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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 computationTue, 13 Dec 2011 15:52:06 -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/13/t1323809540ut6gu0jhutndh0i.htm/, Retrieved Thu, 02 May 2024 20:02:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=154719, Retrieved Thu, 02 May 2024 20:02:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact80
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Time needed to su...] [2010-09-25 09:42:08] [b98453cac15ba1066b407e146608df68]
- R PD    [Central Tendency] [gemiddelde en med...] [2011-12-13 20:52:06] [76a85a4cc6ea7903d92a0f5b9d2872d3] [Current]
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Dataseries X:
6
0
1
2
8
3
2
6
5
2
3
3
7
10
3
4
5
4
4
4
7
2
1
1
3
7
9
8
1
2
4
8
2
1
3
0
7
0
2
6
0
3
4
4
2
1
3
5
7
5
12
3
4
2
4
1
4
0
0
8
5
3
5
9
2
1
5
9
6
3
1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154719&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154719&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154719&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3.901408450704230.32788262215993211.898796053916
Geometric Mean0
Harmonic Mean0
Quadratic Mean4.76932687842209
Winsorized Mean ( 1 / 23 )3.873239436619720.31903373825157112.1405324021421
Winsorized Mean ( 2 / 23 )3.845070422535210.31183747464526512.3303667300065
Winsorized Mean ( 3 / 23 )3.845070422535210.31183747464526512.3303667300065
Winsorized Mean ( 4 / 23 )3.845070422535210.31183747464526512.3303667300065
Winsorized Mean ( 5 / 23 )3.774647887323940.29632027855741312.7384055714992
Winsorized Mean ( 6 / 23 )3.859154929577460.28248379141755513.6615092505362
Winsorized Mean ( 7 / 23 )3.859154929577460.28248379141755513.6615092505362
Winsorized Mean ( 8 / 23 )3.859154929577460.28248379141755513.6615092505362
Winsorized Mean ( 9 / 23 )3.732394366197180.25764585561003614.4865298040983
Winsorized Mean ( 10 / 23 )3.732394366197180.25764585561003614.4865298040983
Winsorized Mean ( 11 / 23 )3.732394366197180.25764585561003614.4865298040983
Winsorized Mean ( 12 / 23 )3.732394366197180.25764585561003614.4865298040983
Winsorized Mean ( 13 / 23 )3.732394366197180.25764585561003614.4865298040983
Winsorized Mean ( 14 / 23 )3.535211267605630.22412897436318215.7731113420308
Winsorized Mean ( 15 / 23 )3.746478873239440.19316104961974919.3956228784977
Winsorized Mean ( 16 / 23 )3.746478873239440.19316104961974919.3956228784977
Winsorized Mean ( 17 / 23 )3.746478873239440.19316104961974919.3956228784977
Winsorized Mean ( 18 / 23 )3.492957746478870.15392025351231622.6932951757345
Winsorized Mean ( 19 / 23 )3.492957746478870.15392025351231622.6932951757345
Winsorized Mean ( 20 / 23 )3.492957746478870.15392025351231622.6932951757345
Winsorized Mean ( 21 / 23 )3.492957746478870.15392025351231622.6932951757345
Winsorized Mean ( 22 / 23 )3.492957746478870.15392025351231622.6932951757345
Winsorized Mean ( 23 / 23 )3.492957746478870.15392025351231622.6932951757345
Trimmed Mean ( 1 / 23 )3.840579710144930.31080512311559612.3568738881969
Trimmed Mean ( 2 / 23 )3.805970149253730.3009398860276412.6469448749116
Trimmed Mean ( 3 / 23 )3.784615384615380.29375904870867412.8834001922734
Trimmed Mean ( 4 / 23 )3.761904761904760.28507352624945313.1962613694718
Trimmed Mean ( 5 / 23 )3.737704918032790.27451063198602613.6158839859545
Trimmed Mean ( 6 / 23 )3.728813559322030.26684128515619313.9739004672362
Trimmed Mean ( 7 / 23 )3.728813559322030.26129246939367214.2706506925926
Trimmed Mean ( 8 / 23 )3.672727272727270.25432891222251314.4408562936565
Trimmed Mean ( 9 / 23 )3.641509433962260.24556197155544214.8292889607302
Trimmed Mean ( 10 / 23 )3.627450980392160.24084945149465215.0610722087225
Trimmed Mean ( 11 / 23 )3.612244897959180.23476780852703915.3864574560832
Trimmed Mean ( 12 / 23 )3.595744680851060.22691180677871915.8464415399837
Trimmed Mean ( 13 / 23 )3.577777777777780.21669903928061216.5103536667958
Trimmed Mean ( 14 / 23 )3.577777777777780.20324696960821617.6031051516999
Trimmed Mean ( 15 / 23 )3.56097560975610.19458768318817818.3001079585928
Trimmed Mean ( 16 / 23 )3.538461538461540.19034081885592718.5901351046508
Trimmed Mean ( 17 / 23 )3.513513513513510.18429975266197119.0641249527759
Trimmed Mean ( 18 / 23 )3.485714285714290.17571667689839819.8371284231022
Trimmed Mean ( 19 / 23 )3.484848484848480.17473579688895119.9435292990548
Trimmed Mean ( 20 / 23 )3.483870967741940.17271374628181720.171358926216
Trimmed Mean ( 21 / 23 )3.482758620689660.16918152473964920.5859276067479
Trimmed Mean ( 22 / 23 )3.481481481481480.16338975451783121.3078322551831
Trimmed Mean ( 23 / 23 )3.480.15405626677721822.5891492296932
Median3
Midrange6
Midmean - Weighted Average at Xnp3.36842105263158
Midmean - Weighted Average at X(n+1)p3.61904761904762
Midmean - Empirical Distribution Function3.61904761904762
Midmean - Empirical Distribution Function - Averaging3.61904761904762
Midmean - Empirical Distribution Function - Interpolation3.36842105263158
Midmean - Closest Observation3.36842105263158
Midmean - True Basic - Statistics Graphics Toolkit3.61904761904762
Midmean - MS Excel (old versions)3.61904761904762
Number of observations71

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3.90140845070423 & 0.327882622159932 & 11.898796053916 \tabularnewline
Geometric Mean & 0 &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 4.76932687842209 &  &  \tabularnewline
Winsorized Mean ( 1 / 23 ) & 3.87323943661972 & 0.319033738251571 & 12.1405324021421 \tabularnewline
Winsorized Mean ( 2 / 23 ) & 3.84507042253521 & 0.311837474645265 & 12.3303667300065 \tabularnewline
Winsorized Mean ( 3 / 23 ) & 3.84507042253521 & 0.311837474645265 & 12.3303667300065 \tabularnewline
Winsorized Mean ( 4 / 23 ) & 3.84507042253521 & 0.311837474645265 & 12.3303667300065 \tabularnewline
Winsorized Mean ( 5 / 23 ) & 3.77464788732394 & 0.296320278557413 & 12.7384055714992 \tabularnewline
Winsorized Mean ( 6 / 23 ) & 3.85915492957746 & 0.282483791417555 & 13.6615092505362 \tabularnewline
Winsorized Mean ( 7 / 23 ) & 3.85915492957746 & 0.282483791417555 & 13.6615092505362 \tabularnewline
Winsorized Mean ( 8 / 23 ) & 3.85915492957746 & 0.282483791417555 & 13.6615092505362 \tabularnewline
Winsorized Mean ( 9 / 23 ) & 3.73239436619718 & 0.257645855610036 & 14.4865298040983 \tabularnewline
Winsorized Mean ( 10 / 23 ) & 3.73239436619718 & 0.257645855610036 & 14.4865298040983 \tabularnewline
Winsorized Mean ( 11 / 23 ) & 3.73239436619718 & 0.257645855610036 & 14.4865298040983 \tabularnewline
Winsorized Mean ( 12 / 23 ) & 3.73239436619718 & 0.257645855610036 & 14.4865298040983 \tabularnewline
Winsorized Mean ( 13 / 23 ) & 3.73239436619718 & 0.257645855610036 & 14.4865298040983 \tabularnewline
Winsorized Mean ( 14 / 23 ) & 3.53521126760563 & 0.224128974363182 & 15.7731113420308 \tabularnewline
Winsorized Mean ( 15 / 23 ) & 3.74647887323944 & 0.193161049619749 & 19.3956228784977 \tabularnewline
Winsorized Mean ( 16 / 23 ) & 3.74647887323944 & 0.193161049619749 & 19.3956228784977 \tabularnewline
Winsorized Mean ( 17 / 23 ) & 3.74647887323944 & 0.193161049619749 & 19.3956228784977 \tabularnewline
Winsorized Mean ( 18 / 23 ) & 3.49295774647887 & 0.153920253512316 & 22.6932951757345 \tabularnewline
Winsorized Mean ( 19 / 23 ) & 3.49295774647887 & 0.153920253512316 & 22.6932951757345 \tabularnewline
Winsorized Mean ( 20 / 23 ) & 3.49295774647887 & 0.153920253512316 & 22.6932951757345 \tabularnewline
Winsorized Mean ( 21 / 23 ) & 3.49295774647887 & 0.153920253512316 & 22.6932951757345 \tabularnewline
Winsorized Mean ( 22 / 23 ) & 3.49295774647887 & 0.153920253512316 & 22.6932951757345 \tabularnewline
Winsorized Mean ( 23 / 23 ) & 3.49295774647887 & 0.153920253512316 & 22.6932951757345 \tabularnewline
Trimmed Mean ( 1 / 23 ) & 3.84057971014493 & 0.310805123115596 & 12.3568738881969 \tabularnewline
Trimmed Mean ( 2 / 23 ) & 3.80597014925373 & 0.30093988602764 & 12.6469448749116 \tabularnewline
Trimmed Mean ( 3 / 23 ) & 3.78461538461538 & 0.293759048708674 & 12.8834001922734 \tabularnewline
Trimmed Mean ( 4 / 23 ) & 3.76190476190476 & 0.285073526249453 & 13.1962613694718 \tabularnewline
Trimmed Mean ( 5 / 23 ) & 3.73770491803279 & 0.274510631986026 & 13.6158839859545 \tabularnewline
Trimmed Mean ( 6 / 23 ) & 3.72881355932203 & 0.266841285156193 & 13.9739004672362 \tabularnewline
Trimmed Mean ( 7 / 23 ) & 3.72881355932203 & 0.261292469393672 & 14.2706506925926 \tabularnewline
Trimmed Mean ( 8 / 23 ) & 3.67272727272727 & 0.254328912222513 & 14.4408562936565 \tabularnewline
Trimmed Mean ( 9 / 23 ) & 3.64150943396226 & 0.245561971555442 & 14.8292889607302 \tabularnewline
Trimmed Mean ( 10 / 23 ) & 3.62745098039216 & 0.240849451494652 & 15.0610722087225 \tabularnewline
Trimmed Mean ( 11 / 23 ) & 3.61224489795918 & 0.234767808527039 & 15.3864574560832 \tabularnewline
Trimmed Mean ( 12 / 23 ) & 3.59574468085106 & 0.226911806778719 & 15.8464415399837 \tabularnewline
Trimmed Mean ( 13 / 23 ) & 3.57777777777778 & 0.216699039280612 & 16.5103536667958 \tabularnewline
Trimmed Mean ( 14 / 23 ) & 3.57777777777778 & 0.203246969608216 & 17.6031051516999 \tabularnewline
Trimmed Mean ( 15 / 23 ) & 3.5609756097561 & 0.194587683188178 & 18.3001079585928 \tabularnewline
Trimmed Mean ( 16 / 23 ) & 3.53846153846154 & 0.190340818855927 & 18.5901351046508 \tabularnewline
Trimmed Mean ( 17 / 23 ) & 3.51351351351351 & 0.184299752661971 & 19.0641249527759 \tabularnewline
Trimmed Mean ( 18 / 23 ) & 3.48571428571429 & 0.175716676898398 & 19.8371284231022 \tabularnewline
Trimmed Mean ( 19 / 23 ) & 3.48484848484848 & 0.174735796888951 & 19.9435292990548 \tabularnewline
Trimmed Mean ( 20 / 23 ) & 3.48387096774194 & 0.172713746281817 & 20.171358926216 \tabularnewline
Trimmed Mean ( 21 / 23 ) & 3.48275862068966 & 0.169181524739649 & 20.5859276067479 \tabularnewline
Trimmed Mean ( 22 / 23 ) & 3.48148148148148 & 0.163389754517831 & 21.3078322551831 \tabularnewline
Trimmed Mean ( 23 / 23 ) & 3.48 & 0.154056266777218 & 22.5891492296932 \tabularnewline
Median & 3 &  &  \tabularnewline
Midrange & 6 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3.36842105263158 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3.61904761904762 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3.61904761904762 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3.61904761904762 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3.36842105263158 &  &  \tabularnewline
Midmean - Closest Observation & 3.36842105263158 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3.61904761904762 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3.61904761904762 &  &  \tabularnewline
Number of observations & 71 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154719&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]3.90140845070423[/C][C]0.327882622159932[/C][C]11.898796053916[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.76932687842209[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 23 )[/C][C]3.87323943661972[/C][C]0.319033738251571[/C][C]12.1405324021421[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 23 )[/C][C]3.84507042253521[/C][C]0.311837474645265[/C][C]12.3303667300065[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 23 )[/C][C]3.84507042253521[/C][C]0.311837474645265[/C][C]12.3303667300065[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 23 )[/C][C]3.84507042253521[/C][C]0.311837474645265[/C][C]12.3303667300065[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 23 )[/C][C]3.77464788732394[/C][C]0.296320278557413[/C][C]12.7384055714992[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 23 )[/C][C]3.85915492957746[/C][C]0.282483791417555[/C][C]13.6615092505362[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 23 )[/C][C]3.85915492957746[/C][C]0.282483791417555[/C][C]13.6615092505362[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 23 )[/C][C]3.85915492957746[/C][C]0.282483791417555[/C][C]13.6615092505362[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 23 )[/C][C]3.73239436619718[/C][C]0.257645855610036[/C][C]14.4865298040983[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 23 )[/C][C]3.73239436619718[/C][C]0.257645855610036[/C][C]14.4865298040983[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 23 )[/C][C]3.73239436619718[/C][C]0.257645855610036[/C][C]14.4865298040983[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 23 )[/C][C]3.73239436619718[/C][C]0.257645855610036[/C][C]14.4865298040983[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 23 )[/C][C]3.73239436619718[/C][C]0.257645855610036[/C][C]14.4865298040983[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 23 )[/C][C]3.53521126760563[/C][C]0.224128974363182[/C][C]15.7731113420308[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 23 )[/C][C]3.74647887323944[/C][C]0.193161049619749[/C][C]19.3956228784977[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 23 )[/C][C]3.74647887323944[/C][C]0.193161049619749[/C][C]19.3956228784977[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 23 )[/C][C]3.74647887323944[/C][C]0.193161049619749[/C][C]19.3956228784977[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 23 )[/C][C]3.49295774647887[/C][C]0.153920253512316[/C][C]22.6932951757345[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 23 )[/C][C]3.49295774647887[/C][C]0.153920253512316[/C][C]22.6932951757345[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 23 )[/C][C]3.49295774647887[/C][C]0.153920253512316[/C][C]22.6932951757345[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 23 )[/C][C]3.49295774647887[/C][C]0.153920253512316[/C][C]22.6932951757345[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 23 )[/C][C]3.49295774647887[/C][C]0.153920253512316[/C][C]22.6932951757345[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 23 )[/C][C]3.49295774647887[/C][C]0.153920253512316[/C][C]22.6932951757345[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 23 )[/C][C]3.84057971014493[/C][C]0.310805123115596[/C][C]12.3568738881969[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 23 )[/C][C]3.80597014925373[/C][C]0.30093988602764[/C][C]12.6469448749116[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 23 )[/C][C]3.78461538461538[/C][C]0.293759048708674[/C][C]12.8834001922734[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 23 )[/C][C]3.76190476190476[/C][C]0.285073526249453[/C][C]13.1962613694718[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 23 )[/C][C]3.73770491803279[/C][C]0.274510631986026[/C][C]13.6158839859545[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 23 )[/C][C]3.72881355932203[/C][C]0.266841285156193[/C][C]13.9739004672362[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 23 )[/C][C]3.72881355932203[/C][C]0.261292469393672[/C][C]14.2706506925926[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 23 )[/C][C]3.67272727272727[/C][C]0.254328912222513[/C][C]14.4408562936565[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 23 )[/C][C]3.64150943396226[/C][C]0.245561971555442[/C][C]14.8292889607302[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 23 )[/C][C]3.62745098039216[/C][C]0.240849451494652[/C][C]15.0610722087225[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 23 )[/C][C]3.61224489795918[/C][C]0.234767808527039[/C][C]15.3864574560832[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 23 )[/C][C]3.59574468085106[/C][C]0.226911806778719[/C][C]15.8464415399837[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 23 )[/C][C]3.57777777777778[/C][C]0.216699039280612[/C][C]16.5103536667958[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 23 )[/C][C]3.57777777777778[/C][C]0.203246969608216[/C][C]17.6031051516999[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 23 )[/C][C]3.5609756097561[/C][C]0.194587683188178[/C][C]18.3001079585928[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 23 )[/C][C]3.53846153846154[/C][C]0.190340818855927[/C][C]18.5901351046508[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 23 )[/C][C]3.51351351351351[/C][C]0.184299752661971[/C][C]19.0641249527759[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 23 )[/C][C]3.48571428571429[/C][C]0.175716676898398[/C][C]19.8371284231022[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 23 )[/C][C]3.48484848484848[/C][C]0.174735796888951[/C][C]19.9435292990548[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 23 )[/C][C]3.48387096774194[/C][C]0.172713746281817[/C][C]20.171358926216[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 23 )[/C][C]3.48275862068966[/C][C]0.169181524739649[/C][C]20.5859276067479[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 23 )[/C][C]3.48148148148148[/C][C]0.163389754517831[/C][C]21.3078322551831[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 23 )[/C][C]3.48[/C][C]0.154056266777218[/C][C]22.5891492296932[/C][/ROW]
[ROW][C]Median[/C][C]3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3.36842105263158[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3.61904761904762[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3.61904761904762[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3.61904761904762[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3.36842105263158[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3.36842105263158[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3.61904761904762[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3.61904761904762[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]71[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154719&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154719&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 Mean3.901408450704230.32788262215993211.898796053916
Geometric Mean0
Harmonic Mean0
Quadratic Mean4.76932687842209
Winsorized Mean ( 1 / 23 )3.873239436619720.31903373825157112.1405324021421
Winsorized Mean ( 2 / 23 )3.845070422535210.31183747464526512.3303667300065
Winsorized Mean ( 3 / 23 )3.845070422535210.31183747464526512.3303667300065
Winsorized Mean ( 4 / 23 )3.845070422535210.31183747464526512.3303667300065
Winsorized Mean ( 5 / 23 )3.774647887323940.29632027855741312.7384055714992
Winsorized Mean ( 6 / 23 )3.859154929577460.28248379141755513.6615092505362
Winsorized Mean ( 7 / 23 )3.859154929577460.28248379141755513.6615092505362
Winsorized Mean ( 8 / 23 )3.859154929577460.28248379141755513.6615092505362
Winsorized Mean ( 9 / 23 )3.732394366197180.25764585561003614.4865298040983
Winsorized Mean ( 10 / 23 )3.732394366197180.25764585561003614.4865298040983
Winsorized Mean ( 11 / 23 )3.732394366197180.25764585561003614.4865298040983
Winsorized Mean ( 12 / 23 )3.732394366197180.25764585561003614.4865298040983
Winsorized Mean ( 13 / 23 )3.732394366197180.25764585561003614.4865298040983
Winsorized Mean ( 14 / 23 )3.535211267605630.22412897436318215.7731113420308
Winsorized Mean ( 15 / 23 )3.746478873239440.19316104961974919.3956228784977
Winsorized Mean ( 16 / 23 )3.746478873239440.19316104961974919.3956228784977
Winsorized Mean ( 17 / 23 )3.746478873239440.19316104961974919.3956228784977
Winsorized Mean ( 18 / 23 )3.492957746478870.15392025351231622.6932951757345
Winsorized Mean ( 19 / 23 )3.492957746478870.15392025351231622.6932951757345
Winsorized Mean ( 20 / 23 )3.492957746478870.15392025351231622.6932951757345
Winsorized Mean ( 21 / 23 )3.492957746478870.15392025351231622.6932951757345
Winsorized Mean ( 22 / 23 )3.492957746478870.15392025351231622.6932951757345
Winsorized Mean ( 23 / 23 )3.492957746478870.15392025351231622.6932951757345
Trimmed Mean ( 1 / 23 )3.840579710144930.31080512311559612.3568738881969
Trimmed Mean ( 2 / 23 )3.805970149253730.3009398860276412.6469448749116
Trimmed Mean ( 3 / 23 )3.784615384615380.29375904870867412.8834001922734
Trimmed Mean ( 4 / 23 )3.761904761904760.28507352624945313.1962613694718
Trimmed Mean ( 5 / 23 )3.737704918032790.27451063198602613.6158839859545
Trimmed Mean ( 6 / 23 )3.728813559322030.26684128515619313.9739004672362
Trimmed Mean ( 7 / 23 )3.728813559322030.26129246939367214.2706506925926
Trimmed Mean ( 8 / 23 )3.672727272727270.25432891222251314.4408562936565
Trimmed Mean ( 9 / 23 )3.641509433962260.24556197155544214.8292889607302
Trimmed Mean ( 10 / 23 )3.627450980392160.24084945149465215.0610722087225
Trimmed Mean ( 11 / 23 )3.612244897959180.23476780852703915.3864574560832
Trimmed Mean ( 12 / 23 )3.595744680851060.22691180677871915.8464415399837
Trimmed Mean ( 13 / 23 )3.577777777777780.21669903928061216.5103536667958
Trimmed Mean ( 14 / 23 )3.577777777777780.20324696960821617.6031051516999
Trimmed Mean ( 15 / 23 )3.56097560975610.19458768318817818.3001079585928
Trimmed Mean ( 16 / 23 )3.538461538461540.19034081885592718.5901351046508
Trimmed Mean ( 17 / 23 )3.513513513513510.18429975266197119.0641249527759
Trimmed Mean ( 18 / 23 )3.485714285714290.17571667689839819.8371284231022
Trimmed Mean ( 19 / 23 )3.484848484848480.17473579688895119.9435292990548
Trimmed Mean ( 20 / 23 )3.483870967741940.17271374628181720.171358926216
Trimmed Mean ( 21 / 23 )3.482758620689660.16918152473964920.5859276067479
Trimmed Mean ( 22 / 23 )3.481481481481480.16338975451783121.3078322551831
Trimmed Mean ( 23 / 23 )3.480.15405626677721822.5891492296932
Median3
Midrange6
Midmean - Weighted Average at Xnp3.36842105263158
Midmean - Weighted Average at X(n+1)p3.61904761904762
Midmean - Empirical Distribution Function3.61904761904762
Midmean - Empirical Distribution Function - Averaging3.61904761904762
Midmean - Empirical Distribution Function - Interpolation3.36842105263158
Midmean - Closest Observation3.36842105263158
Midmean - True Basic - Statistics Graphics Toolkit3.61904761904762
Midmean - MS Excel (old versions)3.61904761904762
Number of observations71



Parameters (Session):
par1 = 5 ; par2 = grey ; par3 = FALSE ; par4 = Unknown ;
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')