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*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Tue, 15 Nov 2011 11:50:20 -0500

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/2011/Nov/15/t13213758433tn57v7xgw7goho.htm/, Retrieved Tue, 23 Apr 2024 19:33:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=143194, Retrieved Tue, 23 Apr 2024 19:33:16 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

132

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

-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
- RM D    [Central Tendency] [Workshop 6 - Mini...] [2011-11-15 16:50:20] [d41d8cd98f00b204e9800998ecf8427e] [Current]
-    D      [Central Tendency] [Workshop 6 - Mini...] [2011-11-15 17:09:25] [ec29c78521a0445a37e4526edb78f709] 

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Dataseries X:

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Boxplots

1,2
1,25
1,3
1,35
1,4
1,45
1,5
1,55
1,6
1,65
1,7
1,75
1,8
1,85
1,8
1,8
1,8
1,8
1,8
1,8
1,75
1,7
1,65
1,6
1,6
1,6
1,6
1,6
1,6
1,6
1,7
1,8
1,9
2
2,1
2,2
2,3
2,4
2,5
2,5
2,5
2,4
2,3
2,2
2,1
1,9
1,7
1,5
1,6
1,6
1,6
1,6
1,65
1,7
1,75
1,75
1,75
1,75
1,8
1,9
1,8
1,7
1,6
1,6
1,6
1,6
1,6
1,7
1,8
1,9
2
2,1

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 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=143194&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=143194&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143194&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	1 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.77638888888889	0.0337846822642253	52.5797127525426
Geometric Mean	1.75487278619762
Harmonic Mean	1.73441248271415
Quadratic Mean	1.79905453564427
Winsorized Mean ( 1 / 24 )	1.77708333333333	0.0336245713099015	52.8507357597161
Winsorized Mean ( 2 / 24 )	1.77847222222222	0.0333307861246373	53.3582441041683
Winsorized Mean ( 3 / 24 )	1.77638888888889	0.0317088337708318	56.0218928809343
Winsorized Mean ( 4 / 24 )	1.77916666666667	0.031207913756997	57.0101122593549
Winsorized Mean ( 5 / 24 )	1.77569444444444	0.0287655696351628	61.7298550651278
Winsorized Mean ( 6 / 24 )	1.77986111111111	0.0281410855969375	63.2477771683694
Winsorized Mean ( 7 / 24 )	1.77013888888889	0.0257261467496919	68.8069964815112
Winsorized Mean ( 8 / 24 )	1.77569444444444	0.0249607096487532	71.1395817439485
Winsorized Mean ( 9 / 24 )	1.76944444444444	0.0213390625457661	82.9204394827328
Winsorized Mean ( 10 / 24 )	1.76944444444444	0.0213390625457661	82.9204394827328
Winsorized Mean ( 11 / 24 )	1.76944444444444	0.0213390625457661	82.9204394827328
Winsorized Mean ( 12 / 24 )	1.75277777777778	0.0178809117217021	98.025078645762
Winsorized Mean ( 13 / 24 )	1.75277777777778	0.0178809117217021	98.025078645762
Winsorized Mean ( 14 / 24 )	1.73333333333333	0.014365832791721	120.656655166712
Winsorized Mean ( 15 / 24 )	1.73333333333333	0.014365832791721	120.656655166712
Winsorized Mean ( 16 / 24 )	1.73333333333333	0.014365832791721	120.656655166712
Winsorized Mean ( 17 / 24 )	1.73333333333333	0.014365832791721	120.656655166712
Winsorized Mean ( 18 / 24 )	1.72083333333333	0.0124215062881421	138.53660686676
Winsorized Mean ( 19 / 24 )	1.70763888888889	0.0106360569008861	160.551876019639
Winsorized Mean ( 20 / 24 )	1.70763888888889	0.0106360569008861	160.551876019639
Winsorized Mean ( 21 / 24 )	1.70763888888889	0.0106360569008861	160.551876019639
Winsorized Mean ( 22 / 24 )	1.70763888888889	0.0106360569008861	160.551876019639
Winsorized Mean ( 23 / 24 )	1.70763888888889	0.0106360569008861	160.551876019639
Winsorized Mean ( 24 / 24 )	1.70763888888889	0.0106360569008861	160.551876019639
Trimmed Mean ( 1 / 24 )	1.77428571428571	0.0321059138973994	55.263516869689
Trimmed Mean ( 2 / 24 )	1.77132352941176	0.030277400836175	58.5031568263089
Trimmed Mean ( 3 / 24 )	1.76742424242424	0.0282449414626985	62.574894862444
Trimmed Mean ( 4 / 24 )	1.7640625	0.0265741687721844	66.3826031633574
Trimmed Mean ( 5 / 24 )	1.75967741935484	0.024709809969365	71.213717205291
Trimmed Mean ( 6 / 24 )	1.75583333333333	0.0232916799318762	75.3845724511421
Trimmed Mean ( 7 / 24 )	1.75086206896552	0.0217048402367091	80.6668950276035
Trimmed Mean ( 8 / 24 )	1.74732142857143	0.0204820020319211	85.3100896019947
Trimmed Mean ( 9 / 24 )	1.74259259259259	0.0191269713547784	91.1065615287416
Trimmed Mean ( 10 / 24 )	1.73846153846154	0.0184022111092457	94.4702529571619
Trimmed Mean ( 11 / 24 )	1.734	0.0174636649027841	99.2918731350346
Trimmed Mean ( 12 / 24 )	1.72916666666667	0.0162287322181674	106.549707236585
Trimmed Mean ( 13 / 24 )	1.72608695652174	0.0155990779514129	110.65314000597
Trimmed Mean ( 14 / 24 )	1.72272727272727	0.0147615423587102	116.703744829941
Trimmed Mean ( 15 / 24 )	1.72142857142857	0.0145731820128763	118.123040658353
Trimmed Mean ( 16 / 24 )	1.72	0.0142999013803305	120.280549792172
Trimmed Mean ( 17 / 24 )	1.71842105263158	0.013911559280689	123.52469036429
Trimmed Mean ( 18 / 24 )	1.71666666666667	0.0133630620956212	128.463570279239
Trimmed Mean ( 19 / 24 )	1.71617647058824	0.0131358913278562	130.647888883557
Trimmed Mean ( 20 / 24 )	1.7171875	0.0132076649834297	130.014465248352
Trimmed Mean ( 21 / 24 )	1.71833333333333	0.013235995273542	129.822752110541
Trimmed Mean ( 22 / 24 )	1.71964285714286	0.0131985463250497	130.29032249401
Trimmed Mean ( 23 / 24 )	1.72115384615385	0.0130599437279613	131.788764332029
Trimmed Mean ( 24 / 24 )	1.72291666666667	0.012761456442405	135.009406993828
Median	1.725
Midrange	1.85
Midmean - Weighted Average at Xnp	1.69333333333333
Midmean - Weighted Average at X(n+1)p	1.69333333333333
Midmean - Empirical Distribution Function	1.69333333333333
Midmean - Empirical Distribution Function - Averaging	1.69333333333333
Midmean - Empirical Distribution Function - Interpolation	1.69333333333333
Midmean - Closest Observation	1.69333333333333
Midmean - True Basic - Statistics Graphics Toolkit	1.69333333333333
Midmean - MS Excel (old versions)	1.71020408163265
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.77638888888889 & 0.0337846822642253 & 52.5797127525426 \tabularnewline
Geometric Mean & 1.75487278619762 &  &  \tabularnewline
Harmonic Mean & 1.73441248271415 &  &  \tabularnewline
Quadratic Mean & 1.79905453564427 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.77708333333333 & 0.0336245713099015 & 52.8507357597161 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.77847222222222 & 0.0333307861246373 & 53.3582441041683 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.77638888888889 & 0.0317088337708318 & 56.0218928809343 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.77916666666667 & 0.031207913756997 & 57.0101122593549 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.77569444444444 & 0.0287655696351628 & 61.7298550651278 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.77986111111111 & 0.0281410855969375 & 63.2477771683694 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.77013888888889 & 0.0257261467496919 & 68.8069964815112 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.77569444444444 & 0.0249607096487532 & 71.1395817439485 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.76944444444444 & 0.0213390625457661 & 82.9204394827328 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.76944444444444 & 0.0213390625457661 & 82.9204394827328 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.76944444444444 & 0.0213390625457661 & 82.9204394827328 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.75277777777778 & 0.0178809117217021 & 98.025078645762 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.75277777777778 & 0.0178809117217021 & 98.025078645762 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.73333333333333 & 0.014365832791721 & 120.656655166712 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.73333333333333 & 0.014365832791721 & 120.656655166712 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.73333333333333 & 0.014365832791721 & 120.656655166712 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.73333333333333 & 0.014365832791721 & 120.656655166712 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.72083333333333 & 0.0124215062881421 & 138.53660686676 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.70763888888889 & 0.0106360569008861 & 160.551876019639 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.70763888888889 & 0.0106360569008861 & 160.551876019639 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.70763888888889 & 0.0106360569008861 & 160.551876019639 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.70763888888889 & 0.0106360569008861 & 160.551876019639 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.70763888888889 & 0.0106360569008861 & 160.551876019639 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.70763888888889 & 0.0106360569008861 & 160.551876019639 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.77428571428571 & 0.0321059138973994 & 55.263516869689 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.77132352941176 & 0.030277400836175 & 58.5031568263089 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.76742424242424 & 0.0282449414626985 & 62.574894862444 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.7640625 & 0.0265741687721844 & 66.3826031633574 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.75967741935484 & 0.024709809969365 & 71.213717205291 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.75583333333333 & 0.0232916799318762 & 75.3845724511421 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.75086206896552 & 0.0217048402367091 & 80.6668950276035 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.74732142857143 & 0.0204820020319211 & 85.3100896019947 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.74259259259259 & 0.0191269713547784 & 91.1065615287416 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.73846153846154 & 0.0184022111092457 & 94.4702529571619 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.734 & 0.0174636649027841 & 99.2918731350346 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.72916666666667 & 0.0162287322181674 & 106.549707236585 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.72608695652174 & 0.0155990779514129 & 110.65314000597 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.72272727272727 & 0.0147615423587102 & 116.703744829941 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.72142857142857 & 0.0145731820128763 & 118.123040658353 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.72 & 0.0142999013803305 & 120.280549792172 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.71842105263158 & 0.013911559280689 & 123.52469036429 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.71666666666667 & 0.0133630620956212 & 128.463570279239 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.71617647058824 & 0.0131358913278562 & 130.647888883557 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.7171875 & 0.0132076649834297 & 130.014465248352 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.71833333333333 & 0.013235995273542 & 129.822752110541 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.71964285714286 & 0.0131985463250497 & 130.29032249401 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.72115384615385 & 0.0130599437279613 & 131.788764332029 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.72291666666667 & 0.012761456442405 & 135.009406993828 \tabularnewline
Median & 1.725 &  &  \tabularnewline
Midrange & 1.85 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.69333333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.69333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.69333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.69333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.69333333333333 &  &  \tabularnewline
Midmean - Closest Observation & 1.69333333333333 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.69333333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.71020408163265 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143194&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]1.77638888888889[/C][C]0.0337846822642253[/C][C]52.5797127525426[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.75487278619762[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.73441248271415[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.79905453564427[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.77708333333333[/C][C]0.0336245713099015[/C][C]52.8507357597161[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.77847222222222[/C][C]0.0333307861246373[/C][C]53.3582441041683[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.77638888888889[/C][C]0.0317088337708318[/C][C]56.0218928809343[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.77916666666667[/C][C]0.031207913756997[/C][C]57.0101122593549[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.77569444444444[/C][C]0.0287655696351628[/C][C]61.7298550651278[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.77986111111111[/C][C]0.0281410855969375[/C][C]63.2477771683694[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.77013888888889[/C][C]0.0257261467496919[/C][C]68.8069964815112[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.77569444444444[/C][C]0.0249607096487532[/C][C]71.1395817439485[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.76944444444444[/C][C]0.0213390625457661[/C][C]82.9204394827328[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.76944444444444[/C][C]0.0213390625457661[/C][C]82.9204394827328[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.76944444444444[/C][C]0.0213390625457661[/C][C]82.9204394827328[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.75277777777778[/C][C]0.0178809117217021[/C][C]98.025078645762[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.75277777777778[/C][C]0.0178809117217021[/C][C]98.025078645762[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.73333333333333[/C][C]0.014365832791721[/C][C]120.656655166712[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.73333333333333[/C][C]0.014365832791721[/C][C]120.656655166712[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.73333333333333[/C][C]0.014365832791721[/C][C]120.656655166712[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.73333333333333[/C][C]0.014365832791721[/C][C]120.656655166712[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.72083333333333[/C][C]0.0124215062881421[/C][C]138.53660686676[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.70763888888889[/C][C]0.0106360569008861[/C][C]160.551876019639[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.70763888888889[/C][C]0.0106360569008861[/C][C]160.551876019639[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.70763888888889[/C][C]0.0106360569008861[/C][C]160.551876019639[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.70763888888889[/C][C]0.0106360569008861[/C][C]160.551876019639[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.70763888888889[/C][C]0.0106360569008861[/C][C]160.551876019639[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.70763888888889[/C][C]0.0106360569008861[/C][C]160.551876019639[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.77428571428571[/C][C]0.0321059138973994[/C][C]55.263516869689[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.77132352941176[/C][C]0.030277400836175[/C][C]58.5031568263089[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.76742424242424[/C][C]0.0282449414626985[/C][C]62.574894862444[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.7640625[/C][C]0.0265741687721844[/C][C]66.3826031633574[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.75967741935484[/C][C]0.024709809969365[/C][C]71.213717205291[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.75583333333333[/C][C]0.0232916799318762[/C][C]75.3845724511421[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.75086206896552[/C][C]0.0217048402367091[/C][C]80.6668950276035[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.74732142857143[/C][C]0.0204820020319211[/C][C]85.3100896019947[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.74259259259259[/C][C]0.0191269713547784[/C][C]91.1065615287416[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.73846153846154[/C][C]0.0184022111092457[/C][C]94.4702529571619[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.734[/C][C]0.0174636649027841[/C][C]99.2918731350346[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.72916666666667[/C][C]0.0162287322181674[/C][C]106.549707236585[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.72608695652174[/C][C]0.0155990779514129[/C][C]110.65314000597[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.72272727272727[/C][C]0.0147615423587102[/C][C]116.703744829941[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.72142857142857[/C][C]0.0145731820128763[/C][C]118.123040658353[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.72[/C][C]0.0142999013803305[/C][C]120.280549792172[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.71842105263158[/C][C]0.013911559280689[/C][C]123.52469036429[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.71666666666667[/C][C]0.0133630620956212[/C][C]128.463570279239[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.71617647058824[/C][C]0.0131358913278562[/C][C]130.647888883557[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.7171875[/C][C]0.0132076649834297[/C][C]130.014465248352[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.71833333333333[/C][C]0.013235995273542[/C][C]129.822752110541[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.71964285714286[/C][C]0.0131985463250497[/C][C]130.29032249401[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.72115384615385[/C][C]0.0130599437279613[/C][C]131.788764332029[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.72291666666667[/C][C]0.012761456442405[/C][C]135.009406993828[/C][/ROW]
[ROW][C]Median[/C][C]1.725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.69333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.69333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.69333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.69333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.69333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.69333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.69333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.71020408163265[/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=143194&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143194&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	1.77638888888889	0.0337846822642253	52.5797127525426
Geometric Mean	1.75487278619762
Harmonic Mean	1.73441248271415
Quadratic Mean	1.79905453564427
Winsorized Mean ( 1 / 24 )	1.77708333333333	0.0336245713099015	52.8507357597161
Winsorized Mean ( 2 / 24 )	1.77847222222222	0.0333307861246373	53.3582441041683
Winsorized Mean ( 3 / 24 )	1.77638888888889	0.0317088337708318	56.0218928809343
Winsorized Mean ( 4 / 24 )	1.77916666666667	0.031207913756997	57.0101122593549
Winsorized Mean ( 5 / 24 )	1.77569444444444	0.0287655696351628	61.7298550651278
Winsorized Mean ( 6 / 24 )	1.77986111111111	0.0281410855969375	63.2477771683694
Winsorized Mean ( 7 / 24 )	1.77013888888889	0.0257261467496919	68.8069964815112
Winsorized Mean ( 8 / 24 )	1.77569444444444	0.0249607096487532	71.1395817439485
Winsorized Mean ( 9 / 24 )	1.76944444444444	0.0213390625457661	82.9204394827328
Winsorized Mean ( 10 / 24 )	1.76944444444444	0.0213390625457661	82.9204394827328
Winsorized Mean ( 11 / 24 )	1.76944444444444	0.0213390625457661	82.9204394827328
Winsorized Mean ( 12 / 24 )	1.75277777777778	0.0178809117217021	98.025078645762
Winsorized Mean ( 13 / 24 )	1.75277777777778	0.0178809117217021	98.025078645762
Winsorized Mean ( 14 / 24 )	1.73333333333333	0.014365832791721	120.656655166712
Winsorized Mean ( 15 / 24 )	1.73333333333333	0.014365832791721	120.656655166712
Winsorized Mean ( 16 / 24 )	1.73333333333333	0.014365832791721	120.656655166712
Winsorized Mean ( 17 / 24 )	1.73333333333333	0.014365832791721	120.656655166712
Winsorized Mean ( 18 / 24 )	1.72083333333333	0.0124215062881421	138.53660686676
Winsorized Mean ( 19 / 24 )	1.70763888888889	0.0106360569008861	160.551876019639
Winsorized Mean ( 20 / 24 )	1.70763888888889	0.0106360569008861	160.551876019639
Winsorized Mean ( 21 / 24 )	1.70763888888889	0.0106360569008861	160.551876019639
Winsorized Mean ( 22 / 24 )	1.70763888888889	0.0106360569008861	160.551876019639
Winsorized Mean ( 23 / 24 )	1.70763888888889	0.0106360569008861	160.551876019639
Winsorized Mean ( 24 / 24 )	1.70763888888889	0.0106360569008861	160.551876019639
Trimmed Mean ( 1 / 24 )	1.77428571428571	0.0321059138973994	55.263516869689
Trimmed Mean ( 2 / 24 )	1.77132352941176	0.030277400836175	58.5031568263089
Trimmed Mean ( 3 / 24 )	1.76742424242424	0.0282449414626985	62.574894862444
Trimmed Mean ( 4 / 24 )	1.7640625	0.0265741687721844	66.3826031633574
Trimmed Mean ( 5 / 24 )	1.75967741935484	0.024709809969365	71.213717205291
Trimmed Mean ( 6 / 24 )	1.75583333333333	0.0232916799318762	75.3845724511421
Trimmed Mean ( 7 / 24 )	1.75086206896552	0.0217048402367091	80.6668950276035
Trimmed Mean ( 8 / 24 )	1.74732142857143	0.0204820020319211	85.3100896019947
Trimmed Mean ( 9 / 24 )	1.74259259259259	0.0191269713547784	91.1065615287416
Trimmed Mean ( 10 / 24 )	1.73846153846154	0.0184022111092457	94.4702529571619
Trimmed Mean ( 11 / 24 )	1.734	0.0174636649027841	99.2918731350346
Trimmed Mean ( 12 / 24 )	1.72916666666667	0.0162287322181674	106.549707236585
Trimmed Mean ( 13 / 24 )	1.72608695652174	0.0155990779514129	110.65314000597
Trimmed Mean ( 14 / 24 )	1.72272727272727	0.0147615423587102	116.703744829941
Trimmed Mean ( 15 / 24 )	1.72142857142857	0.0145731820128763	118.123040658353
Trimmed Mean ( 16 / 24 )	1.72	0.0142999013803305	120.280549792172
Trimmed Mean ( 17 / 24 )	1.71842105263158	0.013911559280689	123.52469036429
Trimmed Mean ( 18 / 24 )	1.71666666666667	0.0133630620956212	128.463570279239
Trimmed Mean ( 19 / 24 )	1.71617647058824	0.0131358913278562	130.647888883557
Trimmed Mean ( 20 / 24 )	1.7171875	0.0132076649834297	130.014465248352
Trimmed Mean ( 21 / 24 )	1.71833333333333	0.013235995273542	129.822752110541
Trimmed Mean ( 22 / 24 )	1.71964285714286	0.0131985463250497	130.29032249401
Trimmed Mean ( 23 / 24 )	1.72115384615385	0.0130599437279613	131.788764332029
Trimmed Mean ( 24 / 24 )	1.72291666666667	0.012761456442405	135.009406993828
Median	1.725
Midrange	1.85
Midmean - Weighted Average at Xnp	1.69333333333333
Midmean - Weighted Average at X(n+1)p	1.69333333333333
Midmean - Empirical Distribution Function	1.69333333333333
Midmean - Empirical Distribution Function - Averaging	1.69333333333333
Midmean - Empirical Distribution Function - Interpolation	1.69333333333333
Midmean - Closest Observation	1.69333333333333
Midmean - True Basic - Statistics Graphics Toolkit	1.69333333333333
Midmean - MS Excel (old versions)	1.71020408163265
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