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Author

*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Wed, 26 Feb 2014 10:00:20 -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/2014/Feb/26/t1393427071fpi4g2lxlgwucyl.htm/, Retrieved Wed, 15 May 2024 15:50:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234058, Retrieved Wed, 15 May 2024 15:50:21 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

148

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

-       [Central Tendency] [] [2014-02-26 15:00:20] [c97636ecf0aef6cf672ffb6fe15d6b60] [Current]

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Dataseries X:

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2,79
3,08
3,89
3,7
4,61
5,07
5,22
4,93
5,15
4,8
3,89
3,54
3,34
2,8
1,6
1,53
0,69
-0,11
-0,67
-0,2
-0,62
-0,58
-0,31
-0,25
-0,08
0,13
0,94
1,05
1,59
2,03
2,15
2,06
2,56
2,55
2,53
2,6
2,71
2,82
2,93
2,88
2,89
3,27
3,32
3,14
3,04
3,08
3,39
3,23
3,38
3,41
3,14
2,96
2,73
2,21
2,23
2,56
2,39
2,49
2,17
2,16
1,48
1,09
1,25
1,26
1,39
1,69
1,55
1,19
1,08
0,93
0,98
1,01

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234058&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234058&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234058&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	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	2.24208333333333	0.170215151698555	13.1720549607945
Geometric Mean	NaN
Harmonic Mean	-192.759065625092
Quadratic Mean	2.66158500187806
Winsorized Mean ( 1 / 24 )	2.24180555555556	0.169812025135529	13.2016890662858
Winsorized Mean ( 2 / 24 )	2.24069444444444	0.169019579940672	13.2570110825678
Winsorized Mean ( 3 / 24 )	2.24611111111111	0.165114196214888	13.6033797371845
Winsorized Mean ( 4 / 24 )	2.24222222222222	0.162765158916308	13.7758119560166
Winsorized Mean ( 5 / 24 )	2.2325	0.159168141477325	14.0260480475487
Winsorized Mean ( 6 / 24 )	2.18	0.146223856724648	14.9086479376968
Winsorized Mean ( 7 / 24 )	2.18291666666667	0.145582908728228	14.994319633644
Winsorized Mean ( 8 / 24 )	2.18513888888889	0.137176136310459	15.9294389509809
Winsorized Mean ( 9 / 24 )	2.23513888888889	0.120305589159778	18.5788449605646
Winsorized Mean ( 10 / 24 )	2.25041666666667	0.11180959906762	20.1272223980131
Winsorized Mean ( 11 / 24 )	2.24888888888889	0.11111163927887	20.2399037894184
Winsorized Mean ( 12 / 24 )	2.25388888888889	0.109772769205213	20.5323132978032
Winsorized Mean ( 13 / 24 )	2.25208333333333	0.107855924863537	20.8804786216681
Winsorized Mean ( 14 / 24 )	2.25597222222222	0.106051198940154	21.2724820159299
Winsorized Mean ( 15 / 24 )	2.25180555555556	0.103595632258505	21.7364912638069
Winsorized Mean ( 16 / 24 )	2.24513888888889	0.102021813513255	22.0064593205568
Winsorized Mean ( 17 / 24 )	2.2475	0.0954502447221975	23.5462989805969
Winsorized Mean ( 18 / 24 )	2.2625	0.0931312260945029	24.2936778015161
Winsorized Mean ( 19 / 24 )	2.24930555555556	0.0906536700133494	24.8120738545315
Winsorized Mean ( 20 / 24 )	2.28541666666667	0.0852027264647476	26.8232809147516
Winsorized Mean ( 21 / 24 )	2.3	0.0798318361665802	28.8105611801378
Winsorized Mean ( 22 / 24 )	2.29083333333333	0.0744835505046225	30.7562316486398
Winsorized Mean ( 23 / 24 )	2.28763888888889	0.072359759418348	31.6147940136575
Winsorized Mean ( 24 / 24 )	2.28763888888889	0.068794246838705	33.2533459411582
Trimmed Mean ( 1 / 24 )	2.24114285714286	0.164538823834832	13.6207540865405
Trimmed Mean ( 2 / 24 )	2.24044117647059	0.158263102339273	14.1564340857396
Trimmed Mean ( 3 / 24 )	2.24030303030303	0.151260279805853	14.8109142279687
Trimmed Mean ( 4 / 24 )	2.238125	0.144693654733848	15.4680245247578
Trimmed Mean ( 5 / 24 )	2.23693548387097	0.137651332751385	16.2507361110055
Trimmed Mean ( 6 / 24 )	2.238	0.130287339985326	17.1774172398643
Trimmed Mean ( 7 / 24 )	2.25	0.125222367244507	17.9680359788015
Trimmed Mean ( 8 / 24 )	2.26232142857143	0.119132685786983	18.9899305436344
Trimmed Mean ( 9 / 24 )	2.27518518518518	0.113840504343236	19.985726506669
Trimmed Mean ( 10 / 24 )	2.28134615384615	0.111509601899109	20.4587418033314
Trimmed Mean ( 11 / 24 )	2.2858	0.110425924935946	20.6998492548367
Trimmed Mean ( 12 / 24 )	2.29083333333333	0.109080958179474	21.0012212174021
Trimmed Mean ( 13 / 24 )	2.29565217391304	0.107536602991664	21.3476352241757
Trimmed Mean ( 14 / 24 )	2.30113636363636	0.105836153191214	21.7424414460616
Trimmed Mean ( 15 / 24 )	2.30666666666667	0.103896595307323	22.201561656988
Trimmed Mean ( 16 / 24 )	2.31325	0.101759134599106	22.732602916813
Trimmed Mean ( 17 / 24 )	2.32131578947368	0.0991228752040115	23.4185679611899
Trimmed Mean ( 18 / 24 )	2.33	0.0970256061767627	24.0142792383608
Trimmed Mean ( 19 / 24 )	2.33794117647059	0.0945811475825543	24.7188920437864
Trimmed Mean ( 20 / 24 )	2.3484375	0.0915856171962483	25.6419902152082
Trimmed Mean ( 21 / 24 )	2.356	0.0888322712407665	26.5218930811126
Trimmed Mean ( 22 / 24 )	2.36285714285714	0.0862871071053359	27.3836639345512
Trimmed Mean ( 23 / 24 )	2.37192307692308	0.0839084101969233	28.2680016384108
Trimmed Mean ( 24 / 24 )	2.38291666666667	0.0806056763533839	29.5626409264244
Median	2.51
Midrange	2.275
Midmean - Weighted Average at Xnp	2.32131578947368
Midmean - Weighted Average at X(n+1)p	2.35189189189189
Midmean - Empirical Distribution Function	2.32131578947368
Midmean - Empirical Distribution Function - Averaging	2.35189189189189
Midmean - Empirical Distribution Function - Interpolation	2.35189189189189
Midmean - Closest Observation	2.32131578947368
Midmean - True Basic - Statistics Graphics Toolkit	2.35189189189189
Midmean - MS Excel (old versions)	2.32131578947368
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.24208333333333 & 0.170215151698555 & 13.1720549607945 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -192.759065625092 &  &  \tabularnewline
Quadratic Mean & 2.66158500187806 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 2.24180555555556 & 0.169812025135529 & 13.2016890662858 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 2.24069444444444 & 0.169019579940672 & 13.2570110825678 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 2.24611111111111 & 0.165114196214888 & 13.6033797371845 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 2.24222222222222 & 0.162765158916308 & 13.7758119560166 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 2.2325 & 0.159168141477325 & 14.0260480475487 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 2.18 & 0.146223856724648 & 14.9086479376968 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 2.18291666666667 & 0.145582908728228 & 14.994319633644 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 2.18513888888889 & 0.137176136310459 & 15.9294389509809 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 2.23513888888889 & 0.120305589159778 & 18.5788449605646 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 2.25041666666667 & 0.11180959906762 & 20.1272223980131 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 2.24888888888889 & 0.11111163927887 & 20.2399037894184 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 2.25388888888889 & 0.109772769205213 & 20.5323132978032 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 2.25208333333333 & 0.107855924863537 & 20.8804786216681 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 2.25597222222222 & 0.106051198940154 & 21.2724820159299 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 2.25180555555556 & 0.103595632258505 & 21.7364912638069 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 2.24513888888889 & 0.102021813513255 & 22.0064593205568 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 2.2475 & 0.0954502447221975 & 23.5462989805969 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 2.2625 & 0.0931312260945029 & 24.2936778015161 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 2.24930555555556 & 0.0906536700133494 & 24.8120738545315 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 2.28541666666667 & 0.0852027264647476 & 26.8232809147516 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 2.3 & 0.0798318361665802 & 28.8105611801378 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 2.29083333333333 & 0.0744835505046225 & 30.7562316486398 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 2.28763888888889 & 0.072359759418348 & 31.6147940136575 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 2.28763888888889 & 0.068794246838705 & 33.2533459411582 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 2.24114285714286 & 0.164538823834832 & 13.6207540865405 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 2.24044117647059 & 0.158263102339273 & 14.1564340857396 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 2.24030303030303 & 0.151260279805853 & 14.8109142279687 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 2.238125 & 0.144693654733848 & 15.4680245247578 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 2.23693548387097 & 0.137651332751385 & 16.2507361110055 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 2.238 & 0.130287339985326 & 17.1774172398643 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 2.25 & 0.125222367244507 & 17.9680359788015 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 2.26232142857143 & 0.119132685786983 & 18.9899305436344 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 2.27518518518518 & 0.113840504343236 & 19.985726506669 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 2.28134615384615 & 0.111509601899109 & 20.4587418033314 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 2.2858 & 0.110425924935946 & 20.6998492548367 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 2.29083333333333 & 0.109080958179474 & 21.0012212174021 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 2.29565217391304 & 0.107536602991664 & 21.3476352241757 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 2.30113636363636 & 0.105836153191214 & 21.7424414460616 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 2.30666666666667 & 0.103896595307323 & 22.201561656988 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 2.31325 & 0.101759134599106 & 22.732602916813 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 2.32131578947368 & 0.0991228752040115 & 23.4185679611899 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 2.33 & 0.0970256061767627 & 24.0142792383608 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 2.33794117647059 & 0.0945811475825543 & 24.7188920437864 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 2.3484375 & 0.0915856171962483 & 25.6419902152082 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 2.356 & 0.0888322712407665 & 26.5218930811126 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 2.36285714285714 & 0.0862871071053359 & 27.3836639345512 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 2.37192307692308 & 0.0839084101969233 & 28.2680016384108 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 2.38291666666667 & 0.0806056763533839 & 29.5626409264244 \tabularnewline
Median & 2.51 &  &  \tabularnewline
Midrange & 2.275 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.32131578947368 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.35189189189189 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.32131578947368 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.35189189189189 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.35189189189189 &  &  \tabularnewline
Midmean - Closest Observation & 2.32131578947368 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.35189189189189 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.32131578947368 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234058&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]2.24208333333333[/C][C]0.170215151698555[/C][C]13.1720549607945[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-192.759065625092[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.66158500187806[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]2.24180555555556[/C][C]0.169812025135529[/C][C]13.2016890662858[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]2.24069444444444[/C][C]0.169019579940672[/C][C]13.2570110825678[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]2.24611111111111[/C][C]0.165114196214888[/C][C]13.6033797371845[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]2.24222222222222[/C][C]0.162765158916308[/C][C]13.7758119560166[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]2.2325[/C][C]0.159168141477325[/C][C]14.0260480475487[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]2.18[/C][C]0.146223856724648[/C][C]14.9086479376968[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]2.18291666666667[/C][C]0.145582908728228[/C][C]14.994319633644[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]2.18513888888889[/C][C]0.137176136310459[/C][C]15.9294389509809[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]2.23513888888889[/C][C]0.120305589159778[/C][C]18.5788449605646[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]2.25041666666667[/C][C]0.11180959906762[/C][C]20.1272223980131[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]2.24888888888889[/C][C]0.11111163927887[/C][C]20.2399037894184[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]2.25388888888889[/C][C]0.109772769205213[/C][C]20.5323132978032[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]2.25208333333333[/C][C]0.107855924863537[/C][C]20.8804786216681[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]2.25597222222222[/C][C]0.106051198940154[/C][C]21.2724820159299[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]2.25180555555556[/C][C]0.103595632258505[/C][C]21.7364912638069[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]2.24513888888889[/C][C]0.102021813513255[/C][C]22.0064593205568[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]2.2475[/C][C]0.0954502447221975[/C][C]23.5462989805969[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]2.2625[/C][C]0.0931312260945029[/C][C]24.2936778015161[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]2.24930555555556[/C][C]0.0906536700133494[/C][C]24.8120738545315[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]2.28541666666667[/C][C]0.0852027264647476[/C][C]26.8232809147516[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]2.3[/C][C]0.0798318361665802[/C][C]28.8105611801378[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]2.29083333333333[/C][C]0.0744835505046225[/C][C]30.7562316486398[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]2.28763888888889[/C][C]0.072359759418348[/C][C]31.6147940136575[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]2.28763888888889[/C][C]0.068794246838705[/C][C]33.2533459411582[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]2.24114285714286[/C][C]0.164538823834832[/C][C]13.6207540865405[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]2.24044117647059[/C][C]0.158263102339273[/C][C]14.1564340857396[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]2.24030303030303[/C][C]0.151260279805853[/C][C]14.8109142279687[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]2.238125[/C][C]0.144693654733848[/C][C]15.4680245247578[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]2.23693548387097[/C][C]0.137651332751385[/C][C]16.2507361110055[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]2.238[/C][C]0.130287339985326[/C][C]17.1774172398643[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]2.25[/C][C]0.125222367244507[/C][C]17.9680359788015[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]2.26232142857143[/C][C]0.119132685786983[/C][C]18.9899305436344[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]2.27518518518518[/C][C]0.113840504343236[/C][C]19.985726506669[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]2.28134615384615[/C][C]0.111509601899109[/C][C]20.4587418033314[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]2.2858[/C][C]0.110425924935946[/C][C]20.6998492548367[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]2.29083333333333[/C][C]0.109080958179474[/C][C]21.0012212174021[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]2.29565217391304[/C][C]0.107536602991664[/C][C]21.3476352241757[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]2.30113636363636[/C][C]0.105836153191214[/C][C]21.7424414460616[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]2.30666666666667[/C][C]0.103896595307323[/C][C]22.201561656988[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]2.31325[/C][C]0.101759134599106[/C][C]22.732602916813[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]2.32131578947368[/C][C]0.0991228752040115[/C][C]23.4185679611899[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]2.33[/C][C]0.0970256061767627[/C][C]24.0142792383608[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]2.33794117647059[/C][C]0.0945811475825543[/C][C]24.7188920437864[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]2.3484375[/C][C]0.0915856171962483[/C][C]25.6419902152082[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]2.356[/C][C]0.0888322712407665[/C][C]26.5218930811126[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]2.36285714285714[/C][C]0.0862871071053359[/C][C]27.3836639345512[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]2.37192307692308[/C][C]0.0839084101969233[/C][C]28.2680016384108[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]2.38291666666667[/C][C]0.0806056763533839[/C][C]29.5626409264244[/C][/ROW]
[ROW][C]Median[/C][C]2.51[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.275[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.32131578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.35189189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.32131578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.35189189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.35189189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.32131578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.35189189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.32131578947368[/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=234058&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234058&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	2.24208333333333	0.170215151698555	13.1720549607945
Geometric Mean	NaN
Harmonic Mean	-192.759065625092
Quadratic Mean	2.66158500187806
Winsorized Mean ( 1 / 24 )	2.24180555555556	0.169812025135529	13.2016890662858
Winsorized Mean ( 2 / 24 )	2.24069444444444	0.169019579940672	13.2570110825678
Winsorized Mean ( 3 / 24 )	2.24611111111111	0.165114196214888	13.6033797371845
Winsorized Mean ( 4 / 24 )	2.24222222222222	0.162765158916308	13.7758119560166
Winsorized Mean ( 5 / 24 )	2.2325	0.159168141477325	14.0260480475487
Winsorized Mean ( 6 / 24 )	2.18	0.146223856724648	14.9086479376968
Winsorized Mean ( 7 / 24 )	2.18291666666667	0.145582908728228	14.994319633644
Winsorized Mean ( 8 / 24 )	2.18513888888889	0.137176136310459	15.9294389509809
Winsorized Mean ( 9 / 24 )	2.23513888888889	0.120305589159778	18.5788449605646
Winsorized Mean ( 10 / 24 )	2.25041666666667	0.11180959906762	20.1272223980131
Winsorized Mean ( 11 / 24 )	2.24888888888889	0.11111163927887	20.2399037894184
Winsorized Mean ( 12 / 24 )	2.25388888888889	0.109772769205213	20.5323132978032
Winsorized Mean ( 13 / 24 )	2.25208333333333	0.107855924863537	20.8804786216681
Winsorized Mean ( 14 / 24 )	2.25597222222222	0.106051198940154	21.2724820159299
Winsorized Mean ( 15 / 24 )	2.25180555555556	0.103595632258505	21.7364912638069
Winsorized Mean ( 16 / 24 )	2.24513888888889	0.102021813513255	22.0064593205568
Winsorized Mean ( 17 / 24 )	2.2475	0.0954502447221975	23.5462989805969
Winsorized Mean ( 18 / 24 )	2.2625	0.0931312260945029	24.2936778015161
Winsorized Mean ( 19 / 24 )	2.24930555555556	0.0906536700133494	24.8120738545315
Winsorized Mean ( 20 / 24 )	2.28541666666667	0.0852027264647476	26.8232809147516
Winsorized Mean ( 21 / 24 )	2.3	0.0798318361665802	28.8105611801378
Winsorized Mean ( 22 / 24 )	2.29083333333333	0.0744835505046225	30.7562316486398
Winsorized Mean ( 23 / 24 )	2.28763888888889	0.072359759418348	31.6147940136575
Winsorized Mean ( 24 / 24 )	2.28763888888889	0.068794246838705	33.2533459411582
Trimmed Mean ( 1 / 24 )	2.24114285714286	0.164538823834832	13.6207540865405
Trimmed Mean ( 2 / 24 )	2.24044117647059	0.158263102339273	14.1564340857396
Trimmed Mean ( 3 / 24 )	2.24030303030303	0.151260279805853	14.8109142279687
Trimmed Mean ( 4 / 24 )	2.238125	0.144693654733848	15.4680245247578
Trimmed Mean ( 5 / 24 )	2.23693548387097	0.137651332751385	16.2507361110055
Trimmed Mean ( 6 / 24 )	2.238	0.130287339985326	17.1774172398643
Trimmed Mean ( 7 / 24 )	2.25	0.125222367244507	17.9680359788015
Trimmed Mean ( 8 / 24 )	2.26232142857143	0.119132685786983	18.9899305436344
Trimmed Mean ( 9 / 24 )	2.27518518518518	0.113840504343236	19.985726506669
Trimmed Mean ( 10 / 24 )	2.28134615384615	0.111509601899109	20.4587418033314
Trimmed Mean ( 11 / 24 )	2.2858	0.110425924935946	20.6998492548367
Trimmed Mean ( 12 / 24 )	2.29083333333333	0.109080958179474	21.0012212174021
Trimmed Mean ( 13 / 24 )	2.29565217391304	0.107536602991664	21.3476352241757
Trimmed Mean ( 14 / 24 )	2.30113636363636	0.105836153191214	21.7424414460616
Trimmed Mean ( 15 / 24 )	2.30666666666667	0.103896595307323	22.201561656988
Trimmed Mean ( 16 / 24 )	2.31325	0.101759134599106	22.732602916813
Trimmed Mean ( 17 / 24 )	2.32131578947368	0.0991228752040115	23.4185679611899
Trimmed Mean ( 18 / 24 )	2.33	0.0970256061767627	24.0142792383608
Trimmed Mean ( 19 / 24 )	2.33794117647059	0.0945811475825543	24.7188920437864
Trimmed Mean ( 20 / 24 )	2.3484375	0.0915856171962483	25.6419902152082
Trimmed Mean ( 21 / 24 )	2.356	0.0888322712407665	26.5218930811126
Trimmed Mean ( 22 / 24 )	2.36285714285714	0.0862871071053359	27.3836639345512
Trimmed Mean ( 23 / 24 )	2.37192307692308	0.0839084101969233	28.2680016384108
Trimmed Mean ( 24 / 24 )	2.38291666666667	0.0806056763533839	29.5626409264244
Median	2.51
Midrange	2.275
Midmean - Weighted Average at Xnp	2.32131578947368
Midmean - Weighted Average at X(n+1)p	2.35189189189189
Midmean - Empirical Distribution Function	2.32131578947368
Midmean - Empirical Distribution Function - Averaging	2.35189189189189
Midmean - Empirical Distribution Function - Interpolation	2.35189189189189
Midmean - Closest Observation	2.32131578947368
Midmean - True Basic - Statistics Graphics Toolkit	2.35189189189189
Midmean - MS Excel (old versions)	2.32131578947368
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