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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 computationMon, 03 Nov 2008 04:19:18 -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/03/t1225711214yx7dejwflh5jd1f.htm/, Retrieved Sat, 18 May 2024 18:53:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=20826, Retrieved Sat, 18 May 2024 18:53:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact163
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Explorative Data Analysis] [Investigating dis...] [2007-10-22 19:45:25] [b9964c45117f7aac638ab9056d451faa]
F    D  [Univariate Explorative Data Analysis] [q7 werkloosheid m...] [2008-10-27 10:19:49] [e43247bc0ab243a5af99ac7f55ba0b41]
- RMP       [Central Tendency] [q7] [2008-11-03 11:19:18] [f24298b2e4c2a19d76cf4460ec5d2246] [Current]
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Dataseries X:
7.8
7.6
7.5
7.6
7.5
7.3
7.6
7.5
7.6
7.9
7.9
8.1
8.2
8.0
7.5
6.8
6.5
6.6
7.6
8.0
8.0
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
7.0
7.1
7.2
7.1
6.9
7.0
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
6.4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=20826&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=20826&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=20826&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' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.257352941176470.075202862212455196.5036798822067
Geometric Mean7.23058214429241
Harmonic Mean7.20318276213011
Quadratic Mean7.28341185402103
Winsorized Mean ( 1 / 22 )7.257352941176470.075202862212455196.5036798822067
Winsorized Mean ( 2 / 22 )7.266176470588230.073050017565899.4685109287374
Winsorized Mean ( 3 / 22 )7.266176470588230.071316797289154101.885905519951
Winsorized Mean ( 4 / 22 )7.266176470588230.071316797289154101.885905519951
Winsorized Mean ( 5 / 22 )7.27352941176470.0698869539668326104.075639284789
Winsorized Mean ( 6 / 22 )7.264705882352940.0683996386056239106.209711490429
Winsorized Mean ( 7 / 22 )7.264705882352940.0683996386056239106.209711490429
Winsorized Mean ( 8 / 22 )7.264705882352940.0683996386056239106.209711490429
Winsorized Mean ( 9 / 22 )7.264705882352940.06392093124818113.651439997752
Winsorized Mean ( 10 / 22 )7.264705882352940.06392093124818113.651439997752
Winsorized Mean ( 11 / 22 )7.264705882352940.06392093124818113.651439997752
Winsorized Mean ( 12 / 22 )7.282352941176470.0608666260389628119.644432673413
Winsorized Mean ( 13 / 22 )7.282352941176470.0608666260389628119.644432673413
Winsorized Mean ( 14 / 22 )7.282352941176470.0544725356478474133.688524952377
Winsorized Mean ( 15 / 22 )7.282352941176470.0544725356478474133.688524952377
Winsorized Mean ( 16 / 22 )7.258823529411760.0512887166812858141.528663595133
Winsorized Mean ( 17 / 22 )7.283823529411760.0473443243568268153.847871489616
Winsorized Mean ( 18 / 22 )7.283823529411760.0473443243568268153.847871489616
Winsorized Mean ( 19 / 22 )7.283823529411770.0473443243568268153.847871489616
Winsorized Mean ( 20 / 22 )7.254411764705880.0436701773267505166.118211758718
Winsorized Mean ( 21 / 22 )7.285294117647060.0389876675016396186.861502226074
Winsorized Mean ( 22 / 22 )7.285294117647060.0389876675016396186.861502226074
Trimmed Mean ( 1 / 22 )7.263636363636360.073273010694298899.131130204829
Trimmed Mean ( 2 / 22 )7.27031250.0709445795712098102.478759391371
Trimmed Mean ( 3 / 22 )7.272580645161290.0695292532220475104.597422065439
Trimmed Mean ( 4 / 22 )7.2750.0685864129780654106.070571183342
Trimmed Mean ( 5 / 22 )7.277586206896550.0674056039759158107.967079554644
Trimmed Mean ( 6 / 22 )7.278571428571430.066387013952439109.638481914339
Trimmed Mean ( 7 / 22 )7.281481481481480.0655074304081054111.155046627818
Trimmed Mean ( 8 / 22 )7.284615384615380.0643674767388322113.172299951610
Trimmed Mean ( 9 / 22 )7.2880.0628986875694492115.868872334625
Trimmed Mean ( 10 / 22 )7.291666666666670.0620878847872292117.441054589872
Trimmed Mean ( 11 / 22 )7.295652173913040.0609867746603299119.626791456782
Trimmed Mean ( 12 / 22 )7.30.0595082029273681122.672163515170
Trimmed Mean ( 13 / 22 )7.302380952380950.0582844256801525125.288717649106
Trimmed Mean ( 14 / 22 )7.3050.0566081900389615129.044931395479
Trimmed Mean ( 15 / 22 )7.30789473684210.055862763529745130.818711339816
Trimmed Mean ( 16 / 22 )7.311111111111110.0547400462471428133.560557806301
Trimmed Mean ( 17 / 22 )7.317647058823530.0538153223241315135.977018120399
Trimmed Mean ( 18 / 22 )7.3218750.0534560369188038136.970030365727
Trimmed Mean ( 19 / 22 )7.326666666666670.0527264319706207138.956238699199
Trimmed Mean ( 20 / 22 )7.332142857142860.0514482252275308142.514981317943
Trimmed Mean ( 21 / 22 )7.342307692307690.0502832215243207146.019039149200
Trimmed Mean ( 22 / 22 )7.350.05147
Median7.5
Midrange7.05
Midmean - Weighted Average at Xnp7.27894736842105
Midmean - Weighted Average at X(n+1)p7.32857142857143
Midmean - Empirical Distribution Function7.27894736842105
Midmean - Empirical Distribution Function - Averaging7.32857142857143
Midmean - Empirical Distribution Function - Interpolation7.32857142857143
Midmean - Closest Observation7.27894736842105
Midmean - True Basic - Statistics Graphics Toolkit7.32857142857143
Midmean - MS Excel (old versions)7.27894736842105
Number of observations68

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.25735294117647 & 0.0752028622124551 & 96.5036798822067 \tabularnewline
Geometric Mean & 7.23058214429241 &  &  \tabularnewline
Harmonic Mean & 7.20318276213011 &  &  \tabularnewline
Quadratic Mean & 7.28341185402103 &  &  \tabularnewline
Winsorized Mean ( 1 / 22 ) & 7.25735294117647 & 0.0752028622124551 & 96.5036798822067 \tabularnewline
Winsorized Mean ( 2 / 22 ) & 7.26617647058823 & 0.0730500175658 & 99.4685109287374 \tabularnewline
Winsorized Mean ( 3 / 22 ) & 7.26617647058823 & 0.071316797289154 & 101.885905519951 \tabularnewline
Winsorized Mean ( 4 / 22 ) & 7.26617647058823 & 0.071316797289154 & 101.885905519951 \tabularnewline
Winsorized Mean ( 5 / 22 ) & 7.2735294117647 & 0.0698869539668326 & 104.075639284789 \tabularnewline
Winsorized Mean ( 6 / 22 ) & 7.26470588235294 & 0.0683996386056239 & 106.209711490429 \tabularnewline
Winsorized Mean ( 7 / 22 ) & 7.26470588235294 & 0.0683996386056239 & 106.209711490429 \tabularnewline
Winsorized Mean ( 8 / 22 ) & 7.26470588235294 & 0.0683996386056239 & 106.209711490429 \tabularnewline
Winsorized Mean ( 9 / 22 ) & 7.26470588235294 & 0.06392093124818 & 113.651439997752 \tabularnewline
Winsorized Mean ( 10 / 22 ) & 7.26470588235294 & 0.06392093124818 & 113.651439997752 \tabularnewline
Winsorized Mean ( 11 / 22 ) & 7.26470588235294 & 0.06392093124818 & 113.651439997752 \tabularnewline
Winsorized Mean ( 12 / 22 ) & 7.28235294117647 & 0.0608666260389628 & 119.644432673413 \tabularnewline
Winsorized Mean ( 13 / 22 ) & 7.28235294117647 & 0.0608666260389628 & 119.644432673413 \tabularnewline
Winsorized Mean ( 14 / 22 ) & 7.28235294117647 & 0.0544725356478474 & 133.688524952377 \tabularnewline
Winsorized Mean ( 15 / 22 ) & 7.28235294117647 & 0.0544725356478474 & 133.688524952377 \tabularnewline
Winsorized Mean ( 16 / 22 ) & 7.25882352941176 & 0.0512887166812858 & 141.528663595133 \tabularnewline
Winsorized Mean ( 17 / 22 ) & 7.28382352941176 & 0.0473443243568268 & 153.847871489616 \tabularnewline
Winsorized Mean ( 18 / 22 ) & 7.28382352941176 & 0.0473443243568268 & 153.847871489616 \tabularnewline
Winsorized Mean ( 19 / 22 ) & 7.28382352941177 & 0.0473443243568268 & 153.847871489616 \tabularnewline
Winsorized Mean ( 20 / 22 ) & 7.25441176470588 & 0.0436701773267505 & 166.118211758718 \tabularnewline
Winsorized Mean ( 21 / 22 ) & 7.28529411764706 & 0.0389876675016396 & 186.861502226074 \tabularnewline
Winsorized Mean ( 22 / 22 ) & 7.28529411764706 & 0.0389876675016396 & 186.861502226074 \tabularnewline
Trimmed Mean ( 1 / 22 ) & 7.26363636363636 & 0.0732730106942988 & 99.131130204829 \tabularnewline
Trimmed Mean ( 2 / 22 ) & 7.2703125 & 0.0709445795712098 & 102.478759391371 \tabularnewline
Trimmed Mean ( 3 / 22 ) & 7.27258064516129 & 0.0695292532220475 & 104.597422065439 \tabularnewline
Trimmed Mean ( 4 / 22 ) & 7.275 & 0.0685864129780654 & 106.070571183342 \tabularnewline
Trimmed Mean ( 5 / 22 ) & 7.27758620689655 & 0.0674056039759158 & 107.967079554644 \tabularnewline
Trimmed Mean ( 6 / 22 ) & 7.27857142857143 & 0.066387013952439 & 109.638481914339 \tabularnewline
Trimmed Mean ( 7 / 22 ) & 7.28148148148148 & 0.0655074304081054 & 111.155046627818 \tabularnewline
Trimmed Mean ( 8 / 22 ) & 7.28461538461538 & 0.0643674767388322 & 113.172299951610 \tabularnewline
Trimmed Mean ( 9 / 22 ) & 7.288 & 0.0628986875694492 & 115.868872334625 \tabularnewline
Trimmed Mean ( 10 / 22 ) & 7.29166666666667 & 0.0620878847872292 & 117.441054589872 \tabularnewline
Trimmed Mean ( 11 / 22 ) & 7.29565217391304 & 0.0609867746603299 & 119.626791456782 \tabularnewline
Trimmed Mean ( 12 / 22 ) & 7.3 & 0.0595082029273681 & 122.672163515170 \tabularnewline
Trimmed Mean ( 13 / 22 ) & 7.30238095238095 & 0.0582844256801525 & 125.288717649106 \tabularnewline
Trimmed Mean ( 14 / 22 ) & 7.305 & 0.0566081900389615 & 129.044931395479 \tabularnewline
Trimmed Mean ( 15 / 22 ) & 7.3078947368421 & 0.055862763529745 & 130.818711339816 \tabularnewline
Trimmed Mean ( 16 / 22 ) & 7.31111111111111 & 0.0547400462471428 & 133.560557806301 \tabularnewline
Trimmed Mean ( 17 / 22 ) & 7.31764705882353 & 0.0538153223241315 & 135.977018120399 \tabularnewline
Trimmed Mean ( 18 / 22 ) & 7.321875 & 0.0534560369188038 & 136.970030365727 \tabularnewline
Trimmed Mean ( 19 / 22 ) & 7.32666666666667 & 0.0527264319706207 & 138.956238699199 \tabularnewline
Trimmed Mean ( 20 / 22 ) & 7.33214285714286 & 0.0514482252275308 & 142.514981317943 \tabularnewline
Trimmed Mean ( 21 / 22 ) & 7.34230769230769 & 0.0502832215243207 & 146.019039149200 \tabularnewline
Trimmed Mean ( 22 / 22 ) & 7.35 & 0.05 & 147 \tabularnewline
Median & 7.5 &  &  \tabularnewline
Midrange & 7.05 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.27894736842105 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.32857142857143 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.27894736842105 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.32857142857143 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.32857142857143 &  &  \tabularnewline
Midmean - Closest Observation & 7.27894736842105 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.32857142857143 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.27894736842105 &  &  \tabularnewline
Number of observations & 68 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=20826&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]7.25735294117647[/C][C]0.0752028622124551[/C][C]96.5036798822067[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.23058214429241[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.20318276213011[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.28341185402103[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 22 )[/C][C]7.25735294117647[/C][C]0.0752028622124551[/C][C]96.5036798822067[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 22 )[/C][C]7.26617647058823[/C][C]0.0730500175658[/C][C]99.4685109287374[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 22 )[/C][C]7.26617647058823[/C][C]0.071316797289154[/C][C]101.885905519951[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 22 )[/C][C]7.26617647058823[/C][C]0.071316797289154[/C][C]101.885905519951[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 22 )[/C][C]7.2735294117647[/C][C]0.0698869539668326[/C][C]104.075639284789[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 22 )[/C][C]7.26470588235294[/C][C]0.0683996386056239[/C][C]106.209711490429[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 22 )[/C][C]7.26470588235294[/C][C]0.0683996386056239[/C][C]106.209711490429[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 22 )[/C][C]7.26470588235294[/C][C]0.0683996386056239[/C][C]106.209711490429[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 22 )[/C][C]7.26470588235294[/C][C]0.06392093124818[/C][C]113.651439997752[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 22 )[/C][C]7.26470588235294[/C][C]0.06392093124818[/C][C]113.651439997752[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 22 )[/C][C]7.26470588235294[/C][C]0.06392093124818[/C][C]113.651439997752[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 22 )[/C][C]7.28235294117647[/C][C]0.0608666260389628[/C][C]119.644432673413[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 22 )[/C][C]7.28235294117647[/C][C]0.0608666260389628[/C][C]119.644432673413[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 22 )[/C][C]7.28235294117647[/C][C]0.0544725356478474[/C][C]133.688524952377[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 22 )[/C][C]7.28235294117647[/C][C]0.0544725356478474[/C][C]133.688524952377[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 22 )[/C][C]7.25882352941176[/C][C]0.0512887166812858[/C][C]141.528663595133[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 22 )[/C][C]7.28382352941176[/C][C]0.0473443243568268[/C][C]153.847871489616[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 22 )[/C][C]7.28382352941176[/C][C]0.0473443243568268[/C][C]153.847871489616[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 22 )[/C][C]7.28382352941177[/C][C]0.0473443243568268[/C][C]153.847871489616[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 22 )[/C][C]7.25441176470588[/C][C]0.0436701773267505[/C][C]166.118211758718[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 22 )[/C][C]7.28529411764706[/C][C]0.0389876675016396[/C][C]186.861502226074[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 22 )[/C][C]7.28529411764706[/C][C]0.0389876675016396[/C][C]186.861502226074[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 22 )[/C][C]7.26363636363636[/C][C]0.0732730106942988[/C][C]99.131130204829[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 22 )[/C][C]7.2703125[/C][C]0.0709445795712098[/C][C]102.478759391371[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 22 )[/C][C]7.27258064516129[/C][C]0.0695292532220475[/C][C]104.597422065439[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 22 )[/C][C]7.275[/C][C]0.0685864129780654[/C][C]106.070571183342[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 22 )[/C][C]7.27758620689655[/C][C]0.0674056039759158[/C][C]107.967079554644[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 22 )[/C][C]7.27857142857143[/C][C]0.066387013952439[/C][C]109.638481914339[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 22 )[/C][C]7.28148148148148[/C][C]0.0655074304081054[/C][C]111.155046627818[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 22 )[/C][C]7.28461538461538[/C][C]0.0643674767388322[/C][C]113.172299951610[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 22 )[/C][C]7.288[/C][C]0.0628986875694492[/C][C]115.868872334625[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 22 )[/C][C]7.29166666666667[/C][C]0.0620878847872292[/C][C]117.441054589872[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 22 )[/C][C]7.29565217391304[/C][C]0.0609867746603299[/C][C]119.626791456782[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 22 )[/C][C]7.3[/C][C]0.0595082029273681[/C][C]122.672163515170[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 22 )[/C][C]7.30238095238095[/C][C]0.0582844256801525[/C][C]125.288717649106[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 22 )[/C][C]7.305[/C][C]0.0566081900389615[/C][C]129.044931395479[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 22 )[/C][C]7.3078947368421[/C][C]0.055862763529745[/C][C]130.818711339816[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 22 )[/C][C]7.31111111111111[/C][C]0.0547400462471428[/C][C]133.560557806301[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 22 )[/C][C]7.31764705882353[/C][C]0.0538153223241315[/C][C]135.977018120399[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 22 )[/C][C]7.321875[/C][C]0.0534560369188038[/C][C]136.970030365727[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 22 )[/C][C]7.32666666666667[/C][C]0.0527264319706207[/C][C]138.956238699199[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 22 )[/C][C]7.33214285714286[/C][C]0.0514482252275308[/C][C]142.514981317943[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 22 )[/C][C]7.34230769230769[/C][C]0.0502832215243207[/C][C]146.019039149200[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 22 )[/C][C]7.35[/C][C]0.05[/C][C]147[/C][/ROW]
[ROW][C]Median[/C][C]7.5[/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]7.27894736842105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.32857142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.27894736842105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.32857142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.32857142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.27894736842105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.32857142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.27894736842105[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]68[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=20826&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=20826&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 Mean7.257352941176470.075202862212455196.5036798822067
Geometric Mean7.23058214429241
Harmonic Mean7.20318276213011
Quadratic Mean7.28341185402103
Winsorized Mean ( 1 / 22 )7.257352941176470.075202862212455196.5036798822067
Winsorized Mean ( 2 / 22 )7.266176470588230.073050017565899.4685109287374
Winsorized Mean ( 3 / 22 )7.266176470588230.071316797289154101.885905519951
Winsorized Mean ( 4 / 22 )7.266176470588230.071316797289154101.885905519951
Winsorized Mean ( 5 / 22 )7.27352941176470.0698869539668326104.075639284789
Winsorized Mean ( 6 / 22 )7.264705882352940.0683996386056239106.209711490429
Winsorized Mean ( 7 / 22 )7.264705882352940.0683996386056239106.209711490429
Winsorized Mean ( 8 / 22 )7.264705882352940.0683996386056239106.209711490429
Winsorized Mean ( 9 / 22 )7.264705882352940.06392093124818113.651439997752
Winsorized Mean ( 10 / 22 )7.264705882352940.06392093124818113.651439997752
Winsorized Mean ( 11 / 22 )7.264705882352940.06392093124818113.651439997752
Winsorized Mean ( 12 / 22 )7.282352941176470.0608666260389628119.644432673413
Winsorized Mean ( 13 / 22 )7.282352941176470.0608666260389628119.644432673413
Winsorized Mean ( 14 / 22 )7.282352941176470.0544725356478474133.688524952377
Winsorized Mean ( 15 / 22 )7.282352941176470.0544725356478474133.688524952377
Winsorized Mean ( 16 / 22 )7.258823529411760.0512887166812858141.528663595133
Winsorized Mean ( 17 / 22 )7.283823529411760.0473443243568268153.847871489616
Winsorized Mean ( 18 / 22 )7.283823529411760.0473443243568268153.847871489616
Winsorized Mean ( 19 / 22 )7.283823529411770.0473443243568268153.847871489616
Winsorized Mean ( 20 / 22 )7.254411764705880.0436701773267505166.118211758718
Winsorized Mean ( 21 / 22 )7.285294117647060.0389876675016396186.861502226074
Winsorized Mean ( 22 / 22 )7.285294117647060.0389876675016396186.861502226074
Trimmed Mean ( 1 / 22 )7.263636363636360.073273010694298899.131130204829
Trimmed Mean ( 2 / 22 )7.27031250.0709445795712098102.478759391371
Trimmed Mean ( 3 / 22 )7.272580645161290.0695292532220475104.597422065439
Trimmed Mean ( 4 / 22 )7.2750.0685864129780654106.070571183342
Trimmed Mean ( 5 / 22 )7.277586206896550.0674056039759158107.967079554644
Trimmed Mean ( 6 / 22 )7.278571428571430.066387013952439109.638481914339
Trimmed Mean ( 7 / 22 )7.281481481481480.0655074304081054111.155046627818
Trimmed Mean ( 8 / 22 )7.284615384615380.0643674767388322113.172299951610
Trimmed Mean ( 9 / 22 )7.2880.0628986875694492115.868872334625
Trimmed Mean ( 10 / 22 )7.291666666666670.0620878847872292117.441054589872
Trimmed Mean ( 11 / 22 )7.295652173913040.0609867746603299119.626791456782
Trimmed Mean ( 12 / 22 )7.30.0595082029273681122.672163515170
Trimmed Mean ( 13 / 22 )7.302380952380950.0582844256801525125.288717649106
Trimmed Mean ( 14 / 22 )7.3050.0566081900389615129.044931395479
Trimmed Mean ( 15 / 22 )7.30789473684210.055862763529745130.818711339816
Trimmed Mean ( 16 / 22 )7.311111111111110.0547400462471428133.560557806301
Trimmed Mean ( 17 / 22 )7.317647058823530.0538153223241315135.977018120399
Trimmed Mean ( 18 / 22 )7.3218750.0534560369188038136.970030365727
Trimmed Mean ( 19 / 22 )7.326666666666670.0527264319706207138.956238699199
Trimmed Mean ( 20 / 22 )7.332142857142860.0514482252275308142.514981317943
Trimmed Mean ( 21 / 22 )7.342307692307690.0502832215243207146.019039149200
Trimmed Mean ( 22 / 22 )7.350.05147
Median7.5
Midrange7.05
Midmean - Weighted Average at Xnp7.27894736842105
Midmean - Weighted Average at X(n+1)p7.32857142857143
Midmean - Empirical Distribution Function7.27894736842105
Midmean - Empirical Distribution Function - Averaging7.32857142857143
Midmean - Empirical Distribution Function - Interpolation7.32857142857143
Midmean - Closest Observation7.27894736842105
Midmean - True Basic - Statistics Graphics Toolkit7.32857142857143
Midmean - MS Excel (old versions)7.27894736842105
Number of observations68



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')