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Author

*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Thu, 26 Feb 2015 11:31:32 +0000

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/2015/Feb/26/t1424950335f8x6xyulx25xrh8.htm/, Retrieved Sat, 18 May 2024 05:43:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=277557, Retrieved Sat, 18 May 2024 05:43:10 +0000

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No (this computation is public)

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Estimated Impact

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

-       [Central Tendency] [Robuustheid centr...] [2015-02-26 11:31:32] [d7b65c9a7c286d706dc95a87d306e880] [Current]

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

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	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277557&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=277557&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277557&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	'Gertrude Mary Cox' @ cox.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	2.04861111111111	0.08718769563741	23.4965621712349
Geometric Mean	1.84619921954584
Harmonic Mean	1.49592756650543
Quadratic Mean	2.17635653737566
Winsorized Mean ( 1 / 24 )	2.05	0.086783056552177	23.6221225829661
Winsorized Mean ( 2 / 24 )	2.05	0.0855114411805225	23.9734001871429
Winsorized Mean ( 3 / 24 )	2.0625	0.0823519086266985	25.0449568734262
Winsorized Mean ( 4 / 24 )	2.0625	0.0801367546901493	25.7372538727667
Winsorized Mean ( 5 / 24 )	2.0625	0.0801367546901493	25.7372538727667
Winsorized Mean ( 6 / 24 )	2.05416666666667	0.0788199722669896	26.0614994852893
Winsorized Mean ( 7 / 24 )	2.07361111111111	0.0746665266481845	27.7716294596319
Winsorized Mean ( 8 / 24 )	2.07361111111111	0.0746665266481845	27.7716294596319
Winsorized Mean ( 9 / 24 )	2.07361111111111	0.0746665266481845	27.7716294596319
Winsorized Mean ( 10 / 24 )	2.07361111111111	0.0697915815094584	29.7114790389166
Winsorized Mean ( 11 / 24 )	2.07361111111111	0.0697915815094584	29.7114790389166
Winsorized Mean ( 12 / 24 )	2.12361111111111	0.0606270396154511	35.0274584505673
Winsorized Mean ( 13 / 24 )	2.14166666666667	0.0576926588007453	37.1219963022227
Winsorized Mean ( 14 / 24 )	2.12222222222222	0.0546801133633292	38.8115914852048
Winsorized Mean ( 15 / 24 )	2.12222222222222	0.0484187452473032	43.8305910527581
Winsorized Mean ( 16 / 24 )	2.12222222222222	0.0484187452473032	43.8305910527581
Winsorized Mean ( 17 / 24 )	2.12222222222222	0.0484187452473032	43.8305910527581
Winsorized Mean ( 18 / 24 )	2.12222222222222	0.0484187452473032	43.8305910527581
Winsorized Mean ( 19 / 24 )	2.12222222222222	0.0484187452473032	43.8305910527581
Winsorized Mean ( 20 / 24 )	2.12222222222222	0.0484187452473032	43.8305910527581
Winsorized Mean ( 21 / 24 )	2.12222222222222	0.0400616808384888	52.9738687395094
Winsorized Mean ( 22 / 24 )	2.15277777777778	0.0356568271179341	60.3749113923546
Winsorized Mean ( 23 / 24 )	2.18472222222222	0.0313780847526956	69.6257352684516
Winsorized Mean ( 24 / 24 )	2.15138888888889	0.0268299764292457	80.1860148689431
Trimmed Mean ( 1 / 24 )	2.05857142857143	0.084036195916962	24.4962471957387
Trimmed Mean ( 2 / 24 )	2.06764705882353	0.0807515503910883	25.6050447181472
Trimmed Mean ( 3 / 24 )	2.07727272727273	0.0776338742824892	26.7572982344547
Trimmed Mean ( 4 / 24 )	2.0828125	0.0753811310485241	27.6304225079783
Trimmed Mean ( 5 / 24 )	2.08870967741935	0.0734834271098451	28.4242278779009
Trimmed Mean ( 6 / 24 )	2.095	0.071165637934321	29.4383646491511
Trimmed Mean ( 7 / 24 )	2.10344827586207	0.0686912270803651	30.6217892046265
Trimmed Mean ( 8 / 24 )	2.10892857142857	0.0668044629562426	31.5686778712664
Trimmed Mean ( 9 / 24 )	2.11481481481481	0.064449906192003	32.8133109847292
Trimmed Mean ( 10 / 24 )	2.12115384615385	0.0614883610159998	34.496835028696
Trimmed Mean ( 11 / 24 )	2.128	0.0589735326313458	36.083983866161
Trimmed Mean ( 12 / 24 )	2.13541666666667	0.055742059140387	38.3088945689752
Trimmed Mean ( 13 / 24 )	2.13695652173913	0.0539599686699463	39.6026271773826
Trimmed Mean ( 14 / 24 )	2.13636363636364	0.0523335889830299	40.8220356730434
Trimmed Mean ( 15 / 24 )	2.13809523809524	0.0508867227049129	42.0167604523058
Trimmed Mean ( 16 / 24 )	2.14	0.0503576949025413	42.4959880340354
Trimmed Mean ( 17 / 24 )	2.14210526315789	0.0495544270151989	43.2273238171211
Trimmed Mean ( 18 / 24 )	2.14444444444444	0.0483775568528907	44.3272580086133
Trimmed Mean ( 19 / 24 )	2.14705882352941	0.0466784987771286	45.9967411073087
Trimmed Mean ( 20 / 24 )	2.15	0.0442226770027587	48.617590469837
Trimmed Mean ( 21 / 24 )	2.15333333333333	0.0406083999388534	53.0267958495223
Trimmed Mean ( 22 / 24 )	2.15714285714286	0.0382931367676661	56.3323623820837
Trimmed Mean ( 23 / 24 )	2.15769230769231	0.0364472545860989	59.2004070593361
Trimmed Mean ( 24 / 24 )	2.15416666666667	0.0350874511336053	61.3942192171233
Median	2.15
Midrange	1.7
Midmean - Weighted Average at Xnp	2.13809523809524
Midmean - Weighted Average at X(n+1)p	2.13809523809524
Midmean - Empirical Distribution Function	2.13809523809524
Midmean - Empirical Distribution Function - Averaging	2.13809523809524
Midmean - Empirical Distribution Function - Interpolation	2.13809523809524
Midmean - Closest Observation	2.13809523809524
Midmean - True Basic - Statistics Graphics Toolkit	2.13809523809524
Midmean - MS Excel (old versions)	2.13809523809524
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.04861111111111 & 0.08718769563741 & 23.4965621712349 \tabularnewline
Geometric Mean & 1.84619921954584 &  &  \tabularnewline
Harmonic Mean & 1.49592756650543 &  &  \tabularnewline
Quadratic Mean & 2.17635653737566 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 2.05 & 0.086783056552177 & 23.6221225829661 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 2.05 & 0.0855114411805225 & 23.9734001871429 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 2.0625 & 0.0823519086266985 & 25.0449568734262 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 2.0625 & 0.0801367546901493 & 25.7372538727667 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 2.0625 & 0.0801367546901493 & 25.7372538727667 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 2.05416666666667 & 0.0788199722669896 & 26.0614994852893 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 2.07361111111111 & 0.0746665266481845 & 27.7716294596319 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 2.07361111111111 & 0.0746665266481845 & 27.7716294596319 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 2.07361111111111 & 0.0746665266481845 & 27.7716294596319 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 2.07361111111111 & 0.0697915815094584 & 29.7114790389166 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 2.07361111111111 & 0.0697915815094584 & 29.7114790389166 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 2.12361111111111 & 0.0606270396154511 & 35.0274584505673 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 2.14166666666667 & 0.0576926588007453 & 37.1219963022227 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 2.12222222222222 & 0.0546801133633292 & 38.8115914852048 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 2.12222222222222 & 0.0484187452473032 & 43.8305910527581 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 2.12222222222222 & 0.0484187452473032 & 43.8305910527581 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 2.12222222222222 & 0.0484187452473032 & 43.8305910527581 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 2.12222222222222 & 0.0484187452473032 & 43.8305910527581 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 2.12222222222222 & 0.0484187452473032 & 43.8305910527581 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 2.12222222222222 & 0.0484187452473032 & 43.8305910527581 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 2.12222222222222 & 0.0400616808384888 & 52.9738687395094 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 2.15277777777778 & 0.0356568271179341 & 60.3749113923546 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 2.18472222222222 & 0.0313780847526956 & 69.6257352684516 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 2.15138888888889 & 0.0268299764292457 & 80.1860148689431 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 2.05857142857143 & 0.084036195916962 & 24.4962471957387 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 2.06764705882353 & 0.0807515503910883 & 25.6050447181472 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 2.07727272727273 & 0.0776338742824892 & 26.7572982344547 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 2.0828125 & 0.0753811310485241 & 27.6304225079783 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 2.08870967741935 & 0.0734834271098451 & 28.4242278779009 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 2.095 & 0.071165637934321 & 29.4383646491511 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 2.10344827586207 & 0.0686912270803651 & 30.6217892046265 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 2.10892857142857 & 0.0668044629562426 & 31.5686778712664 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 2.11481481481481 & 0.064449906192003 & 32.8133109847292 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 2.12115384615385 & 0.0614883610159998 & 34.496835028696 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 2.128 & 0.0589735326313458 & 36.083983866161 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 2.13541666666667 & 0.055742059140387 & 38.3088945689752 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 2.13695652173913 & 0.0539599686699463 & 39.6026271773826 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 2.13636363636364 & 0.0523335889830299 & 40.8220356730434 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 2.13809523809524 & 0.0508867227049129 & 42.0167604523058 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 2.14 & 0.0503576949025413 & 42.4959880340354 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 2.14210526315789 & 0.0495544270151989 & 43.2273238171211 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 2.14444444444444 & 0.0483775568528907 & 44.3272580086133 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 2.14705882352941 & 0.0466784987771286 & 45.9967411073087 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 2.15 & 0.0442226770027587 & 48.617590469837 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 2.15333333333333 & 0.0406083999388534 & 53.0267958495223 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 2.15714285714286 & 0.0382931367676661 & 56.3323623820837 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 2.15769230769231 & 0.0364472545860989 & 59.2004070593361 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 2.15416666666667 & 0.0350874511336053 & 61.3942192171233 \tabularnewline
Median & 2.15 &  &  \tabularnewline
Midrange & 1.7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.13809523809524 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.13809523809524 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.13809523809524 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.13809523809524 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.13809523809524 &  &  \tabularnewline
Midmean - Closest Observation & 2.13809523809524 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.13809523809524 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.13809523809524 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277557&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]2.04861111111111[/C][C]0.08718769563741[/C][C]23.4965621712349[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.84619921954584[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.49592756650543[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.17635653737566[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]2.05[/C][C]0.086783056552177[/C][C]23.6221225829661[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]2.05[/C][C]0.0855114411805225[/C][C]23.9734001871429[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]2.0625[/C][C]0.0823519086266985[/C][C]25.0449568734262[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]2.0625[/C][C]0.0801367546901493[/C][C]25.7372538727667[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]2.0625[/C][C]0.0801367546901493[/C][C]25.7372538727667[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]2.05416666666667[/C][C]0.0788199722669896[/C][C]26.0614994852893[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]2.07361111111111[/C][C]0.0746665266481845[/C][C]27.7716294596319[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]2.07361111111111[/C][C]0.0746665266481845[/C][C]27.7716294596319[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]2.07361111111111[/C][C]0.0746665266481845[/C][C]27.7716294596319[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]2.07361111111111[/C][C]0.0697915815094584[/C][C]29.7114790389166[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]2.07361111111111[/C][C]0.0697915815094584[/C][C]29.7114790389166[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]2.12361111111111[/C][C]0.0606270396154511[/C][C]35.0274584505673[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]2.14166666666667[/C][C]0.0576926588007453[/C][C]37.1219963022227[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]2.12222222222222[/C][C]0.0546801133633292[/C][C]38.8115914852048[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]2.12222222222222[/C][C]0.0484187452473032[/C][C]43.8305910527581[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]2.12222222222222[/C][C]0.0484187452473032[/C][C]43.8305910527581[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]2.12222222222222[/C][C]0.0484187452473032[/C][C]43.8305910527581[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]2.12222222222222[/C][C]0.0484187452473032[/C][C]43.8305910527581[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]2.12222222222222[/C][C]0.0484187452473032[/C][C]43.8305910527581[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]2.12222222222222[/C][C]0.0484187452473032[/C][C]43.8305910527581[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]2.12222222222222[/C][C]0.0400616808384888[/C][C]52.9738687395094[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]2.15277777777778[/C][C]0.0356568271179341[/C][C]60.3749113923546[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]2.18472222222222[/C][C]0.0313780847526956[/C][C]69.6257352684516[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]2.15138888888889[/C][C]0.0268299764292457[/C][C]80.1860148689431[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]2.05857142857143[/C][C]0.084036195916962[/C][C]24.4962471957387[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]2.06764705882353[/C][C]0.0807515503910883[/C][C]25.6050447181472[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]2.07727272727273[/C][C]0.0776338742824892[/C][C]26.7572982344547[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]2.0828125[/C][C]0.0753811310485241[/C][C]27.6304225079783[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]2.08870967741935[/C][C]0.0734834271098451[/C][C]28.4242278779009[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]2.095[/C][C]0.071165637934321[/C][C]29.4383646491511[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]2.10344827586207[/C][C]0.0686912270803651[/C][C]30.6217892046265[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]2.10892857142857[/C][C]0.0668044629562426[/C][C]31.5686778712664[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]2.11481481481481[/C][C]0.064449906192003[/C][C]32.8133109847292[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]2.12115384615385[/C][C]0.0614883610159998[/C][C]34.496835028696[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]2.128[/C][C]0.0589735326313458[/C][C]36.083983866161[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]2.13541666666667[/C][C]0.055742059140387[/C][C]38.3088945689752[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]2.13695652173913[/C][C]0.0539599686699463[/C][C]39.6026271773826[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]2.13636363636364[/C][C]0.0523335889830299[/C][C]40.8220356730434[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]2.13809523809524[/C][C]0.0508867227049129[/C][C]42.0167604523058[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]2.14[/C][C]0.0503576949025413[/C][C]42.4959880340354[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]2.14210526315789[/C][C]0.0495544270151989[/C][C]43.2273238171211[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]2.14444444444444[/C][C]0.0483775568528907[/C][C]44.3272580086133[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]2.14705882352941[/C][C]0.0466784987771286[/C][C]45.9967411073087[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]2.15[/C][C]0.0442226770027587[/C][C]48.617590469837[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]2.15333333333333[/C][C]0.0406083999388534[/C][C]53.0267958495223[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]2.15714285714286[/C][C]0.0382931367676661[/C][C]56.3323623820837[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]2.15769230769231[/C][C]0.0364472545860989[/C][C]59.2004070593361[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]2.15416666666667[/C][C]0.0350874511336053[/C][C]61.3942192171233[/C][/ROW]
[ROW][C]Median[/C][C]2.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.13809523809524[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.13809523809524[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.13809523809524[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.13809523809524[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.13809523809524[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.13809523809524[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.13809523809524[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.13809523809524[/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=277557&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277557&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	2.04861111111111	0.08718769563741	23.4965621712349
Geometric Mean	1.84619921954584
Harmonic Mean	1.49592756650543
Quadratic Mean	2.17635653737566
Winsorized Mean ( 1 / 24 )	2.05	0.086783056552177	23.6221225829661
Winsorized Mean ( 2 / 24 )	2.05	0.0855114411805225	23.9734001871429
Winsorized Mean ( 3 / 24 )	2.0625	0.0823519086266985	25.0449568734262
Winsorized Mean ( 4 / 24 )	2.0625	0.0801367546901493	25.7372538727667
Winsorized Mean ( 5 / 24 )	2.0625	0.0801367546901493	25.7372538727667
Winsorized Mean ( 6 / 24 )	2.05416666666667	0.0788199722669896	26.0614994852893
Winsorized Mean ( 7 / 24 )	2.07361111111111	0.0746665266481845	27.7716294596319
Winsorized Mean ( 8 / 24 )	2.07361111111111	0.0746665266481845	27.7716294596319
Winsorized Mean ( 9 / 24 )	2.07361111111111	0.0746665266481845	27.7716294596319
Winsorized Mean ( 10 / 24 )	2.07361111111111	0.0697915815094584	29.7114790389166
Winsorized Mean ( 11 / 24 )	2.07361111111111	0.0697915815094584	29.7114790389166
Winsorized Mean ( 12 / 24 )	2.12361111111111	0.0606270396154511	35.0274584505673
Winsorized Mean ( 13 / 24 )	2.14166666666667	0.0576926588007453	37.1219963022227
Winsorized Mean ( 14 / 24 )	2.12222222222222	0.0546801133633292	38.8115914852048
Winsorized Mean ( 15 / 24 )	2.12222222222222	0.0484187452473032	43.8305910527581
Winsorized Mean ( 16 / 24 )	2.12222222222222	0.0484187452473032	43.8305910527581
Winsorized Mean ( 17 / 24 )	2.12222222222222	0.0484187452473032	43.8305910527581
Winsorized Mean ( 18 / 24 )	2.12222222222222	0.0484187452473032	43.8305910527581
Winsorized Mean ( 19 / 24 )	2.12222222222222	0.0484187452473032	43.8305910527581
Winsorized Mean ( 20 / 24 )	2.12222222222222	0.0484187452473032	43.8305910527581
Winsorized Mean ( 21 / 24 )	2.12222222222222	0.0400616808384888	52.9738687395094
Winsorized Mean ( 22 / 24 )	2.15277777777778	0.0356568271179341	60.3749113923546
Winsorized Mean ( 23 / 24 )	2.18472222222222	0.0313780847526956	69.6257352684516
Winsorized Mean ( 24 / 24 )	2.15138888888889	0.0268299764292457	80.1860148689431
Trimmed Mean ( 1 / 24 )	2.05857142857143	0.084036195916962	24.4962471957387
Trimmed Mean ( 2 / 24 )	2.06764705882353	0.0807515503910883	25.6050447181472
Trimmed Mean ( 3 / 24 )	2.07727272727273	0.0776338742824892	26.7572982344547
Trimmed Mean ( 4 / 24 )	2.0828125	0.0753811310485241	27.6304225079783
Trimmed Mean ( 5 / 24 )	2.08870967741935	0.0734834271098451	28.4242278779009
Trimmed Mean ( 6 / 24 )	2.095	0.071165637934321	29.4383646491511
Trimmed Mean ( 7 / 24 )	2.10344827586207	0.0686912270803651	30.6217892046265
Trimmed Mean ( 8 / 24 )	2.10892857142857	0.0668044629562426	31.5686778712664
Trimmed Mean ( 9 / 24 )	2.11481481481481	0.064449906192003	32.8133109847292
Trimmed Mean ( 10 / 24 )	2.12115384615385	0.0614883610159998	34.496835028696
Trimmed Mean ( 11 / 24 )	2.128	0.0589735326313458	36.083983866161
Trimmed Mean ( 12 / 24 )	2.13541666666667	0.055742059140387	38.3088945689752
Trimmed Mean ( 13 / 24 )	2.13695652173913	0.0539599686699463	39.6026271773826
Trimmed Mean ( 14 / 24 )	2.13636363636364	0.0523335889830299	40.8220356730434
Trimmed Mean ( 15 / 24 )	2.13809523809524	0.0508867227049129	42.0167604523058
Trimmed Mean ( 16 / 24 )	2.14	0.0503576949025413	42.4959880340354
Trimmed Mean ( 17 / 24 )	2.14210526315789	0.0495544270151989	43.2273238171211
Trimmed Mean ( 18 / 24 )	2.14444444444444	0.0483775568528907	44.3272580086133
Trimmed Mean ( 19 / 24 )	2.14705882352941	0.0466784987771286	45.9967411073087
Trimmed Mean ( 20 / 24 )	2.15	0.0442226770027587	48.617590469837
Trimmed Mean ( 21 / 24 )	2.15333333333333	0.0406083999388534	53.0267958495223
Trimmed Mean ( 22 / 24 )	2.15714285714286	0.0382931367676661	56.3323623820837
Trimmed Mean ( 23 / 24 )	2.15769230769231	0.0364472545860989	59.2004070593361
Trimmed Mean ( 24 / 24 )	2.15416666666667	0.0350874511336053	61.3942192171233
Median	2.15
Midrange	1.7
Midmean - Weighted Average at Xnp	2.13809523809524
Midmean - Weighted Average at X(n+1)p	2.13809523809524
Midmean - Empirical Distribution Function	2.13809523809524
Midmean - Empirical Distribution Function - Averaging	2.13809523809524
Midmean - Empirical Distribution Function - Interpolation	2.13809523809524
Midmean - Closest Observation	2.13809523809524
Midmean - True Basic - Statistics Graphics Toolkit	2.13809523809524
Midmean - MS Excel (old versions)	2.13809523809524
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