Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Thu, 09 Oct 2014 08:26:28 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/09/t14128396164nkicepm96l1kzr.htm/, Retrieved Sat, 11 May 2024 06:58:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=239867, Retrieved Sat, 11 May 2024 06:58:03 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

105

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Central Tendency] [] [2014-10-09 07:26:28] [d4b037465b17855a5e62fa4428b30753] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=239867&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=239867&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=239867&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.57781944444444	0.0188861315504494	83.5438131006188
Geometric Mean	1.56946733704967
Harmonic Mean	1.56078841180037
Quadratic Mean	1.58582436063323
Winsorized Mean ( 1 / 24 )	1.57826388888889	0.0187137233110512	84.3372461297887
Winsorized Mean ( 2 / 24 )	1.57929166666667	0.0184457865453179	85.6180170353072
Winsorized Mean ( 3 / 24 )	1.57858333333333	0.0182095237897925	86.6899844035584
Winsorized Mean ( 4 / 24 )	1.57875	0.0181271995589436	87.0928791215891
Winsorized Mean ( 5 / 24 )	1.58041666666667	0.01756961060311	89.9517184738813
Winsorized Mean ( 6 / 24 )	1.58408333333333	0.0166211908928923	95.3050442378791
Winsorized Mean ( 7 / 24 )	1.58466666666667	0.0163482972557141	96.9316034495757
Winsorized Mean ( 8 / 24 )	1.58511111111111	0.0162681168487385	97.4366686599028
Winsorized Mean ( 9 / 24 )	1.58461111111111	0.0161084032584911	98.3717061016476
Winsorized Mean ( 10 / 24 )	1.58655555555556	0.0155874895776607	101.783904820013
Winsorized Mean ( 11 / 24 )	1.587625	0.0153584255484942	103.371598539647
Winsorized Mean ( 12 / 24 )	1.58645833333333	0.0150265015953687	105.577357661366
Winsorized Mean ( 13 / 24 )	1.58808333333333	0.0147035221686083	108.007000984013
Winsorized Mean ( 14 / 24 )	1.58691666666667	0.0143546182990065	110.550948385475
Winsorized Mean ( 15 / 24 )	1.59108333333333	0.0135113809038163	117.758750542213
Winsorized Mean ( 16 / 24 )	1.59263888888889	0.0132768802775488	119.955807056726
Winsorized Mean ( 17 / 24 )	1.59381944444444	0.0126205350707869	126.287786968217
Winsorized Mean ( 18 / 24 )	1.59581944444444	0.0121912306920159	130.898962111311
Winsorized Mean ( 19 / 24 )	1.59529166666667	0.011741201172312	135.871248882837
Winsorized Mean ( 20 / 24 )	1.59473611111111	0.0107358377989574	148.543238168705
Winsorized Mean ( 21 / 24 )	1.59181944444444	0.0101815354672759	156.343750857684
Winsorized Mean ( 22 / 24 )	1.59273611111111	0.0100567830926181	158.374312783996
Winsorized Mean ( 23 / 24 )	1.59305555555556	0.00984225919570629	161.858728151615
Winsorized Mean ( 24 / 24 )	1.59438888888889	0.00939771880628243	169.657011638083
Trimmed Mean ( 1 / 24 )	1.57991428571429	0.0182900231077618	86.3812077440083
Trimmed Mean ( 2 / 24 )	1.58166176470588	0.0177836180830024	88.9392561920591
Trimmed Mean ( 3 / 24 )	1.58295454545455	0.0173495320374902	91.2390341153858
Trimmed Mean ( 4 / 24 )	1.58459375	0.0169331481809045	93.5793942786698
Trimmed Mean ( 5 / 24 )	1.58629032258065	0.0164577947966898	96.3853506606913
Trimmed Mean ( 6 / 24 )	1.5877	0.0160599565189271	98.8607906957187
Trimmed Mean ( 7 / 24 )	1.58844827586207	0.015841512627631	100.27125017667
Trimmed Mean ( 8 / 24 )	1.58914285714286	0.0156339920322534	101.646646222181
Trimmed Mean ( 9 / 24 )	1.58981481481481	0.0153873597937214	103.319532143748
Trimmed Mean ( 10 / 24 )	1.59061538461538	0.0151076617424038	105.285345392059
Trimmed Mean ( 11 / 24 )	1.5912	0.0148665354925423	107.032334520589
Trimmed Mean ( 12 / 24 )	1.5916875	0.0146015991864998	109.007751799654
Trimmed Mean ( 13 / 24 )	1.59236956521739	0.0143237702744433	111.169722406015
Trimmed Mean ( 14 / 24 )	1.59290909090909	0.0140266214041232	113.563276930027
Trimmed Mean ( 15 / 24 )	1.59364285714286	0.0137038877902384	116.291294962152
Trimmed Mean ( 16 / 24 )	1.59395	0.013461576373573	118.407380812336
Trimmed Mean ( 17 / 24 )	1.59410526315789	0.0131744391009264	120.999858206169
Trimmed Mean ( 18 / 24 )	1.59413888888889	0.0129250680989135	123.33698180073
Trimmed Mean ( 19 / 24 )	1.59394117647059	0.0126647391236597	125.85661346098
Trimmed Mean ( 20 / 24 )	1.59378125	0.012392174818158	128.611908191019
Trimmed Mean ( 21 / 24 )	1.59366666666667	0.0122470107385701	130.12699185832
Trimmed Mean ( 22 / 24 )	1.59389285714286	0.0121420537393732	131.270449905383
Trimmed Mean ( 23 / 24 )	1.59403846153846	0.011962567356194	133.252203651175
Trimmed Mean ( 24 / 24 )	1.59416666666667	0.0116972167299342	136.285981825664
Median	1.605
Midrange	1.5045
Midmean - Weighted Average at Xnp	1.59062162162162
Midmean - Weighted Average at X(n+1)p	1.59413888888889
Midmean - Empirical Distribution Function	1.59062162162162
Midmean - Empirical Distribution Function - Averaging	1.59413888888889
Midmean - Empirical Distribution Function - Interpolation	1.59413888888889
Midmean - Closest Observation	1.59062162162162
Midmean - True Basic - Statistics Graphics Toolkit	1.59413888888889
Midmean - MS Excel (old versions)	1.59410526315789
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.57781944444444 & 0.0188861315504494 & 83.5438131006188 \tabularnewline
Geometric Mean & 1.56946733704967 &  &  \tabularnewline
Harmonic Mean & 1.56078841180037 &  &  \tabularnewline
Quadratic Mean & 1.58582436063323 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.57826388888889 & 0.0187137233110512 & 84.3372461297887 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.57929166666667 & 0.0184457865453179 & 85.6180170353072 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.57858333333333 & 0.0182095237897925 & 86.6899844035584 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.57875 & 0.0181271995589436 & 87.0928791215891 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.58041666666667 & 0.01756961060311 & 89.9517184738813 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.58408333333333 & 0.0166211908928923 & 95.3050442378791 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.58466666666667 & 0.0163482972557141 & 96.9316034495757 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.58511111111111 & 0.0162681168487385 & 97.4366686599028 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.58461111111111 & 0.0161084032584911 & 98.3717061016476 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.58655555555556 & 0.0155874895776607 & 101.783904820013 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.587625 & 0.0153584255484942 & 103.371598539647 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.58645833333333 & 0.0150265015953687 & 105.577357661366 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.58808333333333 & 0.0147035221686083 & 108.007000984013 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.58691666666667 & 0.0143546182990065 & 110.550948385475 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.59108333333333 & 0.0135113809038163 & 117.758750542213 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.59263888888889 & 0.0132768802775488 & 119.955807056726 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.59381944444444 & 0.0126205350707869 & 126.287786968217 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.59581944444444 & 0.0121912306920159 & 130.898962111311 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.59529166666667 & 0.011741201172312 & 135.871248882837 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.59473611111111 & 0.0107358377989574 & 148.543238168705 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.59181944444444 & 0.0101815354672759 & 156.343750857684 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.59273611111111 & 0.0100567830926181 & 158.374312783996 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.59305555555556 & 0.00984225919570629 & 161.858728151615 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.59438888888889 & 0.00939771880628243 & 169.657011638083 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.57991428571429 & 0.0182900231077618 & 86.3812077440083 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.58166176470588 & 0.0177836180830024 & 88.9392561920591 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.58295454545455 & 0.0173495320374902 & 91.2390341153858 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.58459375 & 0.0169331481809045 & 93.5793942786698 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.58629032258065 & 0.0164577947966898 & 96.3853506606913 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.5877 & 0.0160599565189271 & 98.8607906957187 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.58844827586207 & 0.015841512627631 & 100.27125017667 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.58914285714286 & 0.0156339920322534 & 101.646646222181 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.58981481481481 & 0.0153873597937214 & 103.319532143748 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.59061538461538 & 0.0151076617424038 & 105.285345392059 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.5912 & 0.0148665354925423 & 107.032334520589 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.5916875 & 0.0146015991864998 & 109.007751799654 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.59236956521739 & 0.0143237702744433 & 111.169722406015 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.59290909090909 & 0.0140266214041232 & 113.563276930027 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.59364285714286 & 0.0137038877902384 & 116.291294962152 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.59395 & 0.013461576373573 & 118.407380812336 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.59410526315789 & 0.0131744391009264 & 120.999858206169 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.59413888888889 & 0.0129250680989135 & 123.33698180073 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.59394117647059 & 0.0126647391236597 & 125.85661346098 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.59378125 & 0.012392174818158 & 128.611908191019 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.59366666666667 & 0.0122470107385701 & 130.12699185832 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.59389285714286 & 0.0121420537393732 & 131.270449905383 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.59403846153846 & 0.011962567356194 & 133.252203651175 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.59416666666667 & 0.0116972167299342 & 136.285981825664 \tabularnewline
Median & 1.605 &  &  \tabularnewline
Midrange & 1.5045 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.59062162162162 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.59413888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.59062162162162 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.59413888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.59413888888889 &  &  \tabularnewline
Midmean - Closest Observation & 1.59062162162162 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.59413888888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.59410526315789 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=239867&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]1.57781944444444[/C][C]0.0188861315504494[/C][C]83.5438131006188[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.56946733704967[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.56078841180037[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.58582436063323[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.57826388888889[/C][C]0.0187137233110512[/C][C]84.3372461297887[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.57929166666667[/C][C]0.0184457865453179[/C][C]85.6180170353072[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.57858333333333[/C][C]0.0182095237897925[/C][C]86.6899844035584[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.57875[/C][C]0.0181271995589436[/C][C]87.0928791215891[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.58041666666667[/C][C]0.01756961060311[/C][C]89.9517184738813[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.58408333333333[/C][C]0.0166211908928923[/C][C]95.3050442378791[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.58466666666667[/C][C]0.0163482972557141[/C][C]96.9316034495757[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.58511111111111[/C][C]0.0162681168487385[/C][C]97.4366686599028[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.58461111111111[/C][C]0.0161084032584911[/C][C]98.3717061016476[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.58655555555556[/C][C]0.0155874895776607[/C][C]101.783904820013[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.587625[/C][C]0.0153584255484942[/C][C]103.371598539647[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.58645833333333[/C][C]0.0150265015953687[/C][C]105.577357661366[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.58808333333333[/C][C]0.0147035221686083[/C][C]108.007000984013[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.58691666666667[/C][C]0.0143546182990065[/C][C]110.550948385475[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.59108333333333[/C][C]0.0135113809038163[/C][C]117.758750542213[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.59263888888889[/C][C]0.0132768802775488[/C][C]119.955807056726[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.59381944444444[/C][C]0.0126205350707869[/C][C]126.287786968217[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.59581944444444[/C][C]0.0121912306920159[/C][C]130.898962111311[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.59529166666667[/C][C]0.011741201172312[/C][C]135.871248882837[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.59473611111111[/C][C]0.0107358377989574[/C][C]148.543238168705[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.59181944444444[/C][C]0.0101815354672759[/C][C]156.343750857684[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.59273611111111[/C][C]0.0100567830926181[/C][C]158.374312783996[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.59305555555556[/C][C]0.00984225919570629[/C][C]161.858728151615[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.59438888888889[/C][C]0.00939771880628243[/C][C]169.657011638083[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.57991428571429[/C][C]0.0182900231077618[/C][C]86.3812077440083[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.58166176470588[/C][C]0.0177836180830024[/C][C]88.9392561920591[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.58295454545455[/C][C]0.0173495320374902[/C][C]91.2390341153858[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.58459375[/C][C]0.0169331481809045[/C][C]93.5793942786698[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.58629032258065[/C][C]0.0164577947966898[/C][C]96.3853506606913[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.5877[/C][C]0.0160599565189271[/C][C]98.8607906957187[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.58844827586207[/C][C]0.015841512627631[/C][C]100.27125017667[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.58914285714286[/C][C]0.0156339920322534[/C][C]101.646646222181[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.58981481481481[/C][C]0.0153873597937214[/C][C]103.319532143748[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.59061538461538[/C][C]0.0151076617424038[/C][C]105.285345392059[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.5912[/C][C]0.0148665354925423[/C][C]107.032334520589[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.5916875[/C][C]0.0146015991864998[/C][C]109.007751799654[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.59236956521739[/C][C]0.0143237702744433[/C][C]111.169722406015[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.59290909090909[/C][C]0.0140266214041232[/C][C]113.563276930027[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.59364285714286[/C][C]0.0137038877902384[/C][C]116.291294962152[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.59395[/C][C]0.013461576373573[/C][C]118.407380812336[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.59410526315789[/C][C]0.0131744391009264[/C][C]120.999858206169[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.59413888888889[/C][C]0.0129250680989135[/C][C]123.33698180073[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.59394117647059[/C][C]0.0126647391236597[/C][C]125.85661346098[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.59378125[/C][C]0.012392174818158[/C][C]128.611908191019[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.59366666666667[/C][C]0.0122470107385701[/C][C]130.12699185832[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.59389285714286[/C][C]0.0121420537393732[/C][C]131.270449905383[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.59403846153846[/C][C]0.011962567356194[/C][C]133.252203651175[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.59416666666667[/C][C]0.0116972167299342[/C][C]136.285981825664[/C][/ROW]
[ROW][C]Median[/C][C]1.605[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.5045[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.59062162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.59413888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.59062162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.59413888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.59413888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.59062162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.59413888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.59410526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=239867&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=239867&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
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.57781944444444	0.0188861315504494	83.5438131006188
Geometric Mean	1.56946733704967
Harmonic Mean	1.56078841180037
Quadratic Mean	1.58582436063323
Winsorized Mean ( 1 / 24 )	1.57826388888889	0.0187137233110512	84.3372461297887
Winsorized Mean ( 2 / 24 )	1.57929166666667	0.0184457865453179	85.6180170353072
Winsorized Mean ( 3 / 24 )	1.57858333333333	0.0182095237897925	86.6899844035584
Winsorized Mean ( 4 / 24 )	1.57875	0.0181271995589436	87.0928791215891
Winsorized Mean ( 5 / 24 )	1.58041666666667	0.01756961060311	89.9517184738813
Winsorized Mean ( 6 / 24 )	1.58408333333333	0.0166211908928923	95.3050442378791
Winsorized Mean ( 7 / 24 )	1.58466666666667	0.0163482972557141	96.9316034495757
Winsorized Mean ( 8 / 24 )	1.58511111111111	0.0162681168487385	97.4366686599028
Winsorized Mean ( 9 / 24 )	1.58461111111111	0.0161084032584911	98.3717061016476
Winsorized Mean ( 10 / 24 )	1.58655555555556	0.0155874895776607	101.783904820013
Winsorized Mean ( 11 / 24 )	1.587625	0.0153584255484942	103.371598539647
Winsorized Mean ( 12 / 24 )	1.58645833333333	0.0150265015953687	105.577357661366
Winsorized Mean ( 13 / 24 )	1.58808333333333	0.0147035221686083	108.007000984013
Winsorized Mean ( 14 / 24 )	1.58691666666667	0.0143546182990065	110.550948385475
Winsorized Mean ( 15 / 24 )	1.59108333333333	0.0135113809038163	117.758750542213
Winsorized Mean ( 16 / 24 )	1.59263888888889	0.0132768802775488	119.955807056726
Winsorized Mean ( 17 / 24 )	1.59381944444444	0.0126205350707869	126.287786968217
Winsorized Mean ( 18 / 24 )	1.59581944444444	0.0121912306920159	130.898962111311
Winsorized Mean ( 19 / 24 )	1.59529166666667	0.011741201172312	135.871248882837
Winsorized Mean ( 20 / 24 )	1.59473611111111	0.0107358377989574	148.543238168705
Winsorized Mean ( 21 / 24 )	1.59181944444444	0.0101815354672759	156.343750857684
Winsorized Mean ( 22 / 24 )	1.59273611111111	0.0100567830926181	158.374312783996
Winsorized Mean ( 23 / 24 )	1.59305555555556	0.00984225919570629	161.858728151615
Winsorized Mean ( 24 / 24 )	1.59438888888889	0.00939771880628243	169.657011638083
Trimmed Mean ( 1 / 24 )	1.57991428571429	0.0182900231077618	86.3812077440083
Trimmed Mean ( 2 / 24 )	1.58166176470588	0.0177836180830024	88.9392561920591
Trimmed Mean ( 3 / 24 )	1.58295454545455	0.0173495320374902	91.2390341153858
Trimmed Mean ( 4 / 24 )	1.58459375	0.0169331481809045	93.5793942786698
Trimmed Mean ( 5 / 24 )	1.58629032258065	0.0164577947966898	96.3853506606913
Trimmed Mean ( 6 / 24 )	1.5877	0.0160599565189271	98.8607906957187
Trimmed Mean ( 7 / 24 )	1.58844827586207	0.015841512627631	100.27125017667
Trimmed Mean ( 8 / 24 )	1.58914285714286	0.0156339920322534	101.646646222181
Trimmed Mean ( 9 / 24 )	1.58981481481481	0.0153873597937214	103.319532143748
Trimmed Mean ( 10 / 24 )	1.59061538461538	0.0151076617424038	105.285345392059
Trimmed Mean ( 11 / 24 )	1.5912	0.0148665354925423	107.032334520589
Trimmed Mean ( 12 / 24 )	1.5916875	0.0146015991864998	109.007751799654
Trimmed Mean ( 13 / 24 )	1.59236956521739	0.0143237702744433	111.169722406015
Trimmed Mean ( 14 / 24 )	1.59290909090909	0.0140266214041232	113.563276930027
Trimmed Mean ( 15 / 24 )	1.59364285714286	0.0137038877902384	116.291294962152
Trimmed Mean ( 16 / 24 )	1.59395	0.013461576373573	118.407380812336
Trimmed Mean ( 17 / 24 )	1.59410526315789	0.0131744391009264	120.999858206169
Trimmed Mean ( 18 / 24 )	1.59413888888889	0.0129250680989135	123.33698180073
Trimmed Mean ( 19 / 24 )	1.59394117647059	0.0126647391236597	125.85661346098
Trimmed Mean ( 20 / 24 )	1.59378125	0.012392174818158	128.611908191019
Trimmed Mean ( 21 / 24 )	1.59366666666667	0.0122470107385701	130.12699185832
Trimmed Mean ( 22 / 24 )	1.59389285714286	0.0121420537393732	131.270449905383
Trimmed Mean ( 23 / 24 )	1.59403846153846	0.011962567356194	133.252203651175
Trimmed Mean ( 24 / 24 )	1.59416666666667	0.0116972167299342	136.285981825664
Median	1.605
Midrange	1.5045
Midmean - Weighted Average at Xnp	1.59062162162162
Midmean - Weighted Average at X(n+1)p	1.59413888888889
Midmean - Empirical Distribution Function	1.59062162162162
Midmean - Empirical Distribution Function - Averaging	1.59413888888889
Midmean - Empirical Distribution Function - Interpolation	1.59413888888889
Midmean - Closest Observation	1.59062162162162
Midmean - True Basic - Statistics Graphics Toolkit	1.59413888888889
Midmean - MS Excel (old versions)	1.59410526315789
Number of observations	72

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code