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Author

*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Sat, 19 Apr 2008 11:48:36 -0600

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Apr/19/t1208627616p6s3bw3hg8i5lp8.htm/, Retrieved Mon, 13 May 2024 20:36:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10287, Retrieved Mon, 13 May 2024 20:36:45 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

189

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

-       [Central Tendency] [Opgave5,oef1-Grie...] [2008-04-19 17:48:36] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,44
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,57
1,58
1,58
1,58
1,58
1,59
1,6
1,6
1,61
1,61
1,61
1,62
1,63
1,63
1,64
1,64
1,64
1,64
1,64
1,65
1,65
1,65
1,65

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	12 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 12 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10287&T=0

[TABLE]
[ROW][C]Summary of compuational 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]12 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10287&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10287&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	12 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.50958904109589	0.00907737405823762	166.302394438175
Geometric Mean	1.50766653889831
Harmonic Mean	1.50578794474883
Quadratic Mean	1.51155277143139
Winsorized Mean ( 1 / 24 )	1.50958904109589	0.00907737405823762	166.302394438175
Winsorized Mean ( 2 / 24 )	1.50958904109589	0.00907737405823762	166.302394438175
Winsorized Mean ( 3 / 24 )	1.50958904109589	0.00907737405823762	166.302394438175
Winsorized Mean ( 4 / 24 )	1.50904109589041	0.00896289574498816	168.365351871267
Winsorized Mean ( 5 / 24 )	1.50904109589041	0.00896289574498816	168.365351871267
Winsorized Mean ( 6 / 24 )	1.50904109589041	0.00896289574498816	168.365351871267
Winsorized Mean ( 7 / 24 )	1.50904109589041	0.00896289574498816	168.365351871267
Winsorized Mean ( 8 / 24 )	1.50904109589041	0.00896289574498816	168.365351871267
Winsorized Mean ( 9 / 24 )	1.50780821917808	0.00871772494021663	172.958911816804
Winsorized Mean ( 10 / 24 )	1.50780821917808	0.00871772494021663	172.958911816804
Winsorized Mean ( 11 / 24 )	1.50630136986301	0.00842982232695588	178.687202581523
Winsorized Mean ( 12 / 24 )	1.50465753424658	0.00812778974886197	185.125056225434
Winsorized Mean ( 13 / 24 )	1.50465753424658	0.00812778974886197	185.125056225434
Winsorized Mean ( 14 / 24 )	1.50465753424658	0.00812778974886197	185.125056225434
Winsorized Mean ( 15 / 24 )	1.50260273972603	0.00776369854621165	193.542128250102
Winsorized Mean ( 16 / 24 )	1.50260273972603	0.00776369854621165	193.542128250102
Winsorized Mean ( 17 / 24 )	1.50027397260274	0.00736360657412714	203.741734094556
Winsorized Mean ( 18 / 24 )	1.49780821917808	0.00695234533137119	215.439272330086
Winsorized Mean ( 19 / 24 )	1.50041095890411	0.00661060433365809	226.970316656939
Winsorized Mean ( 20 / 24 )	1.5113698630137	0.00545255957829333	277.185391798463
Winsorized Mean ( 21 / 24 )	1.5113698630137	0.00545255957829333	277.185391798463
Winsorized Mean ( 22 / 24 )	1.50835616438356	0.00492722416778705	306.126961757660
Winsorized Mean ( 23 / 24 )	1.48	0	Inf
Winsorized Mean ( 24 / 24 )	1.48	0	Inf
Trimmed Mean ( 1 / 24 )	1.50873239436620	0.00904922726997691	166.724997544464
Trimmed Mean ( 2 / 24 )	1.50782608695652	0.00900854374524254	167.377339734051
Trimmed Mean ( 3 / 24 )	1.50686567164179	0.00895288677478754	168.310591828919
Trimmed Mean ( 4 / 24 )	1.50584615384615	0.0088792441306319	169.591705295188
Trimmed Mean ( 5 / 24 )	1.50492063492063	0.00882460663873283	170.536851842807
Trimmed Mean ( 6 / 24 )	1.50393442622951	0.00875057746267671	171.866877659691
Trimmed Mean ( 7 / 24 )	1.50288135593220	0.0086528301585119	173.686681513539
Trimmed Mean ( 8 / 24 )	1.50175438596491	0.00852580781720632	176.142181264531
Trimmed Mean ( 9 / 24 )	1.50054545454545	0.00836224552920965	179.442884008128
Trimmed Mean ( 10 / 24 )	1.49943396226415	0.00821259208014521	182.577430807648
Trimmed Mean ( 11 / 24 )	1.49823529411765	0.00801814551124177	186.855587993141
Trimmed Mean ( 12 / 24 )	1.49714285714286	0.00783546793900207	191.072552245493
Trimmed Mean ( 13 / 24 )	1.49617021276596	0.00766766455276593	195.127238870439
Trimmed Mean ( 14 / 24 )	1.49511111111111	0.00744421829899237	200.841922020676
Trimmed Mean ( 15 / 24 )	1.49395348837209	0.00714615288771118	209.057028564440
Trimmed Mean ( 16 / 24 )	1.49292682926829	0.00684536430678193	218.093115627053
Trimmed Mean ( 17 / 24 )	1.49179487179487	0.00643530867080215	231.814035364510
Trimmed Mean ( 18 / 24 )	1.49081081081081	0.0059952230530826	248.666446204078
Trimmed Mean ( 19 / 24 )	1.49	0.00551544812932068	270.150306024820
Trimmed Mean ( 20 / 24 )	1.48878787878788	0.00491899487295392	302.660994215235
Trimmed Mean ( 21 / 24 )	1.48612903225806	0.00426734082429773	348.256465430702
Trimmed Mean ( 22 / 24 )	1.48310344827586	0.00310344827586207	477.888888888888
Trimmed Mean ( 23 / 24 )	1.48	0	Inf
Trimmed Mean ( 24 / 24 )	1.48	0	Inf
Median	1.48
Midrange	1.54
Midmean - Weighted Average at Xnp	1.47090909090909
Midmean - Weighted Average at X(n+1)p	1.47090909090909
Midmean - Empirical Distribution Function	1.47090909090909
Midmean - Empirical Distribution Function - Averaging	1.47090909090909
Midmean - Empirical Distribution Function - Interpolation	1.47090909090909
Midmean - Closest Observation	1.47090909090909
Midmean - True Basic - Statistics Graphics Toolkit	1.47090909090909
Midmean - MS Excel (old versions)	1.47090909090909
Number of observations	73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.50958904109589 & 0.00907737405823762 & 166.302394438175 \tabularnewline
Geometric Mean & 1.50766653889831 &  &  \tabularnewline
Harmonic Mean & 1.50578794474883 &  &  \tabularnewline
Quadratic Mean & 1.51155277143139 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.50958904109589 & 0.00907737405823762 & 166.302394438175 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.50958904109589 & 0.00907737405823762 & 166.302394438175 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.50958904109589 & 0.00907737405823762 & 166.302394438175 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.50904109589041 & 0.00896289574498816 & 168.365351871267 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.50904109589041 & 0.00896289574498816 & 168.365351871267 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.50904109589041 & 0.00896289574498816 & 168.365351871267 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.50904109589041 & 0.00896289574498816 & 168.365351871267 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.50904109589041 & 0.00896289574498816 & 168.365351871267 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.50780821917808 & 0.00871772494021663 & 172.958911816804 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.50780821917808 & 0.00871772494021663 & 172.958911816804 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.50630136986301 & 0.00842982232695588 & 178.687202581523 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.50465753424658 & 0.00812778974886197 & 185.125056225434 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.50465753424658 & 0.00812778974886197 & 185.125056225434 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.50465753424658 & 0.00812778974886197 & 185.125056225434 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.50260273972603 & 0.00776369854621165 & 193.542128250102 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.50260273972603 & 0.00776369854621165 & 193.542128250102 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.50027397260274 & 0.00736360657412714 & 203.741734094556 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.49780821917808 & 0.00695234533137119 & 215.439272330086 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.50041095890411 & 0.00661060433365809 & 226.970316656939 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.5113698630137 & 0.00545255957829333 & 277.185391798463 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.5113698630137 & 0.00545255957829333 & 277.185391798463 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.50835616438356 & 0.00492722416778705 & 306.126961757660 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.48 & 0 & Inf \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.48 & 0 & Inf \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.50873239436620 & 0.00904922726997691 & 166.724997544464 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.50782608695652 & 0.00900854374524254 & 167.377339734051 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.50686567164179 & 0.00895288677478754 & 168.310591828919 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.50584615384615 & 0.0088792441306319 & 169.591705295188 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.50492063492063 & 0.00882460663873283 & 170.536851842807 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.50393442622951 & 0.00875057746267671 & 171.866877659691 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.50288135593220 & 0.0086528301585119 & 173.686681513539 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.50175438596491 & 0.00852580781720632 & 176.142181264531 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.50054545454545 & 0.00836224552920965 & 179.442884008128 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.49943396226415 & 0.00821259208014521 & 182.577430807648 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.49823529411765 & 0.00801814551124177 & 186.855587993141 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.49714285714286 & 0.00783546793900207 & 191.072552245493 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.49617021276596 & 0.00766766455276593 & 195.127238870439 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.49511111111111 & 0.00744421829899237 & 200.841922020676 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.49395348837209 & 0.00714615288771118 & 209.057028564440 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.49292682926829 & 0.00684536430678193 & 218.093115627053 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.49179487179487 & 0.00643530867080215 & 231.814035364510 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.49081081081081 & 0.0059952230530826 & 248.666446204078 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.49 & 0.00551544812932068 & 270.150306024820 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.48878787878788 & 0.00491899487295392 & 302.660994215235 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.48612903225806 & 0.00426734082429773 & 348.256465430702 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.48310344827586 & 0.00310344827586207 & 477.888888888888 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.48 & 0 & Inf \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.48 & 0 & Inf \tabularnewline
Median & 1.48 &  &  \tabularnewline
Midrange & 1.54 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.47090909090909 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.47090909090909 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.47090909090909 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.47090909090909 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.47090909090909 &  &  \tabularnewline
Midmean - Closest Observation & 1.47090909090909 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.47090909090909 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.47090909090909 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10287&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]1.50958904109589[/C][C]0.00907737405823762[/C][C]166.302394438175[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.50766653889831[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.50578794474883[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.51155277143139[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.50958904109589[/C][C]0.00907737405823762[/C][C]166.302394438175[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.50958904109589[/C][C]0.00907737405823762[/C][C]166.302394438175[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.50958904109589[/C][C]0.00907737405823762[/C][C]166.302394438175[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.50904109589041[/C][C]0.00896289574498816[/C][C]168.365351871267[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.50904109589041[/C][C]0.00896289574498816[/C][C]168.365351871267[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.50904109589041[/C][C]0.00896289574498816[/C][C]168.365351871267[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.50904109589041[/C][C]0.00896289574498816[/C][C]168.365351871267[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.50904109589041[/C][C]0.00896289574498816[/C][C]168.365351871267[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.50780821917808[/C][C]0.00871772494021663[/C][C]172.958911816804[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.50780821917808[/C][C]0.00871772494021663[/C][C]172.958911816804[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.50630136986301[/C][C]0.00842982232695588[/C][C]178.687202581523[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.50465753424658[/C][C]0.00812778974886197[/C][C]185.125056225434[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.50465753424658[/C][C]0.00812778974886197[/C][C]185.125056225434[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.50465753424658[/C][C]0.00812778974886197[/C][C]185.125056225434[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.50260273972603[/C][C]0.00776369854621165[/C][C]193.542128250102[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.50260273972603[/C][C]0.00776369854621165[/C][C]193.542128250102[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.50027397260274[/C][C]0.00736360657412714[/C][C]203.741734094556[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.49780821917808[/C][C]0.00695234533137119[/C][C]215.439272330086[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.50041095890411[/C][C]0.00661060433365809[/C][C]226.970316656939[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.5113698630137[/C][C]0.00545255957829333[/C][C]277.185391798463[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.5113698630137[/C][C]0.00545255957829333[/C][C]277.185391798463[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.50835616438356[/C][C]0.00492722416778705[/C][C]306.126961757660[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.48[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.48[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.50873239436620[/C][C]0.00904922726997691[/C][C]166.724997544464[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.50782608695652[/C][C]0.00900854374524254[/C][C]167.377339734051[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.50686567164179[/C][C]0.00895288677478754[/C][C]168.310591828919[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.50584615384615[/C][C]0.0088792441306319[/C][C]169.591705295188[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.50492063492063[/C][C]0.00882460663873283[/C][C]170.536851842807[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.50393442622951[/C][C]0.00875057746267671[/C][C]171.866877659691[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.50288135593220[/C][C]0.0086528301585119[/C][C]173.686681513539[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.50175438596491[/C][C]0.00852580781720632[/C][C]176.142181264531[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.50054545454545[/C][C]0.00836224552920965[/C][C]179.442884008128[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.49943396226415[/C][C]0.00821259208014521[/C][C]182.577430807648[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.49823529411765[/C][C]0.00801814551124177[/C][C]186.855587993141[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.49714285714286[/C][C]0.00783546793900207[/C][C]191.072552245493[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.49617021276596[/C][C]0.00766766455276593[/C][C]195.127238870439[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.49511111111111[/C][C]0.00744421829899237[/C][C]200.841922020676[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.49395348837209[/C][C]0.00714615288771118[/C][C]209.057028564440[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.49292682926829[/C][C]0.00684536430678193[/C][C]218.093115627053[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.49179487179487[/C][C]0.00643530867080215[/C][C]231.814035364510[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.49081081081081[/C][C]0.0059952230530826[/C][C]248.666446204078[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.49[/C][C]0.00551544812932068[/C][C]270.150306024820[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.48878787878788[/C][C]0.00491899487295392[/C][C]302.660994215235[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.48612903225806[/C][C]0.00426734082429773[/C][C]348.256465430702[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.48310344827586[/C][C]0.00310344827586207[/C][C]477.888888888888[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.48[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.48[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Median[/C][C]1.48[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.54[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.47090909090909[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.47090909090909[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.47090909090909[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.47090909090909[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.47090909090909[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.47090909090909[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.47090909090909[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.47090909090909[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10287&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10287&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.50958904109589	0.00907737405823762	166.302394438175
Geometric Mean	1.50766653889831
Harmonic Mean	1.50578794474883
Quadratic Mean	1.51155277143139
Winsorized Mean ( 1 / 24 )	1.50958904109589	0.00907737405823762	166.302394438175
Winsorized Mean ( 2 / 24 )	1.50958904109589	0.00907737405823762	166.302394438175
Winsorized Mean ( 3 / 24 )	1.50958904109589	0.00907737405823762	166.302394438175
Winsorized Mean ( 4 / 24 )	1.50904109589041	0.00896289574498816	168.365351871267
Winsorized Mean ( 5 / 24 )	1.50904109589041	0.00896289574498816	168.365351871267
Winsorized Mean ( 6 / 24 )	1.50904109589041	0.00896289574498816	168.365351871267
Winsorized Mean ( 7 / 24 )	1.50904109589041	0.00896289574498816	168.365351871267
Winsorized Mean ( 8 / 24 )	1.50904109589041	0.00896289574498816	168.365351871267
Winsorized Mean ( 9 / 24 )	1.50780821917808	0.00871772494021663	172.958911816804
Winsorized Mean ( 10 / 24 )	1.50780821917808	0.00871772494021663	172.958911816804
Winsorized Mean ( 11 / 24 )	1.50630136986301	0.00842982232695588	178.687202581523
Winsorized Mean ( 12 / 24 )	1.50465753424658	0.00812778974886197	185.125056225434
Winsorized Mean ( 13 / 24 )	1.50465753424658	0.00812778974886197	185.125056225434
Winsorized Mean ( 14 / 24 )	1.50465753424658	0.00812778974886197	185.125056225434
Winsorized Mean ( 15 / 24 )	1.50260273972603	0.00776369854621165	193.542128250102
Winsorized Mean ( 16 / 24 )	1.50260273972603	0.00776369854621165	193.542128250102
Winsorized Mean ( 17 / 24 )	1.50027397260274	0.00736360657412714	203.741734094556
Winsorized Mean ( 18 / 24 )	1.49780821917808	0.00695234533137119	215.439272330086
Winsorized Mean ( 19 / 24 )	1.50041095890411	0.00661060433365809	226.970316656939
Winsorized Mean ( 20 / 24 )	1.5113698630137	0.00545255957829333	277.185391798463
Winsorized Mean ( 21 / 24 )	1.5113698630137	0.00545255957829333	277.185391798463
Winsorized Mean ( 22 / 24 )	1.50835616438356	0.00492722416778705	306.126961757660
Winsorized Mean ( 23 / 24 )	1.48	0	Inf
Winsorized Mean ( 24 / 24 )	1.48	0	Inf
Trimmed Mean ( 1 / 24 )	1.50873239436620	0.00904922726997691	166.724997544464
Trimmed Mean ( 2 / 24 )	1.50782608695652	0.00900854374524254	167.377339734051
Trimmed Mean ( 3 / 24 )	1.50686567164179	0.00895288677478754	168.310591828919
Trimmed Mean ( 4 / 24 )	1.50584615384615	0.0088792441306319	169.591705295188
Trimmed Mean ( 5 / 24 )	1.50492063492063	0.00882460663873283	170.536851842807
Trimmed Mean ( 6 / 24 )	1.50393442622951	0.00875057746267671	171.866877659691
Trimmed Mean ( 7 / 24 )	1.50288135593220	0.0086528301585119	173.686681513539
Trimmed Mean ( 8 / 24 )	1.50175438596491	0.00852580781720632	176.142181264531
Trimmed Mean ( 9 / 24 )	1.50054545454545	0.00836224552920965	179.442884008128
Trimmed Mean ( 10 / 24 )	1.49943396226415	0.00821259208014521	182.577430807648
Trimmed Mean ( 11 / 24 )	1.49823529411765	0.00801814551124177	186.855587993141
Trimmed Mean ( 12 / 24 )	1.49714285714286	0.00783546793900207	191.072552245493
Trimmed Mean ( 13 / 24 )	1.49617021276596	0.00766766455276593	195.127238870439
Trimmed Mean ( 14 / 24 )	1.49511111111111	0.00744421829899237	200.841922020676
Trimmed Mean ( 15 / 24 )	1.49395348837209	0.00714615288771118	209.057028564440
Trimmed Mean ( 16 / 24 )	1.49292682926829	0.00684536430678193	218.093115627053
Trimmed Mean ( 17 / 24 )	1.49179487179487	0.00643530867080215	231.814035364510
Trimmed Mean ( 18 / 24 )	1.49081081081081	0.0059952230530826	248.666446204078
Trimmed Mean ( 19 / 24 )	1.49	0.00551544812932068	270.150306024820
Trimmed Mean ( 20 / 24 )	1.48878787878788	0.00491899487295392	302.660994215235
Trimmed Mean ( 21 / 24 )	1.48612903225806	0.00426734082429773	348.256465430702
Trimmed Mean ( 22 / 24 )	1.48310344827586	0.00310344827586207	477.888888888888
Trimmed Mean ( 23 / 24 )	1.48	0	Inf
Trimmed Mean ( 24 / 24 )	1.48	0	Inf
Median	1.48
Midrange	1.54
Midmean - Weighted Average at Xnp	1.47090909090909
Midmean - Weighted Average at X(n+1)p	1.47090909090909
Midmean - Empirical Distribution Function	1.47090909090909
Midmean - Empirical Distribution Function - Averaging	1.47090909090909
Midmean - Empirical Distribution Function - Interpolation	1.47090909090909
Midmean - Closest Observation	1.47090909090909
Midmean - True Basic - Statistics Graphics Toolkit	1.47090909090909
Midmean - MS Excel (old versions)	1.47090909090909
Number of observations	73

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