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*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Sat, 15 Oct 2011 15:57:38 -0400

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/15/t1318708882dg8cy3fd0i2jp19.htm/, Retrieved Wed, 15 May 2024 07:28:04 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=129898, Retrieved Wed, 15 May 2024 07:28:04 +0000

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No (this computation is public)

User-defined keywords

KDG2011W52a

Estimated Impact

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

-       [Central Tendency] [Centrummaten gem....] [2011-10-15 19:57:38] [e2f4ec8028a6c4bb839b6001939b0660] [Current]

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2,12
2,13
2,16
2,25
2,26
2,39
2,36
2,26
2,26
2,27
2,29
2,21
2,17
2,17
2,08
2,12
2,18
2,13
2,21
2,06
1,91
1,99
2,04
2,02
2,01
2,1
2,01
2,07
2,05
2,1
2,15
2,15
1,96
2,06
2,07
2,05
2,08
2,14
2,16
2,35
2,31
2,2
2,3
2,22
2,14
2,17
2,12
2,1
2,17
2,29
2,17
2,25
2,13
2,23
2,17
2,24
2,13
2,16
2,1
2,05
2,03
2,24
2,17
2,13
2,21
2,18
2,21
2,23
2,09
2,16
2,13
2,12

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	'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=129898&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=129898&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=129898&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	'Gwilym Jenkins' @ jenkins.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	2.15416666666667	0.0112305300133986	191.813446390922
Geometric Mean	2.15208828360839
Harmonic Mean	2.15000906092478
Quadratic Mean	2.156244162633
Winsorized Mean ( 1 / 24 )	2.15444444444445	0.0109199120518897	197.29503627931
Winsorized Mean ( 2 / 24 )	2.155	0.0106516913657638	202.315287403699
Winsorized Mean ( 3 / 24 )	2.15416666666667	0.0100793991859595	213.719749255232
Winsorized Mean ( 4 / 24 )	2.15361111111111	0.00996139959188703	216.195635085766
Winsorized Mean ( 5 / 24 )	2.15361111111111	0.00968257060573469	222.421420798687
Winsorized Mean ( 6 / 24 )	2.15444444444444	0.00952488070583783	226.191226009159
Winsorized Mean ( 7 / 24 )	2.15347222222222	0.00897562279002343	239.924545917398
Winsorized Mean ( 8 / 24 )	2.15347222222222	0.00858347513949641	250.885822726174
Winsorized Mean ( 9 / 24 )	2.15347222222222	0.00858347513949641	250.885822726174
Winsorized Mean ( 10 / 24 )	2.15347222222222	0.00858347513949641	250.885822726174
Winsorized Mean ( 11 / 24 )	2.15347222222222	0.0080665263107678	266.964011429258
Winsorized Mean ( 12 / 24 )	2.15347222222222	0.0080665263107678	266.964011429258
Winsorized Mean ( 13 / 24 )	2.15347222222222	0.00747756090880205	287.991264596362
Winsorized Mean ( 14 / 24 )	2.15347222222222	0.00747756090880205	287.991264596362
Winsorized Mean ( 15 / 24 )	2.15347222222222	0.00682086840390151	315.718189342349
Winsorized Mean ( 16 / 24 )	2.15347222222222	0.00682086840390151	315.718189342349
Winsorized Mean ( 17 / 24 )	2.15347222222222	0.00610023128112252	353.014848615044
Winsorized Mean ( 18 / 24 )	2.15347222222222	0.00536303248711337	401.540029339133
Winsorized Mean ( 19 / 24 )	2.15347222222222	0.00536303248711337	401.540029339133
Winsorized Mean ( 20 / 24 )	2.15347222222222	0.00536303248711337	401.540029339133
Winsorized Mean ( 21 / 24 )	2.15347222222222	0.00536303248711337	401.540029339133
Winsorized Mean ( 22 / 24 )	2.15652777777778	0.00408803610680876	527.521705149818
Winsorized Mean ( 23 / 24 )	2.15013888888889	0.00318012371411425	676.118001116116
Winsorized Mean ( 24 / 24 )	2.15013888888889	0.00318012371411425	676.118001116116
Trimmed Mean ( 1 / 24 )	2.15428571428571	0.0104704482663049	205.749138861461
Trimmed Mean ( 2 / 24 )	2.15411764705882	0.00993224476809483	216.881248635601
Trimmed Mean ( 3 / 24 )	2.15363636363636	0.00946256607971031	227.595384327535
Trimmed Mean ( 4 / 24 )	2.1534375	0.00916996355755166	234.835993238664
Trimmed Mean ( 5 / 24 )	2.15338709677419	0.00886154010840773	243.003707079211
Trimmed Mean ( 6 / 24 )	2.15333333333333	0.00857886862105522	251.004348994037
Trimmed Mean ( 7 / 24 )	2.15310344827586	0.00827976818485286	260.043928791966
Trimmed Mean ( 8 / 24 )	2.15303571428571	0.00806193413541134	267.06193304516
Trimmed Mean ( 9 / 24 )	2.15296296296296	0.00788912346314504	272.902683424943
Trimmed Mean ( 10 / 24 )	2.15288461538462	0.00767130428194839	280.641275102415
Trimmed Mean ( 11 / 24 )	2.1528	0.00739575167627624	291.086030768942
Trimmed Mean ( 12 / 24 )	2.15270833333333	0.00716905524685002	300.277827302168
Trimmed Mean ( 13 / 24 )	2.15260869565217	0.00687665505846489	313.031361519639
Trimmed Mean ( 14 / 24 )	2.1525	0.00664029756841064	324.157159799573
Trimmed Mean ( 15 / 24 )	2.15238095238095	0.00632831444706594	340.119153430955
Trimmed Mean ( 16 / 24 )	2.15225	0.00608157684511812	353.896703899693
Trimmed Mean ( 17 / 24 )	2.15210526315789	0.00574664098481627	374.497949122656
Trimmed Mean ( 18 / 24 )	2.15194444444444	0.00548908649474001	392.040541993021
Trimmed Mean ( 19 / 24 )	2.15176470588235	0.00533161605990274	403.585832458012
Trimmed Mean ( 20 / 24 )	2.1515625	0.00510197176858314	421.711957178765
Trimmed Mean ( 21 / 24 )	2.15133333333333	0.00476417023285932	451.565168367664
Trimmed Mean ( 22 / 24 )	2.15107142857143	0.00425196144325068	505.900972358513
Trimmed Mean ( 23 / 24 )	2.15038461538462	0.00397997948316201	540.30042729672
Trimmed Mean ( 24 / 24 )	2.15041666666667	0.00392313680814969	548.137057621727
Median	2.155
Midrange	2.15
Midmean - Weighted Average at Xnp	2.15027027027027
Midmean - Weighted Average at X(n+1)p	2.15194444444444
Midmean - Empirical Distribution Function	2.15027027027027
Midmean - Empirical Distribution Function - Averaging	2.15194444444444
Midmean - Empirical Distribution Function - Interpolation	2.15194444444444
Midmean - Closest Observation	2.15027027027027
Midmean - True Basic - Statistics Graphics Toolkit	2.15194444444444
Midmean - MS Excel (old versions)	2.15210526315789
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.15416666666667 & 0.0112305300133986 & 191.813446390922 \tabularnewline
Geometric Mean & 2.15208828360839 &  &  \tabularnewline
Harmonic Mean & 2.15000906092478 &  &  \tabularnewline
Quadratic Mean & 2.156244162633 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 2.15444444444445 & 0.0109199120518897 & 197.29503627931 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 2.155 & 0.0106516913657638 & 202.315287403699 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 2.15416666666667 & 0.0100793991859595 & 213.719749255232 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 2.15361111111111 & 0.00996139959188703 & 216.195635085766 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 2.15361111111111 & 0.00968257060573469 & 222.421420798687 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 2.15444444444444 & 0.00952488070583783 & 226.191226009159 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 2.15347222222222 & 0.00897562279002343 & 239.924545917398 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 2.15347222222222 & 0.00858347513949641 & 250.885822726174 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 2.15347222222222 & 0.00858347513949641 & 250.885822726174 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 2.15347222222222 & 0.00858347513949641 & 250.885822726174 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 2.15347222222222 & 0.0080665263107678 & 266.964011429258 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 2.15347222222222 & 0.0080665263107678 & 266.964011429258 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 2.15347222222222 & 0.00747756090880205 & 287.991264596362 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 2.15347222222222 & 0.00747756090880205 & 287.991264596362 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 2.15347222222222 & 0.00682086840390151 & 315.718189342349 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 2.15347222222222 & 0.00682086840390151 & 315.718189342349 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 2.15347222222222 & 0.00610023128112252 & 353.014848615044 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 2.15347222222222 & 0.00536303248711337 & 401.540029339133 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 2.15347222222222 & 0.00536303248711337 & 401.540029339133 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 2.15347222222222 & 0.00536303248711337 & 401.540029339133 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 2.15347222222222 & 0.00536303248711337 & 401.540029339133 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 2.15652777777778 & 0.00408803610680876 & 527.521705149818 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 2.15013888888889 & 0.00318012371411425 & 676.118001116116 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 2.15013888888889 & 0.00318012371411425 & 676.118001116116 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 2.15428571428571 & 0.0104704482663049 & 205.749138861461 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 2.15411764705882 & 0.00993224476809483 & 216.881248635601 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 2.15363636363636 & 0.00946256607971031 & 227.595384327535 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 2.1534375 & 0.00916996355755166 & 234.835993238664 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 2.15338709677419 & 0.00886154010840773 & 243.003707079211 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 2.15333333333333 & 0.00857886862105522 & 251.004348994037 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 2.15310344827586 & 0.00827976818485286 & 260.043928791966 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 2.15303571428571 & 0.00806193413541134 & 267.06193304516 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 2.15296296296296 & 0.00788912346314504 & 272.902683424943 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 2.15288461538462 & 0.00767130428194839 & 280.641275102415 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 2.1528 & 0.00739575167627624 & 291.086030768942 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 2.15270833333333 & 0.00716905524685002 & 300.277827302168 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 2.15260869565217 & 0.00687665505846489 & 313.031361519639 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 2.1525 & 0.00664029756841064 & 324.157159799573 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 2.15238095238095 & 0.00632831444706594 & 340.119153430955 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 2.15225 & 0.00608157684511812 & 353.896703899693 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 2.15210526315789 & 0.00574664098481627 & 374.497949122656 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 2.15194444444444 & 0.00548908649474001 & 392.040541993021 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 2.15176470588235 & 0.00533161605990274 & 403.585832458012 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 2.1515625 & 0.00510197176858314 & 421.711957178765 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 2.15133333333333 & 0.00476417023285932 & 451.565168367664 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 2.15107142857143 & 0.00425196144325068 & 505.900972358513 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 2.15038461538462 & 0.00397997948316201 & 540.30042729672 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 2.15041666666667 & 0.00392313680814969 & 548.137057621727 \tabularnewline
Median & 2.155 &  &  \tabularnewline
Midrange & 2.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.15027027027027 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.15194444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.15027027027027 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.15194444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.15194444444444 &  &  \tabularnewline
Midmean - Closest Observation & 2.15027027027027 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.15194444444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.15210526315789 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=129898&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]2.15416666666667[/C][C]0.0112305300133986[/C][C]191.813446390922[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2.15208828360839[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.15000906092478[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.156244162633[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]2.15444444444445[/C][C]0.0109199120518897[/C][C]197.29503627931[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]2.155[/C][C]0.0106516913657638[/C][C]202.315287403699[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]2.15416666666667[/C][C]0.0100793991859595[/C][C]213.719749255232[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]2.15361111111111[/C][C]0.00996139959188703[/C][C]216.195635085766[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]2.15361111111111[/C][C]0.00968257060573469[/C][C]222.421420798687[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]2.15444444444444[/C][C]0.00952488070583783[/C][C]226.191226009159[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]2.15347222222222[/C][C]0.00897562279002343[/C][C]239.924545917398[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]2.15347222222222[/C][C]0.00858347513949641[/C][C]250.885822726174[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]2.15347222222222[/C][C]0.00858347513949641[/C][C]250.885822726174[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]2.15347222222222[/C][C]0.00858347513949641[/C][C]250.885822726174[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]2.15347222222222[/C][C]0.0080665263107678[/C][C]266.964011429258[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]2.15347222222222[/C][C]0.0080665263107678[/C][C]266.964011429258[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]2.15347222222222[/C][C]0.00747756090880205[/C][C]287.991264596362[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]2.15347222222222[/C][C]0.00747756090880205[/C][C]287.991264596362[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]2.15347222222222[/C][C]0.00682086840390151[/C][C]315.718189342349[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]2.15347222222222[/C][C]0.00682086840390151[/C][C]315.718189342349[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]2.15347222222222[/C][C]0.00610023128112252[/C][C]353.014848615044[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]2.15347222222222[/C][C]0.00536303248711337[/C][C]401.540029339133[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]2.15347222222222[/C][C]0.00536303248711337[/C][C]401.540029339133[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]2.15347222222222[/C][C]0.00536303248711337[/C][C]401.540029339133[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]2.15347222222222[/C][C]0.00536303248711337[/C][C]401.540029339133[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]2.15652777777778[/C][C]0.00408803610680876[/C][C]527.521705149818[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]2.15013888888889[/C][C]0.00318012371411425[/C][C]676.118001116116[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]2.15013888888889[/C][C]0.00318012371411425[/C][C]676.118001116116[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]2.15428571428571[/C][C]0.0104704482663049[/C][C]205.749138861461[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]2.15411764705882[/C][C]0.00993224476809483[/C][C]216.881248635601[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]2.15363636363636[/C][C]0.00946256607971031[/C][C]227.595384327535[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]2.1534375[/C][C]0.00916996355755166[/C][C]234.835993238664[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]2.15338709677419[/C][C]0.00886154010840773[/C][C]243.003707079211[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]2.15333333333333[/C][C]0.00857886862105522[/C][C]251.004348994037[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]2.15310344827586[/C][C]0.00827976818485286[/C][C]260.043928791966[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]2.15303571428571[/C][C]0.00806193413541134[/C][C]267.06193304516[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]2.15296296296296[/C][C]0.00788912346314504[/C][C]272.902683424943[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]2.15288461538462[/C][C]0.00767130428194839[/C][C]280.641275102415[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]2.1528[/C][C]0.00739575167627624[/C][C]291.086030768942[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]2.15270833333333[/C][C]0.00716905524685002[/C][C]300.277827302168[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]2.15260869565217[/C][C]0.00687665505846489[/C][C]313.031361519639[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]2.1525[/C][C]0.00664029756841064[/C][C]324.157159799573[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]2.15238095238095[/C][C]0.00632831444706594[/C][C]340.119153430955[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]2.15225[/C][C]0.00608157684511812[/C][C]353.896703899693[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]2.15210526315789[/C][C]0.00574664098481627[/C][C]374.497949122656[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]2.15194444444444[/C][C]0.00548908649474001[/C][C]392.040541993021[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]2.15176470588235[/C][C]0.00533161605990274[/C][C]403.585832458012[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]2.1515625[/C][C]0.00510197176858314[/C][C]421.711957178765[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]2.15133333333333[/C][C]0.00476417023285932[/C][C]451.565168367664[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]2.15107142857143[/C][C]0.00425196144325068[/C][C]505.900972358513[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]2.15038461538462[/C][C]0.00397997948316201[/C][C]540.30042729672[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]2.15041666666667[/C][C]0.00392313680814969[/C][C]548.137057621727[/C][/ROW]
[ROW][C]Median[/C][C]2.155[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.15027027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.15194444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.15027027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.15194444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.15194444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.15027027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.15194444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.15210526315789[/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=129898&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=129898&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	2.15416666666667	0.0112305300133986	191.813446390922
Geometric Mean	2.15208828360839
Harmonic Mean	2.15000906092478
Quadratic Mean	2.156244162633
Winsorized Mean ( 1 / 24 )	2.15444444444445	0.0109199120518897	197.29503627931
Winsorized Mean ( 2 / 24 )	2.155	0.0106516913657638	202.315287403699
Winsorized Mean ( 3 / 24 )	2.15416666666667	0.0100793991859595	213.719749255232
Winsorized Mean ( 4 / 24 )	2.15361111111111	0.00996139959188703	216.195635085766
Winsorized Mean ( 5 / 24 )	2.15361111111111	0.00968257060573469	222.421420798687
Winsorized Mean ( 6 / 24 )	2.15444444444444	0.00952488070583783	226.191226009159
Winsorized Mean ( 7 / 24 )	2.15347222222222	0.00897562279002343	239.924545917398
Winsorized Mean ( 8 / 24 )	2.15347222222222	0.00858347513949641	250.885822726174
Winsorized Mean ( 9 / 24 )	2.15347222222222	0.00858347513949641	250.885822726174
Winsorized Mean ( 10 / 24 )	2.15347222222222	0.00858347513949641	250.885822726174
Winsorized Mean ( 11 / 24 )	2.15347222222222	0.0080665263107678	266.964011429258
Winsorized Mean ( 12 / 24 )	2.15347222222222	0.0080665263107678	266.964011429258
Winsorized Mean ( 13 / 24 )	2.15347222222222	0.00747756090880205	287.991264596362
Winsorized Mean ( 14 / 24 )	2.15347222222222	0.00747756090880205	287.991264596362
Winsorized Mean ( 15 / 24 )	2.15347222222222	0.00682086840390151	315.718189342349
Winsorized Mean ( 16 / 24 )	2.15347222222222	0.00682086840390151	315.718189342349
Winsorized Mean ( 17 / 24 )	2.15347222222222	0.00610023128112252	353.014848615044
Winsorized Mean ( 18 / 24 )	2.15347222222222	0.00536303248711337	401.540029339133
Winsorized Mean ( 19 / 24 )	2.15347222222222	0.00536303248711337	401.540029339133
Winsorized Mean ( 20 / 24 )	2.15347222222222	0.00536303248711337	401.540029339133
Winsorized Mean ( 21 / 24 )	2.15347222222222	0.00536303248711337	401.540029339133
Winsorized Mean ( 22 / 24 )	2.15652777777778	0.00408803610680876	527.521705149818
Winsorized Mean ( 23 / 24 )	2.15013888888889	0.00318012371411425	676.118001116116
Winsorized Mean ( 24 / 24 )	2.15013888888889	0.00318012371411425	676.118001116116
Trimmed Mean ( 1 / 24 )	2.15428571428571	0.0104704482663049	205.749138861461
Trimmed Mean ( 2 / 24 )	2.15411764705882	0.00993224476809483	216.881248635601
Trimmed Mean ( 3 / 24 )	2.15363636363636	0.00946256607971031	227.595384327535
Trimmed Mean ( 4 / 24 )	2.1534375	0.00916996355755166	234.835993238664
Trimmed Mean ( 5 / 24 )	2.15338709677419	0.00886154010840773	243.003707079211
Trimmed Mean ( 6 / 24 )	2.15333333333333	0.00857886862105522	251.004348994037
Trimmed Mean ( 7 / 24 )	2.15310344827586	0.00827976818485286	260.043928791966
Trimmed Mean ( 8 / 24 )	2.15303571428571	0.00806193413541134	267.06193304516
Trimmed Mean ( 9 / 24 )	2.15296296296296	0.00788912346314504	272.902683424943
Trimmed Mean ( 10 / 24 )	2.15288461538462	0.00767130428194839	280.641275102415
Trimmed Mean ( 11 / 24 )	2.1528	0.00739575167627624	291.086030768942
Trimmed Mean ( 12 / 24 )	2.15270833333333	0.00716905524685002	300.277827302168
Trimmed Mean ( 13 / 24 )	2.15260869565217	0.00687665505846489	313.031361519639
Trimmed Mean ( 14 / 24 )	2.1525	0.00664029756841064	324.157159799573
Trimmed Mean ( 15 / 24 )	2.15238095238095	0.00632831444706594	340.119153430955
Trimmed Mean ( 16 / 24 )	2.15225	0.00608157684511812	353.896703899693
Trimmed Mean ( 17 / 24 )	2.15210526315789	0.00574664098481627	374.497949122656
Trimmed Mean ( 18 / 24 )	2.15194444444444	0.00548908649474001	392.040541993021
Trimmed Mean ( 19 / 24 )	2.15176470588235	0.00533161605990274	403.585832458012
Trimmed Mean ( 20 / 24 )	2.1515625	0.00510197176858314	421.711957178765
Trimmed Mean ( 21 / 24 )	2.15133333333333	0.00476417023285932	451.565168367664
Trimmed Mean ( 22 / 24 )	2.15107142857143	0.00425196144325068	505.900972358513
Trimmed Mean ( 23 / 24 )	2.15038461538462	0.00397997948316201	540.30042729672
Trimmed Mean ( 24 / 24 )	2.15041666666667	0.00392313680814969	548.137057621727
Median	2.155
Midrange	2.15
Midmean - Weighted Average at Xnp	2.15027027027027
Midmean - Weighted Average at X(n+1)p	2.15194444444444
Midmean - Empirical Distribution Function	2.15027027027027
Midmean - Empirical Distribution Function - Averaging	2.15194444444444
Midmean - Empirical Distribution Function - Interpolation	2.15194444444444
Midmean - Closest Observation	2.15027027027027
Midmean - True Basic - Statistics Graphics Toolkit	2.15194444444444
Midmean - MS Excel (old versions)	2.15210526315789
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