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Author

*The author of this computation has been verified*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Fri, 16 Oct 2009 09:08:13 -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/2009/Oct/16/t1255705727qk1esjzaxz3ljvd.htm/, Retrieved Tue, 30 Apr 2024 02:33:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47044, Retrieved Tue, 30 Apr 2024 02:33:54 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

170

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

-     [Univariate Data Series] [Inflatie] [2009-10-11 21:52:09] [badc6a9acdc45286bea7f74742e15a21]
-    D  [Univariate Data Series] [Inflatie] [2009-10-11 22:00:34] [badc6a9acdc45286bea7f74742e15a21]
-         [Univariate Data Series] [Inflatie] [2009-10-12 20:15:52] [badc6a9acdc45286bea7f74742e15a21]
- RMP         [Central Tendency] [ws 3 part 2] [2009-10-16 15:08:13] [0545e25c765ce26b196961216dc11e13] [Current]
- RM            [Variability] [ws 3 part 2] [2009-10-16 15:14:58] [badc6a9acdc45286bea7f74742e15a21] 
- RM            [Percentiles] [ws 3 part 2] [2009-10-16 15:17:36] [badc6a9acdc45286bea7f74742e15a21] 
- RMP           [Harrell-Davis Quantiles] [ws 3 part 2] [2009-10-16 15:24:32] [badc6a9acdc45286bea7f74742e15a21] 

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Dataseries X:

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Histogram

Boxplots

1.4
1.2
1
1.7
2.4
2
2.1
2
1.8
2.7
2.3
1.9
2
2.3
2.8
2.4
2.3
2.7
2.7
2.9
3
2.2
2.3
2.8
2.8
2.8
2.2
2.6
2.8
2.5
2.4
2.3
1.9
1.7
2
2.1
1.7
1.8
1.8
1.8
1.3
1.3
1.3
1.2
1.4
2.2
2.9
3.1
3.5
3.6
4.4
4.1
5.1
5.8
5.9
5.4
5.5
4.8
3.2
2.7
2.1
1.9
0.6
0.7
-0.2
-1
-1.7
-0.7
-1

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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47044&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47044&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47044&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	'George Udny Yule' @ 72.249.76.132

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	2.28260869565217	0.175733228536456	12.9890557105348
Geometric Mean	NaN
Harmonic Mean	3.11917611579511
Quadratic Mean	2.70375476977341
Winsorized Mean ( 1 / 23 )	2.29130434782609	0.172177508207748	13.3078029277867
Winsorized Mean ( 2 / 23 )	2.28260869565217	0.169661371299064	13.4539092674701
Winsorized Mean ( 3 / 23 )	2.29130434782609	0.164854674310715	13.8989346671935
Winsorized Mean ( 4 / 23 )	2.30289855072464	0.152724211018608	15.0788046987785
Winsorized Mean ( 5 / 23 )	2.33913043478261	0.134265984557297	17.4216160742068
Winsorized Mean ( 6 / 23 )	2.31304347826087	0.123581690049227	18.7167166700788
Winsorized Mean ( 7 / 23 )	2.31304347826087	0.110584609483208	20.9165044672162
Winsorized Mean ( 8 / 23 )	2.27826086956522	0.0936124851686102	24.3371476086948
Winsorized Mean ( 9 / 23 )	2.26521739130435	0.0909555714163881	24.9046579118759
Winsorized Mean ( 10 / 23 )	2.23623188405797	0.0802535149401066	27.8645974039502
Winsorized Mean ( 11 / 23 )	2.22028985507246	0.0775141191149673	28.6436829886356
Winsorized Mean ( 12 / 23 )	2.20289855072464	0.0746966303928144	29.4912707459499
Winsorized Mean ( 13 / 23 )	2.20289855072464	0.0685052631282385	32.1566322079651
Winsorized Mean ( 14 / 23 )	2.20289855072464	0.0685052631282385	32.1566322079651
Winsorized Mean ( 15 / 23 )	2.24637681159420	0.0547636832039283	41.0194618070003
Winsorized Mean ( 16 / 23 )	2.24637681159420	0.0547636832039283	41.0194618070003
Winsorized Mean ( 17 / 23 )	2.24637681159420	0.0547636832039283	41.0194618070003
Winsorized Mean ( 18 / 23 )	2.27246376811594	0.0510705535570808	44.4965564271012
Winsorized Mean ( 19 / 23 )	2.27246376811594	0.0510705535570808	44.4965564271012
Winsorized Mean ( 20 / 23 )	2.24347826086957	0.0467839650937781	47.9539999735493
Winsorized Mean ( 21 / 23 )	2.24347826086957	0.0467839650937781	47.9539999735493
Winsorized Mean ( 22 / 23 )	2.27536231884058	0.0424829235590469	53.5594570293181
Winsorized Mean ( 23 / 23 )	2.27536231884058	0.0424829235590469	53.5594570293181
Trimmed Mean ( 1 / 23 )	2.28805970149254	0.16192982477119	14.1299461339232
Trimmed Mean ( 2 / 23 )	2.28461538461538	0.149361312846225	15.2958978538674
Trimmed Mean ( 3 / 23 )	2.28571428571429	0.135464102274001	16.8732102995893
Trimmed Mean ( 4 / 23 )	2.28360655737705	0.120408692201823	18.9654626723242
Trimmed Mean ( 5 / 23 )	2.27796610169492	0.106703097986293	21.3486407113273
Trimmed Mean ( 6 / 23 )	2.26315789473684	0.0965777693480838	23.4335283369407
Trimmed Mean ( 7 / 23 )	2.25272727272727	0.0875346798212633	25.7352546136812
Trimmed Mean ( 8 / 23 )	2.24150943396226	0.080294901046034	27.9159623433271
Trimmed Mean ( 9 / 23 )	2.23529411764706	0.0762772820706944	29.3048474849349
Trimmed Mean ( 10 / 23 )	2.23061224489796	0.0719152516177455	31.0172347967916
Trimmed Mean ( 11 / 23 )	2.23061224489796	0.0692175707199023	32.2260983981136
Trimmed Mean ( 12 / 23 )	2.23111111111111	0.0664254896783783	33.5881770975840
Trimmed Mean ( 13 / 23 )	2.23488372093023	0.063480076044365	35.2060655908527
Trimmed Mean ( 14 / 23 )	2.23902439024390	0.0611752828275468	36.6001477517597
Trimmed Mean ( 15 / 23 )	2.24358974358974	0.0580607518157944	38.642106301135
Trimmed Mean ( 16 / 23 )	2.24324324324324	0.0574143232357635	39.0711431715688
Trimmed Mean ( 17 / 23 )	2.24285714285714	0.0564027704018482	39.7650173365181
Trimmed Mean ( 18 / 23 )	2.24242424242424	0.0548811220493177	40.8596646476932
Trimmed Mean ( 19 / 23 )	2.23870967741935	0.0536170048765503	41.7537250089564
Trimmed Mean ( 20 / 23 )	2.23448275862069	0.0516419708609966	43.2687351269996
Trimmed Mean ( 21 / 23 )	2.23333333333333	0.0500711744132541	44.6031745710794
Trimmed Mean ( 22 / 23 )	2.23333333333333	0.0475114021402582	47.0062602391805
Trimmed Mean ( 23 / 23 )	2.22608695652174	0.0449933641591032	49.47589490419
Median	2.2
Midrange	2.1
Midmean - Weighted Average at Xnp	2.24358974358974
Midmean - Weighted Average at X(n+1)p	2.24358974358974
Midmean - Empirical Distribution Function	2.24358974358974
Midmean - Empirical Distribution Function - Averaging	2.24358974358974
Midmean - Empirical Distribution Function - Interpolation	2.24358974358974
Midmean - Closest Observation	2.24358974358974
Midmean - True Basic - Statistics Graphics Toolkit	2.24358974358974
Midmean - MS Excel (old versions)	2.24358974358974
Number of observations	69

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.28260869565217 & 0.175733228536456 & 12.9890557105348 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 3.11917611579511 &  &  \tabularnewline
Quadratic Mean & 2.70375476977341 &  &  \tabularnewline
Winsorized Mean ( 1 / 23 ) & 2.29130434782609 & 0.172177508207748 & 13.3078029277867 \tabularnewline
Winsorized Mean ( 2 / 23 ) & 2.28260869565217 & 0.169661371299064 & 13.4539092674701 \tabularnewline
Winsorized Mean ( 3 / 23 ) & 2.29130434782609 & 0.164854674310715 & 13.8989346671935 \tabularnewline
Winsorized Mean ( 4 / 23 ) & 2.30289855072464 & 0.152724211018608 & 15.0788046987785 \tabularnewline
Winsorized Mean ( 5 / 23 ) & 2.33913043478261 & 0.134265984557297 & 17.4216160742068 \tabularnewline
Winsorized Mean ( 6 / 23 ) & 2.31304347826087 & 0.123581690049227 & 18.7167166700788 \tabularnewline
Winsorized Mean ( 7 / 23 ) & 2.31304347826087 & 0.110584609483208 & 20.9165044672162 \tabularnewline
Winsorized Mean ( 8 / 23 ) & 2.27826086956522 & 0.0936124851686102 & 24.3371476086948 \tabularnewline
Winsorized Mean ( 9 / 23 ) & 2.26521739130435 & 0.0909555714163881 & 24.9046579118759 \tabularnewline
Winsorized Mean ( 10 / 23 ) & 2.23623188405797 & 0.0802535149401066 & 27.8645974039502 \tabularnewline
Winsorized Mean ( 11 / 23 ) & 2.22028985507246 & 0.0775141191149673 & 28.6436829886356 \tabularnewline
Winsorized Mean ( 12 / 23 ) & 2.20289855072464 & 0.0746966303928144 & 29.4912707459499 \tabularnewline
Winsorized Mean ( 13 / 23 ) & 2.20289855072464 & 0.0685052631282385 & 32.1566322079651 \tabularnewline
Winsorized Mean ( 14 / 23 ) & 2.20289855072464 & 0.0685052631282385 & 32.1566322079651 \tabularnewline
Winsorized Mean ( 15 / 23 ) & 2.24637681159420 & 0.0547636832039283 & 41.0194618070003 \tabularnewline
Winsorized Mean ( 16 / 23 ) & 2.24637681159420 & 0.0547636832039283 & 41.0194618070003 \tabularnewline
Winsorized Mean ( 17 / 23 ) & 2.24637681159420 & 0.0547636832039283 & 41.0194618070003 \tabularnewline
Winsorized Mean ( 18 / 23 ) & 2.27246376811594 & 0.0510705535570808 & 44.4965564271012 \tabularnewline
Winsorized Mean ( 19 / 23 ) & 2.27246376811594 & 0.0510705535570808 & 44.4965564271012 \tabularnewline
Winsorized Mean ( 20 / 23 ) & 2.24347826086957 & 0.0467839650937781 & 47.9539999735493 \tabularnewline
Winsorized Mean ( 21 / 23 ) & 2.24347826086957 & 0.0467839650937781 & 47.9539999735493 \tabularnewline
Winsorized Mean ( 22 / 23 ) & 2.27536231884058 & 0.0424829235590469 & 53.5594570293181 \tabularnewline
Winsorized Mean ( 23 / 23 ) & 2.27536231884058 & 0.0424829235590469 & 53.5594570293181 \tabularnewline
Trimmed Mean ( 1 / 23 ) & 2.28805970149254 & 0.16192982477119 & 14.1299461339232 \tabularnewline
Trimmed Mean ( 2 / 23 ) & 2.28461538461538 & 0.149361312846225 & 15.2958978538674 \tabularnewline
Trimmed Mean ( 3 / 23 ) & 2.28571428571429 & 0.135464102274001 & 16.8732102995893 \tabularnewline
Trimmed Mean ( 4 / 23 ) & 2.28360655737705 & 0.120408692201823 & 18.9654626723242 \tabularnewline
Trimmed Mean ( 5 / 23 ) & 2.27796610169492 & 0.106703097986293 & 21.3486407113273 \tabularnewline
Trimmed Mean ( 6 / 23 ) & 2.26315789473684 & 0.0965777693480838 & 23.4335283369407 \tabularnewline
Trimmed Mean ( 7 / 23 ) & 2.25272727272727 & 0.0875346798212633 & 25.7352546136812 \tabularnewline
Trimmed Mean ( 8 / 23 ) & 2.24150943396226 & 0.080294901046034 & 27.9159623433271 \tabularnewline
Trimmed Mean ( 9 / 23 ) & 2.23529411764706 & 0.0762772820706944 & 29.3048474849349 \tabularnewline
Trimmed Mean ( 10 / 23 ) & 2.23061224489796 & 0.0719152516177455 & 31.0172347967916 \tabularnewline
Trimmed Mean ( 11 / 23 ) & 2.23061224489796 & 0.0692175707199023 & 32.2260983981136 \tabularnewline
Trimmed Mean ( 12 / 23 ) & 2.23111111111111 & 0.0664254896783783 & 33.5881770975840 \tabularnewline
Trimmed Mean ( 13 / 23 ) & 2.23488372093023 & 0.063480076044365 & 35.2060655908527 \tabularnewline
Trimmed Mean ( 14 / 23 ) & 2.23902439024390 & 0.0611752828275468 & 36.6001477517597 \tabularnewline
Trimmed Mean ( 15 / 23 ) & 2.24358974358974 & 0.0580607518157944 & 38.642106301135 \tabularnewline
Trimmed Mean ( 16 / 23 ) & 2.24324324324324 & 0.0574143232357635 & 39.0711431715688 \tabularnewline
Trimmed Mean ( 17 / 23 ) & 2.24285714285714 & 0.0564027704018482 & 39.7650173365181 \tabularnewline
Trimmed Mean ( 18 / 23 ) & 2.24242424242424 & 0.0548811220493177 & 40.8596646476932 \tabularnewline
Trimmed Mean ( 19 / 23 ) & 2.23870967741935 & 0.0536170048765503 & 41.7537250089564 \tabularnewline
Trimmed Mean ( 20 / 23 ) & 2.23448275862069 & 0.0516419708609966 & 43.2687351269996 \tabularnewline
Trimmed Mean ( 21 / 23 ) & 2.23333333333333 & 0.0500711744132541 & 44.6031745710794 \tabularnewline
Trimmed Mean ( 22 / 23 ) & 2.23333333333333 & 0.0475114021402582 & 47.0062602391805 \tabularnewline
Trimmed Mean ( 23 / 23 ) & 2.22608695652174 & 0.0449933641591032 & 49.47589490419 \tabularnewline
Median & 2.2 &  &  \tabularnewline
Midrange & 2.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.24358974358974 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.24358974358974 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.24358974358974 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.24358974358974 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.24358974358974 &  &  \tabularnewline
Midmean - Closest Observation & 2.24358974358974 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.24358974358974 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.24358974358974 &  &  \tabularnewline
Number of observations & 69 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47044&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]2.28260869565217[/C][C]0.175733228536456[/C][C]12.9890557105348[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.11917611579511[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.70375476977341[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 23 )[/C][C]2.29130434782609[/C][C]0.172177508207748[/C][C]13.3078029277867[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 23 )[/C][C]2.28260869565217[/C][C]0.169661371299064[/C][C]13.4539092674701[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 23 )[/C][C]2.29130434782609[/C][C]0.164854674310715[/C][C]13.8989346671935[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 23 )[/C][C]2.30289855072464[/C][C]0.152724211018608[/C][C]15.0788046987785[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 23 )[/C][C]2.33913043478261[/C][C]0.134265984557297[/C][C]17.4216160742068[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 23 )[/C][C]2.31304347826087[/C][C]0.123581690049227[/C][C]18.7167166700788[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 23 )[/C][C]2.31304347826087[/C][C]0.110584609483208[/C][C]20.9165044672162[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 23 )[/C][C]2.27826086956522[/C][C]0.0936124851686102[/C][C]24.3371476086948[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 23 )[/C][C]2.26521739130435[/C][C]0.0909555714163881[/C][C]24.9046579118759[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 23 )[/C][C]2.23623188405797[/C][C]0.0802535149401066[/C][C]27.8645974039502[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 23 )[/C][C]2.22028985507246[/C][C]0.0775141191149673[/C][C]28.6436829886356[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 23 )[/C][C]2.20289855072464[/C][C]0.0746966303928144[/C][C]29.4912707459499[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 23 )[/C][C]2.20289855072464[/C][C]0.0685052631282385[/C][C]32.1566322079651[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 23 )[/C][C]2.20289855072464[/C][C]0.0685052631282385[/C][C]32.1566322079651[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 23 )[/C][C]2.24637681159420[/C][C]0.0547636832039283[/C][C]41.0194618070003[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 23 )[/C][C]2.24637681159420[/C][C]0.0547636832039283[/C][C]41.0194618070003[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 23 )[/C][C]2.24637681159420[/C][C]0.0547636832039283[/C][C]41.0194618070003[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 23 )[/C][C]2.27246376811594[/C][C]0.0510705535570808[/C][C]44.4965564271012[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 23 )[/C][C]2.27246376811594[/C][C]0.0510705535570808[/C][C]44.4965564271012[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 23 )[/C][C]2.24347826086957[/C][C]0.0467839650937781[/C][C]47.9539999735493[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 23 )[/C][C]2.24347826086957[/C][C]0.0467839650937781[/C][C]47.9539999735493[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 23 )[/C][C]2.27536231884058[/C][C]0.0424829235590469[/C][C]53.5594570293181[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 23 )[/C][C]2.27536231884058[/C][C]0.0424829235590469[/C][C]53.5594570293181[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 23 )[/C][C]2.28805970149254[/C][C]0.16192982477119[/C][C]14.1299461339232[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 23 )[/C][C]2.28461538461538[/C][C]0.149361312846225[/C][C]15.2958978538674[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 23 )[/C][C]2.28571428571429[/C][C]0.135464102274001[/C][C]16.8732102995893[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 23 )[/C][C]2.28360655737705[/C][C]0.120408692201823[/C][C]18.9654626723242[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 23 )[/C][C]2.27796610169492[/C][C]0.106703097986293[/C][C]21.3486407113273[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 23 )[/C][C]2.26315789473684[/C][C]0.0965777693480838[/C][C]23.4335283369407[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 23 )[/C][C]2.25272727272727[/C][C]0.0875346798212633[/C][C]25.7352546136812[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 23 )[/C][C]2.24150943396226[/C][C]0.080294901046034[/C][C]27.9159623433271[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 23 )[/C][C]2.23529411764706[/C][C]0.0762772820706944[/C][C]29.3048474849349[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 23 )[/C][C]2.23061224489796[/C][C]0.0719152516177455[/C][C]31.0172347967916[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 23 )[/C][C]2.23061224489796[/C][C]0.0692175707199023[/C][C]32.2260983981136[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 23 )[/C][C]2.23111111111111[/C][C]0.0664254896783783[/C][C]33.5881770975840[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 23 )[/C][C]2.23488372093023[/C][C]0.063480076044365[/C][C]35.2060655908527[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 23 )[/C][C]2.23902439024390[/C][C]0.0611752828275468[/C][C]36.6001477517597[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 23 )[/C][C]2.24358974358974[/C][C]0.0580607518157944[/C][C]38.642106301135[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 23 )[/C][C]2.24324324324324[/C][C]0.0574143232357635[/C][C]39.0711431715688[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 23 )[/C][C]2.24285714285714[/C][C]0.0564027704018482[/C][C]39.7650173365181[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 23 )[/C][C]2.24242424242424[/C][C]0.0548811220493177[/C][C]40.8596646476932[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 23 )[/C][C]2.23870967741935[/C][C]0.0536170048765503[/C][C]41.7537250089564[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 23 )[/C][C]2.23448275862069[/C][C]0.0516419708609966[/C][C]43.2687351269996[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 23 )[/C][C]2.23333333333333[/C][C]0.0500711744132541[/C][C]44.6031745710794[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 23 )[/C][C]2.23333333333333[/C][C]0.0475114021402582[/C][C]47.0062602391805[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 23 )[/C][C]2.22608695652174[/C][C]0.0449933641591032[/C][C]49.47589490419[/C][/ROW]
[ROW][C]Median[/C][C]2.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.24358974358974[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.24358974358974[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.24358974358974[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.24358974358974[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.24358974358974[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.24358974358974[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.24358974358974[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.24358974358974[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]69[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47044&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47044&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	2.28260869565217	0.175733228536456	12.9890557105348
Geometric Mean	NaN
Harmonic Mean	3.11917611579511
Quadratic Mean	2.70375476977341
Winsorized Mean ( 1 / 23 )	2.29130434782609	0.172177508207748	13.3078029277867
Winsorized Mean ( 2 / 23 )	2.28260869565217	0.169661371299064	13.4539092674701
Winsorized Mean ( 3 / 23 )	2.29130434782609	0.164854674310715	13.8989346671935
Winsorized Mean ( 4 / 23 )	2.30289855072464	0.152724211018608	15.0788046987785
Winsorized Mean ( 5 / 23 )	2.33913043478261	0.134265984557297	17.4216160742068
Winsorized Mean ( 6 / 23 )	2.31304347826087	0.123581690049227	18.7167166700788
Winsorized Mean ( 7 / 23 )	2.31304347826087	0.110584609483208	20.9165044672162
Winsorized Mean ( 8 / 23 )	2.27826086956522	0.0936124851686102	24.3371476086948
Winsorized Mean ( 9 / 23 )	2.26521739130435	0.0909555714163881	24.9046579118759
Winsorized Mean ( 10 / 23 )	2.23623188405797	0.0802535149401066	27.8645974039502
Winsorized Mean ( 11 / 23 )	2.22028985507246	0.0775141191149673	28.6436829886356
Winsorized Mean ( 12 / 23 )	2.20289855072464	0.0746966303928144	29.4912707459499
Winsorized Mean ( 13 / 23 )	2.20289855072464	0.0685052631282385	32.1566322079651
Winsorized Mean ( 14 / 23 )	2.20289855072464	0.0685052631282385	32.1566322079651
Winsorized Mean ( 15 / 23 )	2.24637681159420	0.0547636832039283	41.0194618070003
Winsorized Mean ( 16 / 23 )	2.24637681159420	0.0547636832039283	41.0194618070003
Winsorized Mean ( 17 / 23 )	2.24637681159420	0.0547636832039283	41.0194618070003
Winsorized Mean ( 18 / 23 )	2.27246376811594	0.0510705535570808	44.4965564271012
Winsorized Mean ( 19 / 23 )	2.27246376811594	0.0510705535570808	44.4965564271012
Winsorized Mean ( 20 / 23 )	2.24347826086957	0.0467839650937781	47.9539999735493
Winsorized Mean ( 21 / 23 )	2.24347826086957	0.0467839650937781	47.9539999735493
Winsorized Mean ( 22 / 23 )	2.27536231884058	0.0424829235590469	53.5594570293181
Winsorized Mean ( 23 / 23 )	2.27536231884058	0.0424829235590469	53.5594570293181
Trimmed Mean ( 1 / 23 )	2.28805970149254	0.16192982477119	14.1299461339232
Trimmed Mean ( 2 / 23 )	2.28461538461538	0.149361312846225	15.2958978538674
Trimmed Mean ( 3 / 23 )	2.28571428571429	0.135464102274001	16.8732102995893
Trimmed Mean ( 4 / 23 )	2.28360655737705	0.120408692201823	18.9654626723242
Trimmed Mean ( 5 / 23 )	2.27796610169492	0.106703097986293	21.3486407113273
Trimmed Mean ( 6 / 23 )	2.26315789473684	0.0965777693480838	23.4335283369407
Trimmed Mean ( 7 / 23 )	2.25272727272727	0.0875346798212633	25.7352546136812
Trimmed Mean ( 8 / 23 )	2.24150943396226	0.080294901046034	27.9159623433271
Trimmed Mean ( 9 / 23 )	2.23529411764706	0.0762772820706944	29.3048474849349
Trimmed Mean ( 10 / 23 )	2.23061224489796	0.0719152516177455	31.0172347967916
Trimmed Mean ( 11 / 23 )	2.23061224489796	0.0692175707199023	32.2260983981136
Trimmed Mean ( 12 / 23 )	2.23111111111111	0.0664254896783783	33.5881770975840
Trimmed Mean ( 13 / 23 )	2.23488372093023	0.063480076044365	35.2060655908527
Trimmed Mean ( 14 / 23 )	2.23902439024390	0.0611752828275468	36.6001477517597
Trimmed Mean ( 15 / 23 )	2.24358974358974	0.0580607518157944	38.642106301135
Trimmed Mean ( 16 / 23 )	2.24324324324324	0.0574143232357635	39.0711431715688
Trimmed Mean ( 17 / 23 )	2.24285714285714	0.0564027704018482	39.7650173365181
Trimmed Mean ( 18 / 23 )	2.24242424242424	0.0548811220493177	40.8596646476932
Trimmed Mean ( 19 / 23 )	2.23870967741935	0.0536170048765503	41.7537250089564
Trimmed Mean ( 20 / 23 )	2.23448275862069	0.0516419708609966	43.2687351269996
Trimmed Mean ( 21 / 23 )	2.23333333333333	0.0500711744132541	44.6031745710794
Trimmed Mean ( 22 / 23 )	2.23333333333333	0.0475114021402582	47.0062602391805
Trimmed Mean ( 23 / 23 )	2.22608695652174	0.0449933641591032	49.47589490419
Median	2.2
Midrange	2.1
Midmean - Weighted Average at Xnp	2.24358974358974
Midmean - Weighted Average at X(n+1)p	2.24358974358974
Midmean - Empirical Distribution Function	2.24358974358974
Midmean - Empirical Distribution Function - Averaging	2.24358974358974
Midmean - Empirical Distribution Function - Interpolation	2.24358974358974
Midmean - Closest Observation	2.24358974358974
Midmean - True Basic - Statistics Graphics Toolkit	2.24358974358974
Midmean - MS Excel (old versions)	2.24358974358974
Number of observations	69

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