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R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Tue, 27 Oct 2009 09:34:52 -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/2009/Oct/27/t125665777418dzjz75l2w0cmh.htm/, Retrieved Tue, 07 May 2024 14:37:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=51010, Retrieved Tue, 07 May 2024 14:37:16 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

157

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

-     [Univariate Data Series] [] [2009-10-20 12:01:47] [0d317af4a0e6a1186095e8b57838ea16]
-   PD  [Univariate Data Series] [WS3,2] [2009-10-27 15:32:32] [ade6aa003deff66733e677339d38f25a]
- RMPD      [Central Tendency] [Central Tendency 3,2] [2009-10-27 15:34:52] [639ea8fd352c8f9f586ddf87aa833fb6] [Current]

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Dataseries X:

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Histogram

Boxplots

2.8
2.5
2.8
3.4
3.6
3.4
2.5
2.1
2.2
2.8
2.9
2.8
2.3
2.2
2.2
2.5
2.5
2.1
1.2
0.9
1.2
1.7
2.3
2.4
2.3
2.2
2.3
2.4
2.6
2.1
1.4
1.2
1.4
2.1
2.5
2.6
2.7
2.8
3
3.2
2.9
2.3
1.1
0.6
0.9
1.6
2
2.1
2.1
2
1.8
1.8
2
2.1
2.3
2.5
2.7
2.4
2.3
2.5

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	'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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51010&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51010&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51010&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	2.235	0.0812621133951507	27.5035918538315
Geometric Mean	2.12523022544319
Harmonic Mean	1.98065046982324
Quadratic Mean	2.32052436602879
Winsorized Mean ( 1 / 20 )	2.23666666666667	0.0787962640237814	28.3854405329626
Winsorized Mean ( 2 / 20 )	2.23666666666667	0.0787962640237814	28.3854405329626
Winsorized Mean ( 3 / 20 )	2.23666666666667	0.0736830388024022	30.3552446128721
Winsorized Mean ( 4 / 20 )	2.23	0.0692290066896213	32.2119311923381
Winsorized Mean ( 5 / 20 )	2.22166666666667	0.0677354302580345	32.7991814358209
Winsorized Mean ( 6 / 20 )	2.22166666666667	0.0677354302580345	32.7991814358209
Winsorized Mean ( 7 / 20 )	2.23333333333333	0.0600690124136734	37.1794581531186
Winsorized Mean ( 8 / 20 )	2.23333333333333	0.0600690124136734	37.1794581531186
Winsorized Mean ( 9 / 20 )	2.26333333333333	0.0533598098122689	42.4164430363643
Winsorized Mean ( 10 / 20 )	2.28	0.049960436324557	45.6361106454011
Winsorized Mean ( 11 / 20 )	2.29833333333333	0.0464862331037185	49.4411609606089
Winsorized Mean ( 12 / 20 )	2.27833333333333	0.0429880857667653	52.9991808822235
Winsorized Mean ( 13 / 20 )	2.32166666666667	0.0355021815727125	65.3950423275153
Winsorized Mean ( 14 / 20 )	2.29833333333333	0.0314877490899164	72.991350597028
Winsorized Mean ( 15 / 20 )	2.29833333333333	0.0314877490899164	72.991350597028
Winsorized Mean ( 16 / 20 )	2.29833333333333	0.023227159568479	98.9502537560531
Winsorized Mean ( 17 / 20 )	2.29833333333333	0.023227159568479	98.9502537560531
Winsorized Mean ( 18 / 20 )	2.29833333333333	0.023227159568479	98.9502537560531
Winsorized Mean ( 19 / 20 )	2.29833333333333	0.023227159568479	98.9502537560531
Winsorized Mean ( 20 / 20 )	2.29833333333333	0.023227159568479	98.9502537560531
Trimmed Mean ( 1 / 20 )	2.23965517241379	0.0754875123454158	29.6692141895679
Trimmed Mean ( 2 / 20 )	2.24285714285714	0.0713895997580727	31.4171412987019
Trimmed Mean ( 3 / 20 )	2.24629629629630	0.0662309114655965	33.9161314043387
Trimmed Mean ( 4 / 20 )	2.25	0.0624113247255415	36.0511495292648
Trimmed Mean ( 5 / 20 )	2.256	0.059464274989274	37.938745581392
Trimmed Mean ( 6 / 20 )	2.26458333333333	0.0562171561587039	40.2827799922909
Trimmed Mean ( 7 / 20 )	2.27391304347826	0.0519601094308383	43.7626684852341
Trimmed Mean ( 8 / 20 )	2.28181818181818	0.0490148969106538	46.5535648473884
Trimmed Mean ( 9 / 20 )	2.29047619047619	0.045058939825329	50.8328913053707
Trimmed Mean ( 10 / 20 )	2.295	0.0420546043090378	54.5719080635075
Trimmed Mean ( 11 / 20 )	2.29736842105263	0.0391020916564557	58.7530826032766
Trimmed Mean ( 12 / 20 )	2.29722222222222	0.0361842970219129	63.4867169267111
Trimmed Mean ( 13 / 20 )	2.3	0.0332440873008037	69.1852352326242
Trimmed Mean ( 14 / 20 )	2.296875	0.0315858963907382	72.7183731494003
Trimmed Mean ( 15 / 20 )	2.29666666666667	0.0305065786511068	75.2843081137628
Trimmed Mean ( 16 / 20 )	2.29642857142857	0.0288593298977408	79.5731771862223
Trimmed Mean ( 17 / 20 )	2.29615384615385	0.0290785510329781	78.9638329485457
Trimmed Mean ( 18 / 20 )	2.29583333333333	0.0291666666666667	78.7142857142857
Trimmed Mean ( 19 / 20 )	2.29545454545455	0.0290374237758038	79.0515909117011
Trimmed Mean ( 20 / 20 )	2.295	0.0285389853395408	80.4163137790422
Median	2.3
Midrange	2.1
Midmean - Weighted Average at Xnp	2.28787878787879
Midmean - Weighted Average at X(n+1)p	2.28787878787879
Midmean - Empirical Distribution Function	2.28787878787879
Midmean - Empirical Distribution Function - Averaging	2.28787878787879
Midmean - Empirical Distribution Function - Interpolation	2.28787878787879
Midmean - Closest Observation	2.28787878787879
Midmean - True Basic - Statistics Graphics Toolkit	2.28787878787879
Midmean - MS Excel (old versions)	2.28787878787879
Number of observations	60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.235 & 0.0812621133951507 & 27.5035918538315 \tabularnewline
Geometric Mean & 2.12523022544319 &  &  \tabularnewline
Harmonic Mean & 1.98065046982324 &  &  \tabularnewline
Quadratic Mean & 2.32052436602879 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2.23666666666667 & 0.0787962640237814 & 28.3854405329626 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2.23666666666667 & 0.0787962640237814 & 28.3854405329626 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2.23666666666667 & 0.0736830388024022 & 30.3552446128721 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2.23 & 0.0692290066896213 & 32.2119311923381 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2.22166666666667 & 0.0677354302580345 & 32.7991814358209 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2.22166666666667 & 0.0677354302580345 & 32.7991814358209 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2.23333333333333 & 0.0600690124136734 & 37.1794581531186 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2.23333333333333 & 0.0600690124136734 & 37.1794581531186 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2.26333333333333 & 0.0533598098122689 & 42.4164430363643 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2.28 & 0.049960436324557 & 45.6361106454011 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2.29833333333333 & 0.0464862331037185 & 49.4411609606089 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2.27833333333333 & 0.0429880857667653 & 52.9991808822235 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2.32166666666667 & 0.0355021815727125 & 65.3950423275153 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2.29833333333333 & 0.0314877490899164 & 72.991350597028 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2.29833333333333 & 0.0314877490899164 & 72.991350597028 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2.29833333333333 & 0.023227159568479 & 98.9502537560531 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2.29833333333333 & 0.023227159568479 & 98.9502537560531 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2.29833333333333 & 0.023227159568479 & 98.9502537560531 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2.29833333333333 & 0.023227159568479 & 98.9502537560531 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2.29833333333333 & 0.023227159568479 & 98.9502537560531 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2.23965517241379 & 0.0754875123454158 & 29.6692141895679 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2.24285714285714 & 0.0713895997580727 & 31.4171412987019 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2.24629629629630 & 0.0662309114655965 & 33.9161314043387 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2.25 & 0.0624113247255415 & 36.0511495292648 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2.256 & 0.059464274989274 & 37.938745581392 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2.26458333333333 & 0.0562171561587039 & 40.2827799922909 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2.27391304347826 & 0.0519601094308383 & 43.7626684852341 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2.28181818181818 & 0.0490148969106538 & 46.5535648473884 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2.29047619047619 & 0.045058939825329 & 50.8328913053707 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2.295 & 0.0420546043090378 & 54.5719080635075 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2.29736842105263 & 0.0391020916564557 & 58.7530826032766 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2.29722222222222 & 0.0361842970219129 & 63.4867169267111 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2.3 & 0.0332440873008037 & 69.1852352326242 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2.296875 & 0.0315858963907382 & 72.7183731494003 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2.29666666666667 & 0.0305065786511068 & 75.2843081137628 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2.29642857142857 & 0.0288593298977408 & 79.5731771862223 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2.29615384615385 & 0.0290785510329781 & 78.9638329485457 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2.29583333333333 & 0.0291666666666667 & 78.7142857142857 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2.29545454545455 & 0.0290374237758038 & 79.0515909117011 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2.295 & 0.0285389853395408 & 80.4163137790422 \tabularnewline
Median & 2.3 &  &  \tabularnewline
Midrange & 2.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.28787878787879 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.28787878787879 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.28787878787879 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.28787878787879 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.28787878787879 &  &  \tabularnewline
Midmean - Closest Observation & 2.28787878787879 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.28787878787879 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.28787878787879 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51010&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]2.235[/C][C]0.0812621133951507[/C][C]27.5035918538315[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2.12523022544319[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.98065046982324[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.32052436602879[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2.23666666666667[/C][C]0.0787962640237814[/C][C]28.3854405329626[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2.23666666666667[/C][C]0.0787962640237814[/C][C]28.3854405329626[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2.23666666666667[/C][C]0.0736830388024022[/C][C]30.3552446128721[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2.23[/C][C]0.0692290066896213[/C][C]32.2119311923381[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2.22166666666667[/C][C]0.0677354302580345[/C][C]32.7991814358209[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2.22166666666667[/C][C]0.0677354302580345[/C][C]32.7991814358209[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2.23333333333333[/C][C]0.0600690124136734[/C][C]37.1794581531186[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2.23333333333333[/C][C]0.0600690124136734[/C][C]37.1794581531186[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2.26333333333333[/C][C]0.0533598098122689[/C][C]42.4164430363643[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2.28[/C][C]0.049960436324557[/C][C]45.6361106454011[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2.29833333333333[/C][C]0.0464862331037185[/C][C]49.4411609606089[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2.27833333333333[/C][C]0.0429880857667653[/C][C]52.9991808822235[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2.32166666666667[/C][C]0.0355021815727125[/C][C]65.3950423275153[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2.29833333333333[/C][C]0.0314877490899164[/C][C]72.991350597028[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2.29833333333333[/C][C]0.0314877490899164[/C][C]72.991350597028[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2.29833333333333[/C][C]0.023227159568479[/C][C]98.9502537560531[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2.29833333333333[/C][C]0.023227159568479[/C][C]98.9502537560531[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2.29833333333333[/C][C]0.023227159568479[/C][C]98.9502537560531[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2.29833333333333[/C][C]0.023227159568479[/C][C]98.9502537560531[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2.29833333333333[/C][C]0.023227159568479[/C][C]98.9502537560531[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2.23965517241379[/C][C]0.0754875123454158[/C][C]29.6692141895679[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2.24285714285714[/C][C]0.0713895997580727[/C][C]31.4171412987019[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2.24629629629630[/C][C]0.0662309114655965[/C][C]33.9161314043387[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2.25[/C][C]0.0624113247255415[/C][C]36.0511495292648[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2.256[/C][C]0.059464274989274[/C][C]37.938745581392[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2.26458333333333[/C][C]0.0562171561587039[/C][C]40.2827799922909[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2.27391304347826[/C][C]0.0519601094308383[/C][C]43.7626684852341[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2.28181818181818[/C][C]0.0490148969106538[/C][C]46.5535648473884[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2.29047619047619[/C][C]0.045058939825329[/C][C]50.8328913053707[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2.295[/C][C]0.0420546043090378[/C][C]54.5719080635075[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2.29736842105263[/C][C]0.0391020916564557[/C][C]58.7530826032766[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2.29722222222222[/C][C]0.0361842970219129[/C][C]63.4867169267111[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2.3[/C][C]0.0332440873008037[/C][C]69.1852352326242[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2.296875[/C][C]0.0315858963907382[/C][C]72.7183731494003[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2.29666666666667[/C][C]0.0305065786511068[/C][C]75.2843081137628[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2.29642857142857[/C][C]0.0288593298977408[/C][C]79.5731771862223[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2.29615384615385[/C][C]0.0290785510329781[/C][C]78.9638329485457[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2.29583333333333[/C][C]0.0291666666666667[/C][C]78.7142857142857[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2.29545454545455[/C][C]0.0290374237758038[/C][C]79.0515909117011[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2.295[/C][C]0.0285389853395408[/C][C]80.4163137790422[/C][/ROW]
[ROW][C]Median[/C][C]2.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.28787878787879[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.28787878787879[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.28787878787879[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.28787878787879[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.28787878787879[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.28787878787879[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.28787878787879[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.28787878787879[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51010&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51010&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	2.235	0.0812621133951507	27.5035918538315
Geometric Mean	2.12523022544319
Harmonic Mean	1.98065046982324
Quadratic Mean	2.32052436602879
Winsorized Mean ( 1 / 20 )	2.23666666666667	0.0787962640237814	28.3854405329626
Winsorized Mean ( 2 / 20 )	2.23666666666667	0.0787962640237814	28.3854405329626
Winsorized Mean ( 3 / 20 )	2.23666666666667	0.0736830388024022	30.3552446128721
Winsorized Mean ( 4 / 20 )	2.23	0.0692290066896213	32.2119311923381
Winsorized Mean ( 5 / 20 )	2.22166666666667	0.0677354302580345	32.7991814358209
Winsorized Mean ( 6 / 20 )	2.22166666666667	0.0677354302580345	32.7991814358209
Winsorized Mean ( 7 / 20 )	2.23333333333333	0.0600690124136734	37.1794581531186
Winsorized Mean ( 8 / 20 )	2.23333333333333	0.0600690124136734	37.1794581531186
Winsorized Mean ( 9 / 20 )	2.26333333333333	0.0533598098122689	42.4164430363643
Winsorized Mean ( 10 / 20 )	2.28	0.049960436324557	45.6361106454011
Winsorized Mean ( 11 / 20 )	2.29833333333333	0.0464862331037185	49.4411609606089
Winsorized Mean ( 12 / 20 )	2.27833333333333	0.0429880857667653	52.9991808822235
Winsorized Mean ( 13 / 20 )	2.32166666666667	0.0355021815727125	65.3950423275153
Winsorized Mean ( 14 / 20 )	2.29833333333333	0.0314877490899164	72.991350597028
Winsorized Mean ( 15 / 20 )	2.29833333333333	0.0314877490899164	72.991350597028
Winsorized Mean ( 16 / 20 )	2.29833333333333	0.023227159568479	98.9502537560531
Winsorized Mean ( 17 / 20 )	2.29833333333333	0.023227159568479	98.9502537560531
Winsorized Mean ( 18 / 20 )	2.29833333333333	0.023227159568479	98.9502537560531
Winsorized Mean ( 19 / 20 )	2.29833333333333	0.023227159568479	98.9502537560531
Winsorized Mean ( 20 / 20 )	2.29833333333333	0.023227159568479	98.9502537560531
Trimmed Mean ( 1 / 20 )	2.23965517241379	0.0754875123454158	29.6692141895679
Trimmed Mean ( 2 / 20 )	2.24285714285714	0.0713895997580727	31.4171412987019
Trimmed Mean ( 3 / 20 )	2.24629629629630	0.0662309114655965	33.9161314043387
Trimmed Mean ( 4 / 20 )	2.25	0.0624113247255415	36.0511495292648
Trimmed Mean ( 5 / 20 )	2.256	0.059464274989274	37.938745581392
Trimmed Mean ( 6 / 20 )	2.26458333333333	0.0562171561587039	40.2827799922909
Trimmed Mean ( 7 / 20 )	2.27391304347826	0.0519601094308383	43.7626684852341
Trimmed Mean ( 8 / 20 )	2.28181818181818	0.0490148969106538	46.5535648473884
Trimmed Mean ( 9 / 20 )	2.29047619047619	0.045058939825329	50.8328913053707
Trimmed Mean ( 10 / 20 )	2.295	0.0420546043090378	54.5719080635075
Trimmed Mean ( 11 / 20 )	2.29736842105263	0.0391020916564557	58.7530826032766
Trimmed Mean ( 12 / 20 )	2.29722222222222	0.0361842970219129	63.4867169267111
Trimmed Mean ( 13 / 20 )	2.3	0.0332440873008037	69.1852352326242
Trimmed Mean ( 14 / 20 )	2.296875	0.0315858963907382	72.7183731494003
Trimmed Mean ( 15 / 20 )	2.29666666666667	0.0305065786511068	75.2843081137628
Trimmed Mean ( 16 / 20 )	2.29642857142857	0.0288593298977408	79.5731771862223
Trimmed Mean ( 17 / 20 )	2.29615384615385	0.0290785510329781	78.9638329485457
Trimmed Mean ( 18 / 20 )	2.29583333333333	0.0291666666666667	78.7142857142857
Trimmed Mean ( 19 / 20 )	2.29545454545455	0.0290374237758038	79.0515909117011
Trimmed Mean ( 20 / 20 )	2.295	0.0285389853395408	80.4163137790422
Median	2.3
Midrange	2.1
Midmean - Weighted Average at Xnp	2.28787878787879
Midmean - Weighted Average at X(n+1)p	2.28787878787879
Midmean - Empirical Distribution Function	2.28787878787879
Midmean - Empirical Distribution Function - Averaging	2.28787878787879
Midmean - Empirical Distribution Function - Interpolation	2.28787878787879
Midmean - Closest Observation	2.28787878787879
Midmean - True Basic - Statistics Graphics Toolkit	2.28787878787879
Midmean - MS Excel (old versions)	2.28787878787879
Number of observations	60

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