.175390011394[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]7.58524590163934[/C][C]0.072119969327593[/C][C]105.175390011394[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]7.59016393442623[/C][C]0.0711615155876097[/C][C]106.661077574742[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]7.59016393442623[/C][C]0.0711615155876097[/C][C]106.661077574742[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]7.59016393442623[/C][C]0.0680206059277647[/C][C]111.586244063846[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]7.58032786885246[/C][C]0.0661518237249542[/C][C]114.589854701057[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]7.58032786885246[/C][C]0.0661518237249542[/C][C]114.589854701057[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]7.5672131147541[/C][C]0.0638783556848659[/C][C]118.462866390703[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]7.58196721311475[/C][C]0.0614269389970124[/C][C]123.430653340605[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]7.5655737704918[/C][C]0.058808071910809[/C][C]128.648560047439[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]7.5655737704918[/C][C]0.058808071910809[/C][C]128.648560047439[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]7.5655737704918[/C][C]0.058808071910809[/C][C]128.648560047439[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]7.5655737704918[/C][C]0.058808071910809[/C][C]128.648560047439[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]7.54262295081967[/C][C]0.0554888368822361[/C][C]135.930456910232[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]7.5672131147541[/C][C]0.0516250305428883[/C][C]146.58031259599[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]7.5672131147541[/C][C]0.0516250305428883[/C][C]146.58031259599[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]7.5672131147541[/C][C]0.0516250305428883[/C][C]146.58031259599[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]7.5672131147541[/C][C]0.0516250305428883[/C][C]146.58031259599[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]7.5672131147541[/C][C]0.0516250305428883[/C][C]146.58031259599[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]7.5672131147541[/C][C]0.0516250305428883[/C][C]146.58031259599[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]7.58474576271186[/C][C]0.0713407361816269[/C][C]106.317178216409[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]7.58421052631579[/C][C]0.0703459707412239[/C][C]107.813005441566[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]7.58363636363636[/C][C]0.0690855925652507[/C][C]109.771604788273[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]7.5811320754717[/C][C]0.067939645149002[/C][C]111.586277185362[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]7.57843137254902[/C][C]0.0664691422134344[/C][C]114.014279712147[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]7.57551020408163[/C][C]0.0656295139195816[/C][C]115.428406392956[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]7.57446808510638[/C][C]0.0650530335920048[/C][C]116.435278523849[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]7.57333333333333[/C][C]0.0642281287696639[/C][C]117.913030916609[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]7.57441860465116[/C][C]0.0636724925226828[/C][C]118.959040310113[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]7.57317073170732[/C][C]0.0634404262745865[/C][C]119.374524674987[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]7.57435897435897[/C][C]0.0635985584417584[/C][C]119.096394005461[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]7.57567567567568[/C][C]0.0636013066476497[/C][C]119.111950288141[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]7.57714285714286[/C][C]0.0633896466224538[/C][C]119.532814282307[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]7.57878787878788[/C][C]0.0628787878787879[/C][C]120.530120481928[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]7.58387096774194[/C][C]0.0627500202105179[/C][C]120.85846255187[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]7.58620689655172[/C][C]0.0633086383748902[/C][C]119.828937903056[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]7.58888888888889[/C][C]0.0636795157153962[/C][C]119.17315644808[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]7.592[/C][C]0.0637495098020369[/C][C]119.091111815222[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]7.59565217391304[/C][C]0.0633324439236518[/C][C]119.933034371289[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]7.6[/C][C]0.0621059003408119[/C][C]122.371625856711[/C][/ROW]
[ROW][C]Median[/C][C]7.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.596875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.596875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.596875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.596875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.596875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.50263157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.596875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.596875[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156488&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156488&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 Mean7.585245901639340.072119969327593105.175390011394
Geometric Mean7.56464537144303
Harmonic Mean7.54406341822116
Quadratic Mean7.6057894256208
Winsorized Mean ( 1 / 20 )7.585245901639340.072119969327593105.175390011394
Winsorized Mean ( 2 / 20 )7.585245901639340.072119969327593105.175390011394
Winsorized Mean ( 3 / 20 )7.590163934426230.0711615155876097106.661077574742
Winsorized Mean ( 4 / 20 )7.590163934426230.0711615155876097106.661077574742
Winsorized Mean ( 5 / 20 )7.590163934426230.0680206059277647111.586244063846
Winsorized Mean ( 6 / 20 )7.580327868852460.0661518237249542114.589854701057
Winsorized Mean ( 7 / 20 )7.580327868852460.0661518237249542114.589854701057
Winsorized Mean ( 8 / 20 )7.56721311475410.0638783556848659118.462866390703
Winsorized Mean ( 9 / 20 )7.581967213114750.0614269389970124123.430653340605
Winsorized Mean ( 10 / 20 )7.56557377049180.058808071910809128.648560047439
Winsorized Mean ( 11 / 20 )7.56557377049180.058808071910809128.648560047439
Winsorized Mean ( 12 / 20 )7.56557377049180.058808071910809128.648560047439
Winsorized Mean ( 13 / 20 )7.56557377049180.058808071910809128.648560047439
Winsorized Mean ( 14 / 20 )7.542622950819670.0554888368822361135.930456910232
Winsorized Mean ( 15 / 20 )7.56721311475410.0516250305428883146.58031259599
Winsorized Mean ( 16 / 20 )7.56721311475410.0516250305428883146.58031259599
Winsorized Mean ( 17 / 20 )7.56721311475410.0516250305428883146.58031259599
Winsorized Mean ( 18 / 20 )7.56721311475410.0516250305428883146.58031259599
Winsorized Mean ( 19 / 20 )7.56721311475410.0516250305428883146.58031259599
Winsorized Mean ( 20 / 20 )7.56721311475410.0516250305428883146.58031259599
Trimmed Mean ( 1 / 20 )7.584745762711860.0713407361816269106.317178216409
Trimmed Mean ( 2 / 20 )7.584210526315790.0703459707412239107.813005441566
Trimmed Mean ( 3 / 20 )7.583636363636360.0690855925652507109.771604788273
Trimmed Mean ( 4 / 20 )7.58113207547170.067939645149002111.586277185362
Trimmed Mean ( 5 / 20 )7.578431372549020.0664691422134344114.014279712147
Trimmed Mean ( 6 / 20 )7.575510204081630.0656295139195816115.428406392956
Trimmed Mean ( 7 / 20 )7.574468085106380.0650530335920048116.435278523849
Trimmed Mean ( 8 / 20 )7.573333333333330.0642281287696639117.913030916609
Trimmed Mean ( 9 / 20 )7.574418604651160.0636724925226828118.959040310113
Trimmed Mean ( 10 / 20 )7.573170731707320.0634404262745865119.374524674987
Trimmed Mean ( 11 / 20 )7.574358974358970.0635985584417584119.096394005461
Trimmed Mean ( 12 / 20 )7.575675675675680.0636013066476497119.111950288141
Trimmed Mean ( 13 / 20 )7.577142857142860.0633896466224538119.532814282307
Trimmed Mean ( 14 / 20 )7.578787878787880.0628787878787879120.530120481928
Trimmed Mean ( 15 / 20 )7.583870967741940.0627500202105179120.85846255187
Trimmed Mean ( 16 / 20 )7.586206896551720.0633086383748902119.828937903056
Trimmed Mean ( 17 / 20 )7.588888888888890.0636795157153962119.17315644808
Trimmed Mean ( 18 / 20 )7.5920.0637495098020369119.091111815222
Trimmed Mean ( 19 / 20 )7.595652173913040.0633324439236518119.933034371289
Trimmed Mean ( 20 / 20 )7.60.0621059003408119122.371625856711
Median7.7
Midrange7.6
Midmean - Weighted Average at Xnp7.596875
Midmean - Weighted Average at X(n+1)p7.596875
Midmean - Empirical Distribution Function7.596875
Midmean - Empirical Distribution Function - Averaging7.596875
Midmean - Empirical Distribution Function - Interpolation7.596875
Midmean - Closest Observation7.50263157894737
Midmean - True Basic - Statistics Graphics Toolkit7.596875
Midmean - MS Excel (old versions)7.596875
Number of observations61



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')