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R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Sun, 12 Oct 2014 12:15:05 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/12/t14131125368kcpmlq3oj8wlr2.htm/, Retrieved Thu, 16 May 2024 02:52:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240549, Retrieved Thu, 16 May 2024 02:52:47 +0000

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Estimated Impact

126

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

-       [Central Tendency] [] [2014-10-12 11:15:05] [ce030e64aa9efcfbf032d2aff4cc4bf0] [Current]

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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	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240549&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240549&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240549&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	'Gertrude Mary Cox' @ cox.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.57744444444444	0.0190562946698709	82.7781303643713
Geometric Mean	1.56892969817092
Harmonic Mean	1.56006753668801
Quadratic Mean	1.5855958133564
Winsorized Mean ( 1 / 24 )	1.57788888888889	0.0189048618370533	83.4647141295816
Winsorized Mean ( 2 / 24 )	1.57927777777778	0.0185277381848559	85.2385629600834
Winsorized Mean ( 3 / 24 )	1.57865277777778	0.0181637715714661	86.9121686300945
Winsorized Mean ( 4 / 24 )	1.57870833333333	0.0178293668255669	88.5453952896129
Winsorized Mean ( 5 / 24 )	1.57891666666667	0.0177052876419767	89.1776907890093
Winsorized Mean ( 6 / 24 )	1.58025	0.0174191599176847	90.719070693855
Winsorized Mean ( 7 / 24 )	1.58326388888889	0.016705623403756	94.7743074666053
Winsorized Mean ( 8 / 24 )	1.58604166666667	0.0161489113755393	98.213534632993
Winsorized Mean ( 9 / 24 )	1.58729166666667	0.0157608600497258	100.710980343632
Winsorized Mean ( 10 / 24 )	1.58715277777778	0.015195513243702	104.448777235977
Winsorized Mean ( 11 / 24 )	1.58806944444444	0.0149944215812382	105.910683906041
Winsorized Mean ( 12 / 24 )	1.58823611111111	0.0149142632293492	106.49108753731
Winsorized Mean ( 13 / 24 )	1.58751388888889	0.0141871295606407	111.898173771044
Winsorized Mean ( 14 / 24 )	1.58984722222222	0.0137606362293859	115.535880443311
Winsorized Mean ( 15 / 24 )	1.58984722222222	0.0136978011857675	116.06587076721
Winsorized Mean ( 16 / 24 )	1.59095833333333	0.0132623320457256	119.960677190713
Winsorized Mean ( 17 / 24 )	1.59591666666667	0.0113938550758656	140.068190795856
Winsorized Mean ( 18 / 24 )	1.59516666666667	0.0112867726258098	141.330628298381
Winsorized Mean ( 19 / 24 )	1.59411111111111	0.0109926806555604	145.015684623274
Winsorized Mean ( 20 / 24 )	1.59327777777778	0.0108011660788473	147.509793493316
Winsorized Mean ( 21 / 24 )	1.59356944444444	0.0107619502015029	148.074411663966
Winsorized Mean ( 22 / 24 )	1.59204166666667	0.0103049822624202	154.492421832928
Winsorized Mean ( 23 / 24 )	1.58948611111111	0.00953867412234769	166.635959120061
Winsorized Mean ( 24 / 24 )	1.58748611111111	0.00919223904328723	172.698523573579
Trimmed Mean ( 1 / 24 )	1.57957142857143	0.0183987979109152	85.8518820750969
Trimmed Mean ( 2 / 24 )	1.58135294117647	0.0177945889111076	88.8670679090188
Trimmed Mean ( 3 / 24 )	1.58248484848485	0.0173158811516458	91.3892186384313
Trimmed Mean ( 4 / 24 )	1.583921875	0.0169060972242826	93.6893863786008
Trimmed Mean ( 5 / 24 )	1.58543548387097	0.0165318086897691	95.9021189769836
Trimmed Mean ( 6 / 24 )	1.587	0.0161130364457735	98.4916781725691
Trimmed Mean ( 7 / 24 )	1.58839655172414	0.0156826116164183	101.283930927756
Trimmed Mean ( 8 / 24 )	1.58933928571429	0.0153436876649505	103.582614585202
Trimmed Mean ( 9 / 24 )	1.58988888888889	0.0150587404863788	105.579141252019
Trimmed Mean ( 10 / 24 )	1.59028846153846	0.0147880790658341	107.538541987689
Trimmed Mean ( 11 / 24 )	1.59074	0.014566324316094	109.206685604441
Trimmed Mean ( 12 / 24 )	1.59110416666667	0.0143189739092929	111.118588297311
Trimmed Mean ( 13 / 24 )	1.59147826086957	0.0140097874390505	113.597602232959
Trimmed Mean ( 14 / 24 )	1.59197727272727	0.0137613104984458	115.685004920649
Trimmed Mean ( 15 / 24 )	1.5922380952381	0.0135190238706637	117.77759329897
Trimmed Mean ( 16 / 24 )	1.592525	0.0131978527536752	120.665462005289
Trimmed Mean ( 17 / 24 )	1.59271052631579	0.012859339024023	123.856329111503
Trimmed Mean ( 18 / 24 )	1.59233333333333	0.0128201849774932	124.2051761444
Trimmed Mean ( 19 / 24 )	1.592	0.0127494713462105	124.867922501993
Trimmed Mean ( 20 / 24 )	1.59175	0.0126780862502091	125.551283418169
Trimmed Mean ( 21 / 24 )	1.59156666666667	0.0125758099607374	126.557786069895
Trimmed Mean ( 22 / 24 )	1.59132142857143	0.0123835371996537	128.502979634601
Trimmed Mean ( 23 / 24 )	1.59123076923077	0.0121861595758098	130.576885960812
Trimmed Mean ( 24 / 24 )	1.59145833333333	0.012075394068444	131.793490490899
Median	1.597
Midrange	1.503
Midmean - Weighted Average at Xnp	1.58948648648649
Midmean - Weighted Average at X(n+1)p	1.58948648648649
Midmean - Empirical Distribution Function	1.58948648648649
Midmean - Empirical Distribution Function - Averaging	1.58948648648649
Midmean - Empirical Distribution Function - Interpolation	1.58948648648649
Midmean - Closest Observation	1.58948648648649
Midmean - True Basic - Statistics Graphics Toolkit	1.58948648648649
Midmean - MS Excel (old versions)	1.59271052631579
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.57744444444444 & 0.0190562946698709 & 82.7781303643713 \tabularnewline
Geometric Mean & 1.56892969817092 &  &  \tabularnewline
Harmonic Mean & 1.56006753668801 &  &  \tabularnewline
Quadratic Mean & 1.5855958133564 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.57788888888889 & 0.0189048618370533 & 83.4647141295816 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.57927777777778 & 0.0185277381848559 & 85.2385629600834 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.57865277777778 & 0.0181637715714661 & 86.9121686300945 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.57870833333333 & 0.0178293668255669 & 88.5453952896129 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.57891666666667 & 0.0177052876419767 & 89.1776907890093 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.58025 & 0.0174191599176847 & 90.719070693855 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.58326388888889 & 0.016705623403756 & 94.7743074666053 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.58604166666667 & 0.0161489113755393 & 98.213534632993 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.58729166666667 & 0.0157608600497258 & 100.710980343632 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.58715277777778 & 0.015195513243702 & 104.448777235977 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.58806944444444 & 0.0149944215812382 & 105.910683906041 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.58823611111111 & 0.0149142632293492 & 106.49108753731 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.58751388888889 & 0.0141871295606407 & 111.898173771044 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.58984722222222 & 0.0137606362293859 & 115.535880443311 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.58984722222222 & 0.0136978011857675 & 116.06587076721 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.59095833333333 & 0.0132623320457256 & 119.960677190713 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.59591666666667 & 0.0113938550758656 & 140.068190795856 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.59516666666667 & 0.0112867726258098 & 141.330628298381 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.59411111111111 & 0.0109926806555604 & 145.015684623274 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.59327777777778 & 0.0108011660788473 & 147.509793493316 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.59356944444444 & 0.0107619502015029 & 148.074411663966 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.59204166666667 & 0.0103049822624202 & 154.492421832928 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.58948611111111 & 0.00953867412234769 & 166.635959120061 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.58748611111111 & 0.00919223904328723 & 172.698523573579 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.57957142857143 & 0.0183987979109152 & 85.8518820750969 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.58135294117647 & 0.0177945889111076 & 88.8670679090188 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.58248484848485 & 0.0173158811516458 & 91.3892186384313 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.583921875 & 0.0169060972242826 & 93.6893863786008 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.58543548387097 & 0.0165318086897691 & 95.9021189769836 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.587 & 0.0161130364457735 & 98.4916781725691 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.58839655172414 & 0.0156826116164183 & 101.283930927756 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.58933928571429 & 0.0153436876649505 & 103.582614585202 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.58988888888889 & 0.0150587404863788 & 105.579141252019 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.59028846153846 & 0.0147880790658341 & 107.538541987689 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.59074 & 0.014566324316094 & 109.206685604441 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.59110416666667 & 0.0143189739092929 & 111.118588297311 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.59147826086957 & 0.0140097874390505 & 113.597602232959 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.59197727272727 & 0.0137613104984458 & 115.685004920649 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.5922380952381 & 0.0135190238706637 & 117.77759329897 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.592525 & 0.0131978527536752 & 120.665462005289 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.59271052631579 & 0.012859339024023 & 123.856329111503 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.59233333333333 & 0.0128201849774932 & 124.2051761444 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.592 & 0.0127494713462105 & 124.867922501993 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.59175 & 0.0126780862502091 & 125.551283418169 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.59156666666667 & 0.0125758099607374 & 126.557786069895 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.59132142857143 & 0.0123835371996537 & 128.502979634601 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.59123076923077 & 0.0121861595758098 & 130.576885960812 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.59145833333333 & 0.012075394068444 & 131.793490490899 \tabularnewline
Median & 1.597 &  &  \tabularnewline
Midrange & 1.503 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.58948648648649 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.58948648648649 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.58948648648649 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.58948648648649 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.58948648648649 &  &  \tabularnewline
Midmean - Closest Observation & 1.58948648648649 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.58948648648649 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.59271052631579 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240549&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]1.57744444444444[/C][C]0.0190562946698709[/C][C]82.7781303643713[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.56892969817092[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.56006753668801[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.5855958133564[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.57788888888889[/C][C]0.0189048618370533[/C][C]83.4647141295816[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.57927777777778[/C][C]0.0185277381848559[/C][C]85.2385629600834[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.57865277777778[/C][C]0.0181637715714661[/C][C]86.9121686300945[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.57870833333333[/C][C]0.0178293668255669[/C][C]88.5453952896129[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.57891666666667[/C][C]0.0177052876419767[/C][C]89.1776907890093[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.58025[/C][C]0.0174191599176847[/C][C]90.719070693855[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.58326388888889[/C][C]0.016705623403756[/C][C]94.7743074666053[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.58604166666667[/C][C]0.0161489113755393[/C][C]98.213534632993[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.58729166666667[/C][C]0.0157608600497258[/C][C]100.710980343632[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.58715277777778[/C][C]0.015195513243702[/C][C]104.448777235977[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.58806944444444[/C][C]0.0149944215812382[/C][C]105.910683906041[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.58823611111111[/C][C]0.0149142632293492[/C][C]106.49108753731[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.58751388888889[/C][C]0.0141871295606407[/C][C]111.898173771044[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.58984722222222[/C][C]0.0137606362293859[/C][C]115.535880443311[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.58984722222222[/C][C]0.0136978011857675[/C][C]116.06587076721[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.59095833333333[/C][C]0.0132623320457256[/C][C]119.960677190713[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.59591666666667[/C][C]0.0113938550758656[/C][C]140.068190795856[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.59516666666667[/C][C]0.0112867726258098[/C][C]141.330628298381[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.59411111111111[/C][C]0.0109926806555604[/C][C]145.015684623274[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.59327777777778[/C][C]0.0108011660788473[/C][C]147.509793493316[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.59356944444444[/C][C]0.0107619502015029[/C][C]148.074411663966[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.59204166666667[/C][C]0.0103049822624202[/C][C]154.492421832928[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.58948611111111[/C][C]0.00953867412234769[/C][C]166.635959120061[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.58748611111111[/C][C]0.00919223904328723[/C][C]172.698523573579[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.57957142857143[/C][C]0.0183987979109152[/C][C]85.8518820750969[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.58135294117647[/C][C]0.0177945889111076[/C][C]88.8670679090188[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.58248484848485[/C][C]0.0173158811516458[/C][C]91.3892186384313[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.583921875[/C][C]0.0169060972242826[/C][C]93.6893863786008[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.58543548387097[/C][C]0.0165318086897691[/C][C]95.9021189769836[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.587[/C][C]0.0161130364457735[/C][C]98.4916781725691[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.58839655172414[/C][C]0.0156826116164183[/C][C]101.283930927756[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.58933928571429[/C][C]0.0153436876649505[/C][C]103.582614585202[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.58988888888889[/C][C]0.0150587404863788[/C][C]105.579141252019[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.59028846153846[/C][C]0.0147880790658341[/C][C]107.538541987689[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.59074[/C][C]0.014566324316094[/C][C]109.206685604441[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.59110416666667[/C][C]0.0143189739092929[/C][C]111.118588297311[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.59147826086957[/C][C]0.0140097874390505[/C][C]113.597602232959[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.59197727272727[/C][C]0.0137613104984458[/C][C]115.685004920649[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.5922380952381[/C][C]0.0135190238706637[/C][C]117.77759329897[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.592525[/C][C]0.0131978527536752[/C][C]120.665462005289[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.59271052631579[/C][C]0.012859339024023[/C][C]123.856329111503[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.59233333333333[/C][C]0.0128201849774932[/C][C]124.2051761444[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.592[/C][C]0.0127494713462105[/C][C]124.867922501993[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.59175[/C][C]0.0126780862502091[/C][C]125.551283418169[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.59156666666667[/C][C]0.0125758099607374[/C][C]126.557786069895[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.59132142857143[/C][C]0.0123835371996537[/C][C]128.502979634601[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.59123076923077[/C][C]0.0121861595758098[/C][C]130.576885960812[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.59145833333333[/C][C]0.012075394068444[/C][C]131.793490490899[/C][/ROW]
[ROW][C]Median[/C][C]1.597[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.503[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.58948648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.58948648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.58948648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.58948648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.58948648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.58948648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.58948648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.59271052631579[/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=240549&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240549&T=1

As an alternative you can also use a QR Code:

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

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.57744444444444	0.0190562946698709	82.7781303643713
Geometric Mean	1.56892969817092
Harmonic Mean	1.56006753668801
Quadratic Mean	1.5855958133564
Winsorized Mean ( 1 / 24 )	1.57788888888889	0.0189048618370533	83.4647141295816
Winsorized Mean ( 2 / 24 )	1.57927777777778	0.0185277381848559	85.2385629600834
Winsorized Mean ( 3 / 24 )	1.57865277777778	0.0181637715714661	86.9121686300945
Winsorized Mean ( 4 / 24 )	1.57870833333333	0.0178293668255669	88.5453952896129
Winsorized Mean ( 5 / 24 )	1.57891666666667	0.0177052876419767	89.1776907890093
Winsorized Mean ( 6 / 24 )	1.58025	0.0174191599176847	90.719070693855
Winsorized Mean ( 7 / 24 )	1.58326388888889	0.016705623403756	94.7743074666053
Winsorized Mean ( 8 / 24 )	1.58604166666667	0.0161489113755393	98.213534632993
Winsorized Mean ( 9 / 24 )	1.58729166666667	0.0157608600497258	100.710980343632
Winsorized Mean ( 10 / 24 )	1.58715277777778	0.015195513243702	104.448777235977
Winsorized Mean ( 11 / 24 )	1.58806944444444	0.0149944215812382	105.910683906041
Winsorized Mean ( 12 / 24 )	1.58823611111111	0.0149142632293492	106.49108753731
Winsorized Mean ( 13 / 24 )	1.58751388888889	0.0141871295606407	111.898173771044
Winsorized Mean ( 14 / 24 )	1.58984722222222	0.0137606362293859	115.535880443311
Winsorized Mean ( 15 / 24 )	1.58984722222222	0.0136978011857675	116.06587076721
Winsorized Mean ( 16 / 24 )	1.59095833333333	0.0132623320457256	119.960677190713
Winsorized Mean ( 17 / 24 )	1.59591666666667	0.0113938550758656	140.068190795856
Winsorized Mean ( 18 / 24 )	1.59516666666667	0.0112867726258098	141.330628298381
Winsorized Mean ( 19 / 24 )	1.59411111111111	0.0109926806555604	145.015684623274
Winsorized Mean ( 20 / 24 )	1.59327777777778	0.0108011660788473	147.509793493316
Winsorized Mean ( 21 / 24 )	1.59356944444444	0.0107619502015029	148.074411663966
Winsorized Mean ( 22 / 24 )	1.59204166666667	0.0103049822624202	154.492421832928
Winsorized Mean ( 23 / 24 )	1.58948611111111	0.00953867412234769	166.635959120061
Winsorized Mean ( 24 / 24 )	1.58748611111111	0.00919223904328723	172.698523573579
Trimmed Mean ( 1 / 24 )	1.57957142857143	0.0183987979109152	85.8518820750969
Trimmed Mean ( 2 / 24 )	1.58135294117647	0.0177945889111076	88.8670679090188
Trimmed Mean ( 3 / 24 )	1.58248484848485	0.0173158811516458	91.3892186384313
Trimmed Mean ( 4 / 24 )	1.583921875	0.0169060972242826	93.6893863786008
Trimmed Mean ( 5 / 24 )	1.58543548387097	0.0165318086897691	95.9021189769836
Trimmed Mean ( 6 / 24 )	1.587	0.0161130364457735	98.4916781725691
Trimmed Mean ( 7 / 24 )	1.58839655172414	0.0156826116164183	101.283930927756
Trimmed Mean ( 8 / 24 )	1.58933928571429	0.0153436876649505	103.582614585202
Trimmed Mean ( 9 / 24 )	1.58988888888889	0.0150587404863788	105.579141252019
Trimmed Mean ( 10 / 24 )	1.59028846153846	0.0147880790658341	107.538541987689
Trimmed Mean ( 11 / 24 )	1.59074	0.014566324316094	109.206685604441
Trimmed Mean ( 12 / 24 )	1.59110416666667	0.0143189739092929	111.118588297311
Trimmed Mean ( 13 / 24 )	1.59147826086957	0.0140097874390505	113.597602232959
Trimmed Mean ( 14 / 24 )	1.59197727272727	0.0137613104984458	115.685004920649
Trimmed Mean ( 15 / 24 )	1.5922380952381	0.0135190238706637	117.77759329897
Trimmed Mean ( 16 / 24 )	1.592525	0.0131978527536752	120.665462005289
Trimmed Mean ( 17 / 24 )	1.59271052631579	0.012859339024023	123.856329111503
Trimmed Mean ( 18 / 24 )	1.59233333333333	0.0128201849774932	124.2051761444
Trimmed Mean ( 19 / 24 )	1.592	0.0127494713462105	124.867922501993
Trimmed Mean ( 20 / 24 )	1.59175	0.0126780862502091	125.551283418169
Trimmed Mean ( 21 / 24 )	1.59156666666667	0.0125758099607374	126.557786069895
Trimmed Mean ( 22 / 24 )	1.59132142857143	0.0123835371996537	128.502979634601
Trimmed Mean ( 23 / 24 )	1.59123076923077	0.0121861595758098	130.576885960812
Trimmed Mean ( 24 / 24 )	1.59145833333333	0.012075394068444	131.793490490899
Median	1.597
Midrange	1.503
Midmean - Weighted Average at Xnp	1.58948648648649
Midmean - Weighted Average at X(n+1)p	1.58948648648649
Midmean - Empirical Distribution Function	1.58948648648649
Midmean - Empirical Distribution Function - Averaging	1.58948648648649
Midmean - Empirical Distribution Function - Interpolation	1.58948648648649
Midmean - Closest Observation	1.58948648648649
Midmean - True Basic - Statistics Graphics Toolkit	1.58948648648649
Midmean - MS Excel (old versions)	1.59271052631579
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