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Author

*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Thu, 07 Mar 2013 04:37:43 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Mar/07/t1362649141bhpqa1me5tt26dv.htm/, Retrieved Tue, 30 Apr 2024 11:09:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207540, Retrieved Tue, 30 Apr 2024 11:09:32 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

106

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

-       [Central Tendency] [Registraties nieu...] [2013-03-07 09:37:43] [618e20b48371a4632e04cdc6ff96552f] [Current]

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Dataseries X:

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-5,3
-7,1
-8
-8,9
-7,7
-1,1
4
9,6
10,9
13
14,9
20,1
10,8
11
3,8
10,8
7,6
10,2
2,2
-0,1
-1,7
-4,8
-9,9
-13,5
-18,1
-18
-15,7
-15,2
-15,1
-17,9
-14,5
-9,4
-4,2
-2,2
4,5
12,4
15,8
11,5
14,1
18,8
26,1
27,9
25,4
23,4
11,5
9,9
8,1
12,6
8,2
5,4
1
-2,9
-3,7
-7
-7,2
-11,8
-2,1
1,2
2,5
4,8
-6,6
-16
-22,7
-17,7
-18,2
-18,9
-16
-12,2
-17,1
-18,6
-17,5
-24,9

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=207540&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=207540&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207540&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	-0.909722222222222	1.56251592758357	-0.582216287311135
Geometric Mean	NaN
Harmonic Mean	-6.98630001860437
Quadratic Mean	13.1973850524345
Winsorized Mean ( 1 / 24 )	-0.904166666666667	1.54987055532483	-0.583382053140021
Winsorized Mean ( 2 / 24 )	-0.818055555555556	1.52585608797438	-0.536128906259795
Winsorized Mean ( 3 / 24 )	-0.888888888888889	1.50421233730304	-0.59093311951065
Winsorized Mean ( 4 / 24 )	-1.05	1.46096308835641	-0.718703989421973
Winsorized Mean ( 5 / 24 )	-1.13333333333333	1.44181761265738	-0.786044866829249
Winsorized Mean ( 6 / 24 )	-1.375	1.39435727084132	-0.986117423958612
Winsorized Mean ( 7 / 24 )	-1.45277777777778	1.37781859668697	-1.05440424542901
Winsorized Mean ( 8 / 24 )	-1.51944444444444	1.35946464724476	-1.11767852700246
Winsorized Mean ( 9 / 24 )	-1.63194444444444	1.3335193919316	-1.22378756118468
Winsorized Mean ( 10 / 24 )	-1.63194444444444	1.31573900045846	-1.24032535622628
Winsorized Mean ( 11 / 24 )	-1.49444444444444	1.28379037177322	-1.16408759350661
Winsorized Mean ( 12 / 24 )	-1.64444444444444	1.26134583105193	-1.30372210694431
Winsorized Mean ( 13 / 24 )	-1.59027777777778	1.25270780221242	-1.26947223843355
Winsorized Mean ( 14 / 24 )	-1.59027777777778	1.22317405629623	-1.3001238618428
Winsorized Mean ( 15 / 24 )	-1.59027777777778	1.21689682002532	-1.30683041619313
Winsorized Mean ( 16 / 24 )	-1.47916666666667	1.19300572767922	-1.23986551979438
Winsorized Mean ( 17 / 24 )	-1.24305555555556	1.15723860923518	-1.07415665674782
Winsorized Mean ( 18 / 24 )	-1.06805555555556	1.08760772205655	-0.982022777050516
Winsorized Mean ( 19 / 24 )	-1.04166666666667	1.06093447677331	-0.981838831211099
Winsorized Mean ( 20 / 24 )	-0.597222222222222	0.975523959815738	-0.612206615955418
Winsorized Mean ( 21 / 24 )	-0.859722222222223	0.896798469557609	-0.958657102354695
Winsorized Mean ( 22 / 24 )	-0.7375	0.872126261255333	-0.845634437080759
Winsorized Mean ( 23 / 24 )	-0.609722222222222	0.811958642865432	-0.750927682807206
Winsorized Mean ( 24 / 24 )	-1.24305555555556	0.697398548522139	-1.782417755514
Trimmed Mean ( 1 / 24 )	-0.978571428571429	1.5142427920789	-0.646244732806652
Trimmed Mean ( 2 / 24 )	-1.05735294117647	1.47181348211919	-0.718401451014053
Trimmed Mean ( 3 / 24 )	-1.18787878787879	1.4362839178059	-0.827050120907447
Trimmed Mean ( 4 / 24 )	-1.3	1.40341667833038	-0.926310781447024
Trimmed Mean ( 5 / 24 )	-1.37258064516129	1.37952116048677	-0.994968895349867
Trimmed Mean ( 6 / 24 )	-1.43	1.35614379351917	-1.05446045384994
Trimmed Mean ( 7 / 24 )	-1.44137931034483	1.34031678696862	-1.07540196792191
Trimmed Mean ( 8 / 24 )	-1.43928571428571	1.3242412151562	-1.08687578804587
Trimmed Mean ( 9 / 24 )	-1.42592592592593	1.30783315810094	-1.0902965084602
Trimmed Mean ( 10 / 24 )	-1.39423076923077	1.29226557942408	-1.07890420624848
Trimmed Mean ( 11 / 24 )	-1.36	1.27553750174871	-1.06621718149054
Trimmed Mean ( 12 / 24 )	-1.34166666666667	1.26014617430465	-1.06469129853685
Trimmed Mean ( 13 / 24 )	-1.30217391304348	1.24384664824569	-1.04689264941145
Trimmed Mean ( 14 / 24 )	-1.26590909090909	1.2233110338924	-1.0348219347627
Trimmed Mean ( 15 / 24 )	-1.22619047619048	1.20169286091907	-1.02038592061925
Trimmed Mean ( 16 / 24 )	-1.1825	1.17317172273527	-1.00795133149219
Trimmed Mean ( 17 / 24 )	-1.14736842105263	1.13964343230845	-1.00677842606309
Trimmed Mean ( 18 / 24 )	-1.13611111111111	1.10222108214867	-1.03074703388578
Trimmed Mean ( 19 / 24 )	-1.14411764705882	1.06802657721335	-1.07124454715725
Trimmed Mean ( 20 / 24 )	-1.15625	1.0260315177436	-1.12691469999165
Trimmed Mean ( 21 / 24 )	-1.22333333333333	0.989620655678525	-1.2361639041321
Trimmed Mean ( 22 / 24 )	-1.26785714285714	0.959718509924531	-1.32107188696073
Trimmed Mean ( 23 / 24 )	-1.33461538461538	0.92003247948842	-1.45061768401643
Trimmed Mean ( 24 / 24 )	-1.42916666666667	0.878207973756264	-1.6273669897961
Median	-1.9
Midrange	1.5
Midmean - Weighted Average at Xnp	-1.47027027027027
Midmean - Weighted Average at X(n+1)p	-1.13611111111111
Midmean - Empirical Distribution Function	-1.47027027027027
Midmean - Empirical Distribution Function - Averaging	-1.13611111111111
Midmean - Empirical Distribution Function - Interpolation	-1.13611111111111
Midmean - Closest Observation	-1.47027027027027
Midmean - True Basic - Statistics Graphics Toolkit	-1.13611111111111
Midmean - MS Excel (old versions)	-0.841025641025641
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -0.909722222222222 & 1.56251592758357 & -0.582216287311135 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -6.98630001860437 &  &  \tabularnewline
Quadratic Mean & 13.1973850524345 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & -0.904166666666667 & 1.54987055532483 & -0.583382053140021 \tabularnewline
Winsorized Mean ( 2 / 24 ) & -0.818055555555556 & 1.52585608797438 & -0.536128906259795 \tabularnewline
Winsorized Mean ( 3 / 24 ) & -0.888888888888889 & 1.50421233730304 & -0.59093311951065 \tabularnewline
Winsorized Mean ( 4 / 24 ) & -1.05 & 1.46096308835641 & -0.718703989421973 \tabularnewline
Winsorized Mean ( 5 / 24 ) & -1.13333333333333 & 1.44181761265738 & -0.786044866829249 \tabularnewline
Winsorized Mean ( 6 / 24 ) & -1.375 & 1.39435727084132 & -0.986117423958612 \tabularnewline
Winsorized Mean ( 7 / 24 ) & -1.45277777777778 & 1.37781859668697 & -1.05440424542901 \tabularnewline
Winsorized Mean ( 8 / 24 ) & -1.51944444444444 & 1.35946464724476 & -1.11767852700246 \tabularnewline
Winsorized Mean ( 9 / 24 ) & -1.63194444444444 & 1.3335193919316 & -1.22378756118468 \tabularnewline
Winsorized Mean ( 10 / 24 ) & -1.63194444444444 & 1.31573900045846 & -1.24032535622628 \tabularnewline
Winsorized Mean ( 11 / 24 ) & -1.49444444444444 & 1.28379037177322 & -1.16408759350661 \tabularnewline
Winsorized Mean ( 12 / 24 ) & -1.64444444444444 & 1.26134583105193 & -1.30372210694431 \tabularnewline
Winsorized Mean ( 13 / 24 ) & -1.59027777777778 & 1.25270780221242 & -1.26947223843355 \tabularnewline
Winsorized Mean ( 14 / 24 ) & -1.59027777777778 & 1.22317405629623 & -1.3001238618428 \tabularnewline
Winsorized Mean ( 15 / 24 ) & -1.59027777777778 & 1.21689682002532 & -1.30683041619313 \tabularnewline
Winsorized Mean ( 16 / 24 ) & -1.47916666666667 & 1.19300572767922 & -1.23986551979438 \tabularnewline
Winsorized Mean ( 17 / 24 ) & -1.24305555555556 & 1.15723860923518 & -1.07415665674782 \tabularnewline
Winsorized Mean ( 18 / 24 ) & -1.06805555555556 & 1.08760772205655 & -0.982022777050516 \tabularnewline
Winsorized Mean ( 19 / 24 ) & -1.04166666666667 & 1.06093447677331 & -0.981838831211099 \tabularnewline
Winsorized Mean ( 20 / 24 ) & -0.597222222222222 & 0.975523959815738 & -0.612206615955418 \tabularnewline
Winsorized Mean ( 21 / 24 ) & -0.859722222222223 & 0.896798469557609 & -0.958657102354695 \tabularnewline
Winsorized Mean ( 22 / 24 ) & -0.7375 & 0.872126261255333 & -0.845634437080759 \tabularnewline
Winsorized Mean ( 23 / 24 ) & -0.609722222222222 & 0.811958642865432 & -0.750927682807206 \tabularnewline
Winsorized Mean ( 24 / 24 ) & -1.24305555555556 & 0.697398548522139 & -1.782417755514 \tabularnewline
Trimmed Mean ( 1 / 24 ) & -0.978571428571429 & 1.5142427920789 & -0.646244732806652 \tabularnewline
Trimmed Mean ( 2 / 24 ) & -1.05735294117647 & 1.47181348211919 & -0.718401451014053 \tabularnewline
Trimmed Mean ( 3 / 24 ) & -1.18787878787879 & 1.4362839178059 & -0.827050120907447 \tabularnewline
Trimmed Mean ( 4 / 24 ) & -1.3 & 1.40341667833038 & -0.926310781447024 \tabularnewline
Trimmed Mean ( 5 / 24 ) & -1.37258064516129 & 1.37952116048677 & -0.994968895349867 \tabularnewline
Trimmed Mean ( 6 / 24 ) & -1.43 & 1.35614379351917 & -1.05446045384994 \tabularnewline
Trimmed Mean ( 7 / 24 ) & -1.44137931034483 & 1.34031678696862 & -1.07540196792191 \tabularnewline
Trimmed Mean ( 8 / 24 ) & -1.43928571428571 & 1.3242412151562 & -1.08687578804587 \tabularnewline
Trimmed Mean ( 9 / 24 ) & -1.42592592592593 & 1.30783315810094 & -1.0902965084602 \tabularnewline
Trimmed Mean ( 10 / 24 ) & -1.39423076923077 & 1.29226557942408 & -1.07890420624848 \tabularnewline
Trimmed Mean ( 11 / 24 ) & -1.36 & 1.27553750174871 & -1.06621718149054 \tabularnewline
Trimmed Mean ( 12 / 24 ) & -1.34166666666667 & 1.26014617430465 & -1.06469129853685 \tabularnewline
Trimmed Mean ( 13 / 24 ) & -1.30217391304348 & 1.24384664824569 & -1.04689264941145 \tabularnewline
Trimmed Mean ( 14 / 24 ) & -1.26590909090909 & 1.2233110338924 & -1.0348219347627 \tabularnewline
Trimmed Mean ( 15 / 24 ) & -1.22619047619048 & 1.20169286091907 & -1.02038592061925 \tabularnewline
Trimmed Mean ( 16 / 24 ) & -1.1825 & 1.17317172273527 & -1.00795133149219 \tabularnewline
Trimmed Mean ( 17 / 24 ) & -1.14736842105263 & 1.13964343230845 & -1.00677842606309 \tabularnewline
Trimmed Mean ( 18 / 24 ) & -1.13611111111111 & 1.10222108214867 & -1.03074703388578 \tabularnewline
Trimmed Mean ( 19 / 24 ) & -1.14411764705882 & 1.06802657721335 & -1.07124454715725 \tabularnewline
Trimmed Mean ( 20 / 24 ) & -1.15625 & 1.0260315177436 & -1.12691469999165 \tabularnewline
Trimmed Mean ( 21 / 24 ) & -1.22333333333333 & 0.989620655678525 & -1.2361639041321 \tabularnewline
Trimmed Mean ( 22 / 24 ) & -1.26785714285714 & 0.959718509924531 & -1.32107188696073 \tabularnewline
Trimmed Mean ( 23 / 24 ) & -1.33461538461538 & 0.92003247948842 & -1.45061768401643 \tabularnewline
Trimmed Mean ( 24 / 24 ) & -1.42916666666667 & 0.878207973756264 & -1.6273669897961 \tabularnewline
Median & -1.9 &  &  \tabularnewline
Midrange & 1.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -1.47027027027027 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -1.13611111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -1.47027027027027 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -1.13611111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -1.13611111111111 &  &  \tabularnewline
Midmean - Closest Observation & -1.47027027027027 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -1.13611111111111 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -0.841025641025641 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207540&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]-0.909722222222222[/C][C]1.56251592758357[/C][C]-0.582216287311135[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-6.98630001860437[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]13.1973850524345[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]-0.904166666666667[/C][C]1.54987055532483[/C][C]-0.583382053140021[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]-0.818055555555556[/C][C]1.52585608797438[/C][C]-0.536128906259795[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]-0.888888888888889[/C][C]1.50421233730304[/C][C]-0.59093311951065[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]-1.05[/C][C]1.46096308835641[/C][C]-0.718703989421973[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]-1.13333333333333[/C][C]1.44181761265738[/C][C]-0.786044866829249[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]-1.375[/C][C]1.39435727084132[/C][C]-0.986117423958612[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]-1.45277777777778[/C][C]1.37781859668697[/C][C]-1.05440424542901[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]-1.51944444444444[/C][C]1.35946464724476[/C][C]-1.11767852700246[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]-1.63194444444444[/C][C]1.3335193919316[/C][C]-1.22378756118468[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]-1.63194444444444[/C][C]1.31573900045846[/C][C]-1.24032535622628[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]-1.49444444444444[/C][C]1.28379037177322[/C][C]-1.16408759350661[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]-1.64444444444444[/C][C]1.26134583105193[/C][C]-1.30372210694431[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]-1.59027777777778[/C][C]1.25270780221242[/C][C]-1.26947223843355[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]-1.59027777777778[/C][C]1.22317405629623[/C][C]-1.3001238618428[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]-1.59027777777778[/C][C]1.21689682002532[/C][C]-1.30683041619313[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]-1.47916666666667[/C][C]1.19300572767922[/C][C]-1.23986551979438[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]-1.24305555555556[/C][C]1.15723860923518[/C][C]-1.07415665674782[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]-1.06805555555556[/C][C]1.08760772205655[/C][C]-0.982022777050516[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]-1.04166666666667[/C][C]1.06093447677331[/C][C]-0.981838831211099[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]-0.597222222222222[/C][C]0.975523959815738[/C][C]-0.612206615955418[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]-0.859722222222223[/C][C]0.896798469557609[/C][C]-0.958657102354695[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]-0.7375[/C][C]0.872126261255333[/C][C]-0.845634437080759[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]-0.609722222222222[/C][C]0.811958642865432[/C][C]-0.750927682807206[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]-1.24305555555556[/C][C]0.697398548522139[/C][C]-1.782417755514[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]-0.978571428571429[/C][C]1.5142427920789[/C][C]-0.646244732806652[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]-1.05735294117647[/C][C]1.47181348211919[/C][C]-0.718401451014053[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]-1.18787878787879[/C][C]1.4362839178059[/C][C]-0.827050120907447[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]-1.3[/C][C]1.40341667833038[/C][C]-0.926310781447024[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]-1.37258064516129[/C][C]1.37952116048677[/C][C]-0.994968895349867[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]-1.43[/C][C]1.35614379351917[/C][C]-1.05446045384994[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]-1.44137931034483[/C][C]1.34031678696862[/C][C]-1.07540196792191[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]-1.43928571428571[/C][C]1.3242412151562[/C][C]-1.08687578804587[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]-1.42592592592593[/C][C]1.30783315810094[/C][C]-1.0902965084602[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]-1.39423076923077[/C][C]1.29226557942408[/C][C]-1.07890420624848[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]-1.36[/C][C]1.27553750174871[/C][C]-1.06621718149054[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]-1.34166666666667[/C][C]1.26014617430465[/C][C]-1.06469129853685[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]-1.30217391304348[/C][C]1.24384664824569[/C][C]-1.04689264941145[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]-1.26590909090909[/C][C]1.2233110338924[/C][C]-1.0348219347627[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]-1.22619047619048[/C][C]1.20169286091907[/C][C]-1.02038592061925[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]-1.1825[/C][C]1.17317172273527[/C][C]-1.00795133149219[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]-1.14736842105263[/C][C]1.13964343230845[/C][C]-1.00677842606309[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]-1.13611111111111[/C][C]1.10222108214867[/C][C]-1.03074703388578[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]-1.14411764705882[/C][C]1.06802657721335[/C][C]-1.07124454715725[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]-1.15625[/C][C]1.0260315177436[/C][C]-1.12691469999165[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]-1.22333333333333[/C][C]0.989620655678525[/C][C]-1.2361639041321[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]-1.26785714285714[/C][C]0.959718509924531[/C][C]-1.32107188696073[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]-1.33461538461538[/C][C]0.92003247948842[/C][C]-1.45061768401643[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]-1.42916666666667[/C][C]0.878207973756264[/C][C]-1.6273669897961[/C][/ROW]
[ROW][C]Median[/C][C]-1.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-1.47027027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-1.13611111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-1.47027027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-1.13611111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-1.13611111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-1.47027027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-1.13611111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-0.841025641025641[/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=207540&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207540&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	-0.909722222222222	1.56251592758357	-0.582216287311135
Geometric Mean	NaN
Harmonic Mean	-6.98630001860437
Quadratic Mean	13.1973850524345
Winsorized Mean ( 1 / 24 )	-0.904166666666667	1.54987055532483	-0.583382053140021
Winsorized Mean ( 2 / 24 )	-0.818055555555556	1.52585608797438	-0.536128906259795
Winsorized Mean ( 3 / 24 )	-0.888888888888889	1.50421233730304	-0.59093311951065
Winsorized Mean ( 4 / 24 )	-1.05	1.46096308835641	-0.718703989421973
Winsorized Mean ( 5 / 24 )	-1.13333333333333	1.44181761265738	-0.786044866829249
Winsorized Mean ( 6 / 24 )	-1.375	1.39435727084132	-0.986117423958612
Winsorized Mean ( 7 / 24 )	-1.45277777777778	1.37781859668697	-1.05440424542901
Winsorized Mean ( 8 / 24 )	-1.51944444444444	1.35946464724476	-1.11767852700246
Winsorized Mean ( 9 / 24 )	-1.63194444444444	1.3335193919316	-1.22378756118468
Winsorized Mean ( 10 / 24 )	-1.63194444444444	1.31573900045846	-1.24032535622628
Winsorized Mean ( 11 / 24 )	-1.49444444444444	1.28379037177322	-1.16408759350661
Winsorized Mean ( 12 / 24 )	-1.64444444444444	1.26134583105193	-1.30372210694431
Winsorized Mean ( 13 / 24 )	-1.59027777777778	1.25270780221242	-1.26947223843355
Winsorized Mean ( 14 / 24 )	-1.59027777777778	1.22317405629623	-1.3001238618428
Winsorized Mean ( 15 / 24 )	-1.59027777777778	1.21689682002532	-1.30683041619313
Winsorized Mean ( 16 / 24 )	-1.47916666666667	1.19300572767922	-1.23986551979438
Winsorized Mean ( 17 / 24 )	-1.24305555555556	1.15723860923518	-1.07415665674782
Winsorized Mean ( 18 / 24 )	-1.06805555555556	1.08760772205655	-0.982022777050516
Winsorized Mean ( 19 / 24 )	-1.04166666666667	1.06093447677331	-0.981838831211099
Winsorized Mean ( 20 / 24 )	-0.597222222222222	0.975523959815738	-0.612206615955418
Winsorized Mean ( 21 / 24 )	-0.859722222222223	0.896798469557609	-0.958657102354695
Winsorized Mean ( 22 / 24 )	-0.7375	0.872126261255333	-0.845634437080759
Winsorized Mean ( 23 / 24 )	-0.609722222222222	0.811958642865432	-0.750927682807206
Winsorized Mean ( 24 / 24 )	-1.24305555555556	0.697398548522139	-1.782417755514
Trimmed Mean ( 1 / 24 )	-0.978571428571429	1.5142427920789	-0.646244732806652
Trimmed Mean ( 2 / 24 )	-1.05735294117647	1.47181348211919	-0.718401451014053
Trimmed Mean ( 3 / 24 )	-1.18787878787879	1.4362839178059	-0.827050120907447
Trimmed Mean ( 4 / 24 )	-1.3	1.40341667833038	-0.926310781447024
Trimmed Mean ( 5 / 24 )	-1.37258064516129	1.37952116048677	-0.994968895349867
Trimmed Mean ( 6 / 24 )	-1.43	1.35614379351917	-1.05446045384994
Trimmed Mean ( 7 / 24 )	-1.44137931034483	1.34031678696862	-1.07540196792191
Trimmed Mean ( 8 / 24 )	-1.43928571428571	1.3242412151562	-1.08687578804587
Trimmed Mean ( 9 / 24 )	-1.42592592592593	1.30783315810094	-1.0902965084602
Trimmed Mean ( 10 / 24 )	-1.39423076923077	1.29226557942408	-1.07890420624848
Trimmed Mean ( 11 / 24 )	-1.36	1.27553750174871	-1.06621718149054
Trimmed Mean ( 12 / 24 )	-1.34166666666667	1.26014617430465	-1.06469129853685
Trimmed Mean ( 13 / 24 )	-1.30217391304348	1.24384664824569	-1.04689264941145
Trimmed Mean ( 14 / 24 )	-1.26590909090909	1.2233110338924	-1.0348219347627
Trimmed Mean ( 15 / 24 )	-1.22619047619048	1.20169286091907	-1.02038592061925
Trimmed Mean ( 16 / 24 )	-1.1825	1.17317172273527	-1.00795133149219
Trimmed Mean ( 17 / 24 )	-1.14736842105263	1.13964343230845	-1.00677842606309
Trimmed Mean ( 18 / 24 )	-1.13611111111111	1.10222108214867	-1.03074703388578
Trimmed Mean ( 19 / 24 )	-1.14411764705882	1.06802657721335	-1.07124454715725
Trimmed Mean ( 20 / 24 )	-1.15625	1.0260315177436	-1.12691469999165
Trimmed Mean ( 21 / 24 )	-1.22333333333333	0.989620655678525	-1.2361639041321
Trimmed Mean ( 22 / 24 )	-1.26785714285714	0.959718509924531	-1.32107188696073
Trimmed Mean ( 23 / 24 )	-1.33461538461538	0.92003247948842	-1.45061768401643
Trimmed Mean ( 24 / 24 )	-1.42916666666667	0.878207973756264	-1.6273669897961
Median	-1.9
Midrange	1.5
Midmean - Weighted Average at Xnp	-1.47027027027027
Midmean - Weighted Average at X(n+1)p	-1.13611111111111
Midmean - Empirical Distribution Function	-1.47027027027027
Midmean - Empirical Distribution Function - Averaging	-1.13611111111111
Midmean - Empirical Distribution Function - Interpolation	-1.13611111111111
Midmean - Closest Observation	-1.47027027027027
Midmean - True Basic - Statistics Graphics Toolkit	-1.13611111111111
Midmean - MS Excel (old versions)	-0.841025641025641
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