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*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Sun, 12 Oct 2014 20:17:17 +0100

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/Oct/12/t1413141471h21nk43ndkwl7ox.htm/, Retrieved Thu, 16 May 2024 02:01:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240670, Retrieved Thu, 16 May 2024 02:01:36 +0000

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Estimated Impact

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

-       [Central Tendency] [Gemiddelde consum...] [2014-10-12 19:17:17] [42c148e2fe69cef5ba6629e36c38849a] [Current]

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2,37
2,45
2,53
2,56
2,62
2,67
2,62
2,6
2,53
2,49
2,48
2,44
2,36
2,35
2,44
2,5
2,58
2,55
2,44
2,3
2,24
2,19
2,25
2,28
2,27
2,37
2,47
2,5
2,47
2,61
2,61
2,65
2,43
2,43
2,33
2,27
2,22
2,17
2,28
2,3
2,33
2,44
2,41
2,4
2,34
2,37
2,38
2,3
2,29
2,34
2,35
2,38
2,37
2,45
2,51
2,46
2,42
2,48
2,44
2,43
2,36
2,42
2,42
2,43
2,47
2,54
2,55
2,55
2,49
2,54
2,55
2,5

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Herman Ole Andreas Wold' @ wold.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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240670&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240670&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240670&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	2.42958333333333	0.0135421406562045	179.409104883296
Geometric Mean	2.42689133529159
Harmonic Mean	2.42418705660104
Quadratic Mean	2.43226146483747
Winsorized Mean ( 1 / 24 )	2.42958333333333	0.0134027499046959	181.274988387427
Winsorized Mean ( 2 / 24 )	2.42958333333333	0.0130207453048668	186.593261479835
Winsorized Mean ( 3 / 24 )	2.43041666666667	0.0128391967277341	189.296629548225
Winsorized Mean ( 4 / 24 )	2.43041666666667	0.0126116880422038	192.711448184693
Winsorized Mean ( 5 / 24 )	2.43180555555556	0.0123434268887826	197.012189359304
Winsorized Mean ( 6 / 24 )	2.43097222222222	0.0121772250190109	199.632692869437
Winsorized Mean ( 7 / 24 )	2.43	0.0116314021023684	208.917203499069
Winsorized Mean ( 8 / 24 )	2.42777777777778	0.011245277607736	215.893094191613
Winsorized Mean ( 9 / 24 )	2.42777777777778	0.0108143065529661	224.496852006834
Winsorized Mean ( 10 / 24 )	2.42916666666667	0.0105701139205881	229.81461552039
Winsorized Mean ( 11 / 24 )	2.42916666666667	0.0105701139205881	229.81461552039
Winsorized Mean ( 12 / 24 )	2.42916666666667	0.0105701139205881	229.81461552039
Winsorized Mean ( 13 / 24 )	2.43277777777778	0.00939321464183581	258.993099864086
Winsorized Mean ( 14 / 24 )	2.43277777777778	0.00939321464183581	258.993099864086
Winsorized Mean ( 15 / 24 )	2.43277777777778	0.00874616442251806	278.153675171518
Winsorized Mean ( 16 / 24 )	2.43277777777778	0.00874616442251806	278.153675171518
Winsorized Mean ( 17 / 24 )	2.43041666666667	0.00767961118888967	316.476525554162
Winsorized Mean ( 18 / 24 )	2.42791666666667	0.0073236638662397	331.516671301474
Winsorized Mean ( 19 / 24 )	2.43055555555556	0.0069366936401736	350.3910770225
Winsorized Mean ( 20 / 24 )	2.43055555555556	0.0069366936401736	350.3910770225
Winsorized Mean ( 21 / 24 )	2.43055555555556	0.00611857560907078	397.242056133499
Winsorized Mean ( 22 / 24 )	2.43055555555556	0.00611857560907078	397.242056133499
Winsorized Mean ( 23 / 24 )	2.42736111111111	0.00569158101983125	426.482747527168
Winsorized Mean ( 24 / 24 )	2.42736111111111	0.00569158101983125	426.482747527167
Trimmed Mean ( 1 / 24 )	2.42985714285714	0.0129683367499362	187.368448993206
Trimmed Mean ( 2 / 24 )	2.43014705882353	0.0124509443863992	195.177729769487
Trimmed Mean ( 3 / 24 )	2.43045454545455	0.0120805992113187	201.186588756076
Trimmed Mean ( 4 / 24 )	2.43046875	0.0117206017055558	207.367233445695
Trimmed Mean ( 5 / 24 )	2.43048387096774	0.0113718631389459	213.727851036469
Trimmed Mean ( 6 / 24 )	2.43016666666667	0.0110353609006301	220.216328994542
Trimmed Mean ( 7 / 24 )	2.43	0.010673054651026	227.676150779047
Trimmed Mean ( 8 / 24 )	2.43	0.0103760463406028	234.193248587479
Trimmed Mean ( 9 / 24 )	2.43037037037037	0.0101041500318451	240.531896568302
Trimmed Mean ( 10 / 24 )	2.43076923076923	0.00986655362224088	246.364569011196
Trimmed Mean ( 11 / 24 )	2.431	0.00962246521088509	252.637961969456
Trimmed Mean ( 12 / 24 )	2.43125	0.00930961239680382	261.154803913716
Trimmed Mean ( 13 / 24 )	2.43152173913043	0.00890620687492553	273.014289166819
Trimmed Mean ( 14 / 24 )	2.43136363636364	0.00866690937334179	280.534101792061
Trimmed Mean ( 15 / 24 )	2.43119047619048	0.0083492464622216	291.186813946749
Trimmed Mean ( 16 / 24 )	2.431	0.00808448974017373	300.699249814096
Trimmed Mean ( 17 / 24 )	2.43078947368421	0.00772372873847307	314.717095329368
Trimmed Mean ( 18 / 24 )	2.43083333333333	0.00751057455583328	323.654777043038
Trimmed Mean ( 19 / 24 )	2.43117647058824	0.00729765310212766	333.144976414324
Trimmed Mean ( 20 / 24 )	2.43125	0.00709597227873991	342.623942780078
Trimmed Mean ( 21 / 24 )	2.43133333333333	0.00679305482605079	357.914575340887
Trimmed Mean ( 22 / 24 )	2.43142857142857	0.00660115201013597	368.333976811191
Trimmed Mean ( 23 / 24 )	2.43153846153846	0.00629266502652849	386.408374081193
Trimmed Mean ( 24 / 24 )	2.43208333333333	0.00595816230625123	408.193534906161
Median	2.435
Midrange	2.42
Midmean - Weighted Average at Xnp	2.42864864864865
Midmean - Weighted Average at X(n+1)p	2.42864864864865
Midmean - Empirical Distribution Function	2.42864864864865
Midmean - Empirical Distribution Function - Averaging	2.42864864864865
Midmean - Empirical Distribution Function - Interpolation	2.42864864864865
Midmean - Closest Observation	2.42864864864865
Midmean - True Basic - Statistics Graphics Toolkit	2.42864864864865
Midmean - MS Excel (old versions)	2.43078947368421
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.42958333333333 & 0.0135421406562045 & 179.409104883296 \tabularnewline
Geometric Mean & 2.42689133529159 &  &  \tabularnewline
Harmonic Mean & 2.42418705660104 &  &  \tabularnewline
Quadratic Mean & 2.43226146483747 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 2.42958333333333 & 0.0134027499046959 & 181.274988387427 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 2.42958333333333 & 0.0130207453048668 & 186.593261479835 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 2.43041666666667 & 0.0128391967277341 & 189.296629548225 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 2.43041666666667 & 0.0126116880422038 & 192.711448184693 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 2.43180555555556 & 0.0123434268887826 & 197.012189359304 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 2.43097222222222 & 0.0121772250190109 & 199.632692869437 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 2.43 & 0.0116314021023684 & 208.917203499069 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 2.42777777777778 & 0.011245277607736 & 215.893094191613 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 2.42777777777778 & 0.0108143065529661 & 224.496852006834 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 2.42916666666667 & 0.0105701139205881 & 229.81461552039 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 2.42916666666667 & 0.0105701139205881 & 229.81461552039 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 2.42916666666667 & 0.0105701139205881 & 229.81461552039 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 2.43277777777778 & 0.00939321464183581 & 258.993099864086 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 2.43277777777778 & 0.00939321464183581 & 258.993099864086 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 2.43277777777778 & 0.00874616442251806 & 278.153675171518 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 2.43277777777778 & 0.00874616442251806 & 278.153675171518 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 2.43041666666667 & 0.00767961118888967 & 316.476525554162 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 2.42791666666667 & 0.0073236638662397 & 331.516671301474 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 2.43055555555556 & 0.0069366936401736 & 350.3910770225 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 2.43055555555556 & 0.0069366936401736 & 350.3910770225 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 2.43055555555556 & 0.00611857560907078 & 397.242056133499 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 2.43055555555556 & 0.00611857560907078 & 397.242056133499 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 2.42736111111111 & 0.00569158101983125 & 426.482747527168 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 2.42736111111111 & 0.00569158101983125 & 426.482747527167 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 2.42985714285714 & 0.0129683367499362 & 187.368448993206 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 2.43014705882353 & 0.0124509443863992 & 195.177729769487 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 2.43045454545455 & 0.0120805992113187 & 201.186588756076 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 2.43046875 & 0.0117206017055558 & 207.367233445695 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 2.43048387096774 & 0.0113718631389459 & 213.727851036469 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 2.43016666666667 & 0.0110353609006301 & 220.216328994542 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 2.43 & 0.010673054651026 & 227.676150779047 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 2.43 & 0.0103760463406028 & 234.193248587479 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 2.43037037037037 & 0.0101041500318451 & 240.531896568302 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 2.43076923076923 & 0.00986655362224088 & 246.364569011196 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 2.431 & 0.00962246521088509 & 252.637961969456 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 2.43125 & 0.00930961239680382 & 261.154803913716 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 2.43152173913043 & 0.00890620687492553 & 273.014289166819 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 2.43136363636364 & 0.00866690937334179 & 280.534101792061 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 2.43119047619048 & 0.0083492464622216 & 291.186813946749 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 2.431 & 0.00808448974017373 & 300.699249814096 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 2.43078947368421 & 0.00772372873847307 & 314.717095329368 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 2.43083333333333 & 0.00751057455583328 & 323.654777043038 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 2.43117647058824 & 0.00729765310212766 & 333.144976414324 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 2.43125 & 0.00709597227873991 & 342.623942780078 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 2.43133333333333 & 0.00679305482605079 & 357.914575340887 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 2.43142857142857 & 0.00660115201013597 & 368.333976811191 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 2.43153846153846 & 0.00629266502652849 & 386.408374081193 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 2.43208333333333 & 0.00595816230625123 & 408.193534906161 \tabularnewline
Median & 2.435 &  &  \tabularnewline
Midrange & 2.42 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.42864864864865 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.42864864864865 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.42864864864865 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.42864864864865 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.42864864864865 &  &  \tabularnewline
Midmean - Closest Observation & 2.42864864864865 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.42864864864865 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.43078947368421 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240670&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]2.42958333333333[/C][C]0.0135421406562045[/C][C]179.409104883296[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2.42689133529159[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.42418705660104[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.43226146483747[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]2.42958333333333[/C][C]0.0134027499046959[/C][C]181.274988387427[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]2.42958333333333[/C][C]0.0130207453048668[/C][C]186.593261479835[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]2.43041666666667[/C][C]0.0128391967277341[/C][C]189.296629548225[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]2.43041666666667[/C][C]0.0126116880422038[/C][C]192.711448184693[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]2.43180555555556[/C][C]0.0123434268887826[/C][C]197.012189359304[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]2.43097222222222[/C][C]0.0121772250190109[/C][C]199.632692869437[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]2.43[/C][C]0.0116314021023684[/C][C]208.917203499069[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]2.42777777777778[/C][C]0.011245277607736[/C][C]215.893094191613[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]2.42777777777778[/C][C]0.0108143065529661[/C][C]224.496852006834[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]2.42916666666667[/C][C]0.0105701139205881[/C][C]229.81461552039[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]2.42916666666667[/C][C]0.0105701139205881[/C][C]229.81461552039[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]2.42916666666667[/C][C]0.0105701139205881[/C][C]229.81461552039[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]2.43277777777778[/C][C]0.00939321464183581[/C][C]258.993099864086[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]2.43277777777778[/C][C]0.00939321464183581[/C][C]258.993099864086[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]2.43277777777778[/C][C]0.00874616442251806[/C][C]278.153675171518[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]2.43277777777778[/C][C]0.00874616442251806[/C][C]278.153675171518[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]2.43041666666667[/C][C]0.00767961118888967[/C][C]316.476525554162[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]2.42791666666667[/C][C]0.0073236638662397[/C][C]331.516671301474[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]2.43055555555556[/C][C]0.0069366936401736[/C][C]350.3910770225[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]2.43055555555556[/C][C]0.0069366936401736[/C][C]350.3910770225[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]2.43055555555556[/C][C]0.00611857560907078[/C][C]397.242056133499[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]2.43055555555556[/C][C]0.00611857560907078[/C][C]397.242056133499[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]2.42736111111111[/C][C]0.00569158101983125[/C][C]426.482747527168[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]2.42736111111111[/C][C]0.00569158101983125[/C][C]426.482747527167[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]2.42985714285714[/C][C]0.0129683367499362[/C][C]187.368448993206[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]2.43014705882353[/C][C]0.0124509443863992[/C][C]195.177729769487[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]2.43045454545455[/C][C]0.0120805992113187[/C][C]201.186588756076[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]2.43046875[/C][C]0.0117206017055558[/C][C]207.367233445695[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]2.43048387096774[/C][C]0.0113718631389459[/C][C]213.727851036469[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]2.43016666666667[/C][C]0.0110353609006301[/C][C]220.216328994542[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]2.43[/C][C]0.010673054651026[/C][C]227.676150779047[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]2.43[/C][C]0.0103760463406028[/C][C]234.193248587479[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]2.43037037037037[/C][C]0.0101041500318451[/C][C]240.531896568302[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]2.43076923076923[/C][C]0.00986655362224088[/C][C]246.364569011196[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]2.431[/C][C]0.00962246521088509[/C][C]252.637961969456[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]2.43125[/C][C]0.00930961239680382[/C][C]261.154803913716[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]2.43152173913043[/C][C]0.00890620687492553[/C][C]273.014289166819[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]2.43136363636364[/C][C]0.00866690937334179[/C][C]280.534101792061[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]2.43119047619048[/C][C]0.0083492464622216[/C][C]291.186813946749[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]2.431[/C][C]0.00808448974017373[/C][C]300.699249814096[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]2.43078947368421[/C][C]0.00772372873847307[/C][C]314.717095329368[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]2.43083333333333[/C][C]0.00751057455583328[/C][C]323.654777043038[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]2.43117647058824[/C][C]0.00729765310212766[/C][C]333.144976414324[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]2.43125[/C][C]0.00709597227873991[/C][C]342.623942780078[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]2.43133333333333[/C][C]0.00679305482605079[/C][C]357.914575340887[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]2.43142857142857[/C][C]0.00660115201013597[/C][C]368.333976811191[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]2.43153846153846[/C][C]0.00629266502652849[/C][C]386.408374081193[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]2.43208333333333[/C][C]0.00595816230625123[/C][C]408.193534906161[/C][/ROW]
[ROW][C]Median[/C][C]2.435[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.42[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.42864864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.42864864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.42864864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.42864864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.42864864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.42864864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.42864864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.43078947368421[/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=240670&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240670&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	2.42958333333333	0.0135421406562045	179.409104883296
Geometric Mean	2.42689133529159
Harmonic Mean	2.42418705660104
Quadratic Mean	2.43226146483747
Winsorized Mean ( 1 / 24 )	2.42958333333333	0.0134027499046959	181.274988387427
Winsorized Mean ( 2 / 24 )	2.42958333333333	0.0130207453048668	186.593261479835
Winsorized Mean ( 3 / 24 )	2.43041666666667	0.0128391967277341	189.296629548225
Winsorized Mean ( 4 / 24 )	2.43041666666667	0.0126116880422038	192.711448184693
Winsorized Mean ( 5 / 24 )	2.43180555555556	0.0123434268887826	197.012189359304
Winsorized Mean ( 6 / 24 )	2.43097222222222	0.0121772250190109	199.632692869437
Winsorized Mean ( 7 / 24 )	2.43	0.0116314021023684	208.917203499069
Winsorized Mean ( 8 / 24 )	2.42777777777778	0.011245277607736	215.893094191613
Winsorized Mean ( 9 / 24 )	2.42777777777778	0.0108143065529661	224.496852006834
Winsorized Mean ( 10 / 24 )	2.42916666666667	0.0105701139205881	229.81461552039
Winsorized Mean ( 11 / 24 )	2.42916666666667	0.0105701139205881	229.81461552039
Winsorized Mean ( 12 / 24 )	2.42916666666667	0.0105701139205881	229.81461552039
Winsorized Mean ( 13 / 24 )	2.43277777777778	0.00939321464183581	258.993099864086
Winsorized Mean ( 14 / 24 )	2.43277777777778	0.00939321464183581	258.993099864086
Winsorized Mean ( 15 / 24 )	2.43277777777778	0.00874616442251806	278.153675171518
Winsorized Mean ( 16 / 24 )	2.43277777777778	0.00874616442251806	278.153675171518
Winsorized Mean ( 17 / 24 )	2.43041666666667	0.00767961118888967	316.476525554162
Winsorized Mean ( 18 / 24 )	2.42791666666667	0.0073236638662397	331.516671301474
Winsorized Mean ( 19 / 24 )	2.43055555555556	0.0069366936401736	350.3910770225
Winsorized Mean ( 20 / 24 )	2.43055555555556	0.0069366936401736	350.3910770225
Winsorized Mean ( 21 / 24 )	2.43055555555556	0.00611857560907078	397.242056133499
Winsorized Mean ( 22 / 24 )	2.43055555555556	0.00611857560907078	397.242056133499
Winsorized Mean ( 23 / 24 )	2.42736111111111	0.00569158101983125	426.482747527168
Winsorized Mean ( 24 / 24 )	2.42736111111111	0.00569158101983125	426.482747527167
Trimmed Mean ( 1 / 24 )	2.42985714285714	0.0129683367499362	187.368448993206
Trimmed Mean ( 2 / 24 )	2.43014705882353	0.0124509443863992	195.177729769487
Trimmed Mean ( 3 / 24 )	2.43045454545455	0.0120805992113187	201.186588756076
Trimmed Mean ( 4 / 24 )	2.43046875	0.0117206017055558	207.367233445695
Trimmed Mean ( 5 / 24 )	2.43048387096774	0.0113718631389459	213.727851036469
Trimmed Mean ( 6 / 24 )	2.43016666666667	0.0110353609006301	220.216328994542
Trimmed Mean ( 7 / 24 )	2.43	0.010673054651026	227.676150779047
Trimmed Mean ( 8 / 24 )	2.43	0.0103760463406028	234.193248587479
Trimmed Mean ( 9 / 24 )	2.43037037037037	0.0101041500318451	240.531896568302
Trimmed Mean ( 10 / 24 )	2.43076923076923	0.00986655362224088	246.364569011196
Trimmed Mean ( 11 / 24 )	2.431	0.00962246521088509	252.637961969456
Trimmed Mean ( 12 / 24 )	2.43125	0.00930961239680382	261.154803913716
Trimmed Mean ( 13 / 24 )	2.43152173913043	0.00890620687492553	273.014289166819
Trimmed Mean ( 14 / 24 )	2.43136363636364	0.00866690937334179	280.534101792061
Trimmed Mean ( 15 / 24 )	2.43119047619048	0.0083492464622216	291.186813946749
Trimmed Mean ( 16 / 24 )	2.431	0.00808448974017373	300.699249814096
Trimmed Mean ( 17 / 24 )	2.43078947368421	0.00772372873847307	314.717095329368
Trimmed Mean ( 18 / 24 )	2.43083333333333	0.00751057455583328	323.654777043038
Trimmed Mean ( 19 / 24 )	2.43117647058824	0.00729765310212766	333.144976414324
Trimmed Mean ( 20 / 24 )	2.43125	0.00709597227873991	342.623942780078
Trimmed Mean ( 21 / 24 )	2.43133333333333	0.00679305482605079	357.914575340887
Trimmed Mean ( 22 / 24 )	2.43142857142857	0.00660115201013597	368.333976811191
Trimmed Mean ( 23 / 24 )	2.43153846153846	0.00629266502652849	386.408374081193
Trimmed Mean ( 24 / 24 )	2.43208333333333	0.00595816230625123	408.193534906161
Median	2.435
Midrange	2.42
Midmean - Weighted Average at Xnp	2.42864864864865
Midmean - Weighted Average at X(n+1)p	2.42864864864865
Midmean - Empirical Distribution Function	2.42864864864865
Midmean - Empirical Distribution Function - Averaging	2.42864864864865
Midmean - Empirical Distribution Function - Interpolation	2.42864864864865
Midmean - Closest Observation	2.42864864864865
Midmean - True Basic - Statistics Graphics Toolkit	2.42864864864865
Midmean - MS Excel (old versions)	2.43078947368421
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