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Author

*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Mon, 20 Oct 2008 05:11:00 -0600

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/2008/Oct/20/t1224501195md4qrnntxb5k9h9.htm/, Retrieved Sun, 19 May 2024 15:54:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17195, Retrieved Sun, 19 May 2024 15:54:09 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Gezondheidsindex (Central tendency)

Estimated Impact

134

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

-       [Central Tendency] [Gezondheidsindex ...] [2008-10-20 11:11:00] [d8c5724db236abb5950452133b88474d] [Current]

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Dataseries X:

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Boxplots

1,2
1,2
1,4
1,5
1,4
1,8
2
2,3
2,6
2,3
2,5
2,3
2,1
2,2
2,2
2,7
3,1
3,2
3,1
3,1
2,8
3
2,8
2,7
3,2
3,1
3
2
1,7
1,2
1,4
1,3
1,3
1,1
0,9
1,2
0,9
1,3
1,4
1,5
1,1
1,6
1,5
1,6
1,7
1,6
1,7
1,6
1,6
1,3
1,1
1,6
1,9
1,6
1,7
1,6
1,4
2,1
1,9
1,7
1,8
2
2,5
2,1
2,1
2,3
2,4
2,4
2,3
1,7
2
2,3

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	8 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 8 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17195&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]8 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17195&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17195&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	8 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.94166666666667	0.0732316302869968	26.514043986966
Geometric Mean	1.84515108938921
Harmonic Mean	1.75174608389431
Quadratic Mean	2.03735940210198
Winsorized Mean ( 1 / 24 )	1.94166666666667	0.0732316302869968	26.514043986966
Winsorized Mean ( 2 / 24 )	1.94444444444444	0.0715601044442963	27.1721856688741
Winsorized Mean ( 3 / 24 )	1.94444444444444	0.0715601044442963	27.1721856688741
Winsorized Mean ( 4 / 24 )	1.94444444444444	0.0715601044442963	27.1721856688741
Winsorized Mean ( 5 / 24 )	1.95138888888889	0.0704610641645895	27.6945702144187
Winsorized Mean ( 6 / 24 )	1.94305555555556	0.0685995155978077	28.3246250155395
Winsorized Mean ( 7 / 24 )	1.94305555555556	0.0685995155978077	28.3246250155395
Winsorized Mean ( 8 / 24 )	1.92083333333333	0.0640305549861235	29.9986988048067
Winsorized Mean ( 9 / 24 )	1.93333333333333	0.0621409876604632	31.1120470742599
Winsorized Mean ( 10 / 24 )	1.91944444444444	0.0594918126982658	32.2640100778169
Winsorized Mean ( 11 / 24 )	1.91944444444444	0.0594918126982658	32.2640100778169
Winsorized Mean ( 12 / 24 )	1.90277777777778	0.0565011467685297	33.6767992616673
Winsorized Mean ( 13 / 24 )	1.90277777777778	0.050813885382455	37.44602018634
Winsorized Mean ( 14 / 24 )	1.90277777777778	0.050813885382455	37.44602018634
Winsorized Mean ( 15 / 24 )	1.88194444444444	0.0474847141572425	39.6326371095445
Winsorized Mean ( 16 / 24 )	1.88194444444444	0.0474847141572425	39.6326371095445
Winsorized Mean ( 17 / 24 )	1.85833333333333	0.043995927397238	42.2387580685479
Winsorized Mean ( 18 / 24 )	1.88333333333333	0.0404880244664471	46.5158119753182
Winsorized Mean ( 19 / 24 )	1.88333333333333	0.0404880244664471	46.5158119753182
Winsorized Mean ( 20 / 24 )	1.88333333333333	0.0404880244664471	46.5158119753182
Winsorized Mean ( 21 / 24 )	1.9125	0.0367890350320792	51.98559838094
Winsorized Mean ( 22 / 24 )	1.9125	0.0367890350320792	51.98559838094
Winsorized Mean ( 23 / 24 )	1.88055555555556	0.0321770634933993	58.4439769011652
Winsorized Mean ( 24 / 24 )	1.88055555555556	0.0321770634933993	58.4439769011652
Trimmed Mean ( 1 / 24 )	1.93857142857143	0.0715776911340843	27.0834585169835
Trimmed Mean ( 2 / 24 )	1.93529411764706	0.069608358371924	27.8026111075138
Trimmed Mean ( 3 / 24 )	1.93030303030303	0.0683119710870512	28.2571707357589
Trimmed Mean ( 4 / 24 )	1.925	0.0667410299543323	28.8428272880593
Trimmed Mean ( 5 / 24 )	1.91935483870968	0.0648326450565709	29.6047590999089
Trimmed Mean ( 6 / 24 )	1.91166666666667	0.0628464035020701	30.4180758188286
Trimmed Mean ( 7 / 24 )	1.90517241379310	0.0609673190942363	31.2490764248352
Trimmed Mean ( 8 / 24 )	1.89821428571429	0.0586366243108788	32.3725028175285
Trimmed Mean ( 9 / 24 )	1.89444444444444	0.0569684078023763	33.254298610842
Trimmed Mean ( 10 / 24 )	1.88846153846154	0.0553103029191069	34.1430337350254
Trimmed Mean ( 11 / 24 )	1.884	0.0538599847677631	34.9795865729177
Trimmed Mean ( 12 / 24 )	1.87916666666667	0.0519954933035265	36.1409527494418
Trimmed Mean ( 13 / 24 )	1.87608695652174	0.0503307689728463	37.2751498697327
Trimmed Mean ( 14 / 24 )	1.87272727272727	0.0494540635469618	37.868016061995
Trimmed Mean ( 15 / 24 )	1.86904761904762	0.0482550443570537	38.7326888608364
Trimmed Mean ( 16 / 24 )	1.8675	0.0474189592073433	39.3829816431483
Trimmed Mean ( 17 / 24 )	1.86578947368421	0.0462346534900993	40.3547844061111
Trimmed Mean ( 18 / 24 )	1.86666666666667	0.0454256762579498	41.0927655994992
Trimmed Mean ( 19 / 24 )	1.86470588235294	0.0450553933061806	41.3869627034672
Trimmed Mean ( 20 / 24 )	1.8625	0.0443933117601318	41.9545180603681
Trimmed Mean ( 21 / 24 )	1.86	0.0433112233602968	42.9449887510002
Trimmed Mean ( 22 / 24 )	1.85357142857143	0.0425640329501636	43.5478337013246
Trimmed Mean ( 23 / 24 )	1.84615384615385	0.0412238800214593	44.7836022517245
Trimmed Mean ( 24 / 24 )	1.84166666666667	0.0407878332716408	45.1523535070236
Median	1.8
Midrange	2.05
Midmean - Weighted Average at Xnp	1.82142857142857
Midmean - Weighted Average at X(n+1)p	1.87837837837838
Midmean - Empirical Distribution Function	1.82142857142857
Midmean - Empirical Distribution Function - Averaging	1.87837837837838
Midmean - Empirical Distribution Function - Interpolation	1.87837837837838
Midmean - Closest Observation	1.82142857142857
Midmean - True Basic - Statistics Graphics Toolkit	1.87837837837838
Midmean - MS Excel (old versions)	1.82142857142857
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.94166666666667 & 0.0732316302869968 & 26.514043986966 \tabularnewline
Geometric Mean & 1.84515108938921 &  &  \tabularnewline
Harmonic Mean & 1.75174608389431 &  &  \tabularnewline
Quadratic Mean & 2.03735940210198 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.94166666666667 & 0.0732316302869968 & 26.514043986966 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.94444444444444 & 0.0715601044442963 & 27.1721856688741 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.94444444444444 & 0.0715601044442963 & 27.1721856688741 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.94444444444444 & 0.0715601044442963 & 27.1721856688741 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.95138888888889 & 0.0704610641645895 & 27.6945702144187 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.94305555555556 & 0.0685995155978077 & 28.3246250155395 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.94305555555556 & 0.0685995155978077 & 28.3246250155395 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.92083333333333 & 0.0640305549861235 & 29.9986988048067 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.93333333333333 & 0.0621409876604632 & 31.1120470742599 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.91944444444444 & 0.0594918126982658 & 32.2640100778169 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.91944444444444 & 0.0594918126982658 & 32.2640100778169 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.90277777777778 & 0.0565011467685297 & 33.6767992616673 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.90277777777778 & 0.050813885382455 & 37.44602018634 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.90277777777778 & 0.050813885382455 & 37.44602018634 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.88194444444444 & 0.0474847141572425 & 39.6326371095445 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.88194444444444 & 0.0474847141572425 & 39.6326371095445 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.85833333333333 & 0.043995927397238 & 42.2387580685479 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.88333333333333 & 0.0404880244664471 & 46.5158119753182 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.88333333333333 & 0.0404880244664471 & 46.5158119753182 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.88333333333333 & 0.0404880244664471 & 46.5158119753182 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.9125 & 0.0367890350320792 & 51.98559838094 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.9125 & 0.0367890350320792 & 51.98559838094 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.88055555555556 & 0.0321770634933993 & 58.4439769011652 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.88055555555556 & 0.0321770634933993 & 58.4439769011652 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.93857142857143 & 0.0715776911340843 & 27.0834585169835 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.93529411764706 & 0.069608358371924 & 27.8026111075138 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.93030303030303 & 0.0683119710870512 & 28.2571707357589 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.925 & 0.0667410299543323 & 28.8428272880593 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.91935483870968 & 0.0648326450565709 & 29.6047590999089 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.91166666666667 & 0.0628464035020701 & 30.4180758188286 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.90517241379310 & 0.0609673190942363 & 31.2490764248352 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.89821428571429 & 0.0586366243108788 & 32.3725028175285 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.89444444444444 & 0.0569684078023763 & 33.254298610842 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.88846153846154 & 0.0553103029191069 & 34.1430337350254 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.884 & 0.0538599847677631 & 34.9795865729177 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.87916666666667 & 0.0519954933035265 & 36.1409527494418 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.87608695652174 & 0.0503307689728463 & 37.2751498697327 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.87272727272727 & 0.0494540635469618 & 37.868016061995 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.86904761904762 & 0.0482550443570537 & 38.7326888608364 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.8675 & 0.0474189592073433 & 39.3829816431483 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.86578947368421 & 0.0462346534900993 & 40.3547844061111 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.86666666666667 & 0.0454256762579498 & 41.0927655994992 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.86470588235294 & 0.0450553933061806 & 41.3869627034672 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.8625 & 0.0443933117601318 & 41.9545180603681 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.86 & 0.0433112233602968 & 42.9449887510002 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.85357142857143 & 0.0425640329501636 & 43.5478337013246 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.84615384615385 & 0.0412238800214593 & 44.7836022517245 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.84166666666667 & 0.0407878332716408 & 45.1523535070236 \tabularnewline
Median & 1.8 &  &  \tabularnewline
Midrange & 2.05 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.82142857142857 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.87837837837838 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.82142857142857 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.87837837837838 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.87837837837838 &  &  \tabularnewline
Midmean - Closest Observation & 1.82142857142857 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.87837837837838 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.82142857142857 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17195&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]1.94166666666667[/C][C]0.0732316302869968[/C][C]26.514043986966[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.84515108938921[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.75174608389431[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.03735940210198[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.94166666666667[/C][C]0.0732316302869968[/C][C]26.514043986966[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.94444444444444[/C][C]0.0715601044442963[/C][C]27.1721856688741[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.94444444444444[/C][C]0.0715601044442963[/C][C]27.1721856688741[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.94444444444444[/C][C]0.0715601044442963[/C][C]27.1721856688741[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.95138888888889[/C][C]0.0704610641645895[/C][C]27.6945702144187[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.94305555555556[/C][C]0.0685995155978077[/C][C]28.3246250155395[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.94305555555556[/C][C]0.0685995155978077[/C][C]28.3246250155395[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.92083333333333[/C][C]0.0640305549861235[/C][C]29.9986988048067[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.93333333333333[/C][C]0.0621409876604632[/C][C]31.1120470742599[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.91944444444444[/C][C]0.0594918126982658[/C][C]32.2640100778169[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.91944444444444[/C][C]0.0594918126982658[/C][C]32.2640100778169[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.90277777777778[/C][C]0.0565011467685297[/C][C]33.6767992616673[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.90277777777778[/C][C]0.050813885382455[/C][C]37.44602018634[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.90277777777778[/C][C]0.050813885382455[/C][C]37.44602018634[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.88194444444444[/C][C]0.0474847141572425[/C][C]39.6326371095445[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.88194444444444[/C][C]0.0474847141572425[/C][C]39.6326371095445[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.85833333333333[/C][C]0.043995927397238[/C][C]42.2387580685479[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.88333333333333[/C][C]0.0404880244664471[/C][C]46.5158119753182[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.88333333333333[/C][C]0.0404880244664471[/C][C]46.5158119753182[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.88333333333333[/C][C]0.0404880244664471[/C][C]46.5158119753182[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.9125[/C][C]0.0367890350320792[/C][C]51.98559838094[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.9125[/C][C]0.0367890350320792[/C][C]51.98559838094[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.88055555555556[/C][C]0.0321770634933993[/C][C]58.4439769011652[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.88055555555556[/C][C]0.0321770634933993[/C][C]58.4439769011652[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.93857142857143[/C][C]0.0715776911340843[/C][C]27.0834585169835[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.93529411764706[/C][C]0.069608358371924[/C][C]27.8026111075138[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.93030303030303[/C][C]0.0683119710870512[/C][C]28.2571707357589[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.925[/C][C]0.0667410299543323[/C][C]28.8428272880593[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.91935483870968[/C][C]0.0648326450565709[/C][C]29.6047590999089[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.91166666666667[/C][C]0.0628464035020701[/C][C]30.4180758188286[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.90517241379310[/C][C]0.0609673190942363[/C][C]31.2490764248352[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.89821428571429[/C][C]0.0586366243108788[/C][C]32.3725028175285[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.89444444444444[/C][C]0.0569684078023763[/C][C]33.254298610842[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.88846153846154[/C][C]0.0553103029191069[/C][C]34.1430337350254[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.884[/C][C]0.0538599847677631[/C][C]34.9795865729177[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.87916666666667[/C][C]0.0519954933035265[/C][C]36.1409527494418[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.87608695652174[/C][C]0.0503307689728463[/C][C]37.2751498697327[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.87272727272727[/C][C]0.0494540635469618[/C][C]37.868016061995[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.86904761904762[/C][C]0.0482550443570537[/C][C]38.7326888608364[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.8675[/C][C]0.0474189592073433[/C][C]39.3829816431483[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.86578947368421[/C][C]0.0462346534900993[/C][C]40.3547844061111[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.86666666666667[/C][C]0.0454256762579498[/C][C]41.0927655994992[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.86470588235294[/C][C]0.0450553933061806[/C][C]41.3869627034672[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.8625[/C][C]0.0443933117601318[/C][C]41.9545180603681[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.86[/C][C]0.0433112233602968[/C][C]42.9449887510002[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.85357142857143[/C][C]0.0425640329501636[/C][C]43.5478337013246[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.84615384615385[/C][C]0.0412238800214593[/C][C]44.7836022517245[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.84166666666667[/C][C]0.0407878332716408[/C][C]45.1523535070236[/C][/ROW]
[ROW][C]Median[/C][C]1.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.82142857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.87837837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.82142857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.87837837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.87837837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.82142857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.87837837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.82142857142857[/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=17195&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17195&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	1.94166666666667	0.0732316302869968	26.514043986966
Geometric Mean	1.84515108938921
Harmonic Mean	1.75174608389431
Quadratic Mean	2.03735940210198
Winsorized Mean ( 1 / 24 )	1.94166666666667	0.0732316302869968	26.514043986966
Winsorized Mean ( 2 / 24 )	1.94444444444444	0.0715601044442963	27.1721856688741
Winsorized Mean ( 3 / 24 )	1.94444444444444	0.0715601044442963	27.1721856688741
Winsorized Mean ( 4 / 24 )	1.94444444444444	0.0715601044442963	27.1721856688741
Winsorized Mean ( 5 / 24 )	1.95138888888889	0.0704610641645895	27.6945702144187
Winsorized Mean ( 6 / 24 )	1.94305555555556	0.0685995155978077	28.3246250155395
Winsorized Mean ( 7 / 24 )	1.94305555555556	0.0685995155978077	28.3246250155395
Winsorized Mean ( 8 / 24 )	1.92083333333333	0.0640305549861235	29.9986988048067
Winsorized Mean ( 9 / 24 )	1.93333333333333	0.0621409876604632	31.1120470742599
Winsorized Mean ( 10 / 24 )	1.91944444444444	0.0594918126982658	32.2640100778169
Winsorized Mean ( 11 / 24 )	1.91944444444444	0.0594918126982658	32.2640100778169
Winsorized Mean ( 12 / 24 )	1.90277777777778	0.0565011467685297	33.6767992616673
Winsorized Mean ( 13 / 24 )	1.90277777777778	0.050813885382455	37.44602018634
Winsorized Mean ( 14 / 24 )	1.90277777777778	0.050813885382455	37.44602018634
Winsorized Mean ( 15 / 24 )	1.88194444444444	0.0474847141572425	39.6326371095445
Winsorized Mean ( 16 / 24 )	1.88194444444444	0.0474847141572425	39.6326371095445
Winsorized Mean ( 17 / 24 )	1.85833333333333	0.043995927397238	42.2387580685479
Winsorized Mean ( 18 / 24 )	1.88333333333333	0.0404880244664471	46.5158119753182
Winsorized Mean ( 19 / 24 )	1.88333333333333	0.0404880244664471	46.5158119753182
Winsorized Mean ( 20 / 24 )	1.88333333333333	0.0404880244664471	46.5158119753182
Winsorized Mean ( 21 / 24 )	1.9125	0.0367890350320792	51.98559838094
Winsorized Mean ( 22 / 24 )	1.9125	0.0367890350320792	51.98559838094
Winsorized Mean ( 23 / 24 )	1.88055555555556	0.0321770634933993	58.4439769011652
Winsorized Mean ( 24 / 24 )	1.88055555555556	0.0321770634933993	58.4439769011652
Trimmed Mean ( 1 / 24 )	1.93857142857143	0.0715776911340843	27.0834585169835
Trimmed Mean ( 2 / 24 )	1.93529411764706	0.069608358371924	27.8026111075138
Trimmed Mean ( 3 / 24 )	1.93030303030303	0.0683119710870512	28.2571707357589
Trimmed Mean ( 4 / 24 )	1.925	0.0667410299543323	28.8428272880593
Trimmed Mean ( 5 / 24 )	1.91935483870968	0.0648326450565709	29.6047590999089
Trimmed Mean ( 6 / 24 )	1.91166666666667	0.0628464035020701	30.4180758188286
Trimmed Mean ( 7 / 24 )	1.90517241379310	0.0609673190942363	31.2490764248352
Trimmed Mean ( 8 / 24 )	1.89821428571429	0.0586366243108788	32.3725028175285
Trimmed Mean ( 9 / 24 )	1.89444444444444	0.0569684078023763	33.254298610842
Trimmed Mean ( 10 / 24 )	1.88846153846154	0.0553103029191069	34.1430337350254
Trimmed Mean ( 11 / 24 )	1.884	0.0538599847677631	34.9795865729177
Trimmed Mean ( 12 / 24 )	1.87916666666667	0.0519954933035265	36.1409527494418
Trimmed Mean ( 13 / 24 )	1.87608695652174	0.0503307689728463	37.2751498697327
Trimmed Mean ( 14 / 24 )	1.87272727272727	0.0494540635469618	37.868016061995
Trimmed Mean ( 15 / 24 )	1.86904761904762	0.0482550443570537	38.7326888608364
Trimmed Mean ( 16 / 24 )	1.8675	0.0474189592073433	39.3829816431483
Trimmed Mean ( 17 / 24 )	1.86578947368421	0.0462346534900993	40.3547844061111
Trimmed Mean ( 18 / 24 )	1.86666666666667	0.0454256762579498	41.0927655994992
Trimmed Mean ( 19 / 24 )	1.86470588235294	0.0450553933061806	41.3869627034672
Trimmed Mean ( 20 / 24 )	1.8625	0.0443933117601318	41.9545180603681
Trimmed Mean ( 21 / 24 )	1.86	0.0433112233602968	42.9449887510002
Trimmed Mean ( 22 / 24 )	1.85357142857143	0.0425640329501636	43.5478337013246
Trimmed Mean ( 23 / 24 )	1.84615384615385	0.0412238800214593	44.7836022517245
Trimmed Mean ( 24 / 24 )	1.84166666666667	0.0407878332716408	45.1523535070236
Median	1.8
Midrange	2.05
Midmean - Weighted Average at Xnp	1.82142857142857
Midmean - Weighted Average at X(n+1)p	1.87837837837838
Midmean - Empirical Distribution Function	1.82142857142857
Midmean - Empirical Distribution Function - Averaging	1.87837837837838
Midmean - Empirical Distribution Function - Interpolation	1.87837837837838
Midmean - Closest Observation	1.82142857142857
Midmean - True Basic - Statistics Graphics Toolkit	1.87837837837838
Midmean - MS Excel (old versions)	1.82142857142857
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