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Author

*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Thu, 27 Dec 2007 06:40:45 -0700

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/2007/Dec/27/t1198761646w1r440hland7fpr.htm/, Retrieved Sat, 27 Apr 2024 23:51:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4899, Retrieved Sat, 27 Apr 2024 23:51:14 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

276

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

-       [Central Tendency] [s 0650692 paper] [2007-12-27 13:40:45] [011cc8cdd02d5893b5258ac3f5e21d83] [Current]

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Dataseries X:

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0,36
0,35
0,35
0,35
0,33
0,78
0,71
0,62
0,52
0,46
0,43
0,43
0,42
0,42
0,42
0,42
0,43
0,99
1,03
0,83
0,64
0,6
0,58
0,58
0,58
0,57
0,57
0,56
0,56
0,88
0,84
0,69
0,59
0,54
0,52
0,52
0,51
0,52
0,51
0,51
0,53
0,95
0,98
0,88
0,81
0,77
0,76
0,75
0,73
0,74
0,73
0,75
0,77
1,09
1,03
0,9
0,76
0,66
0,63
0,61
0,61
0,61
0,61
0,61
0,62
0,76
0,83
0,81
0,77
0,75
0,76
0,76

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4899&T=0

[TABLE]
[ROW][C]Summary of compuational 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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4899&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4899&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	0.650694444444444	0.0214701510499289	30.3069337021082
Geometric Mean	0.625084470460239
Harmonic Mean	0.59914984335744
Quadratic Mean	0.675375410008718
Winsorized Mean ( 1 / 24 )	0.650138888888889	0.0211878226456759	30.6845540365882
Winsorized Mean ( 2 / 24 )	0.650138888888889	0.0211878226456759	30.6845540365882
Winsorized Mean ( 3 / 24 )	0.648472222222222	0.0207843647241947	31.200002060556
Winsorized Mean ( 4 / 24 )	0.648472222222222	0.0205458186027905	31.5622480057401
Winsorized Mean ( 5 / 24 )	0.650555555555556	0.0193172679819973	33.6774100852067
Winsorized Mean ( 6 / 24 )	0.646388888888889	0.0184580749359880	35.0193013697552
Winsorized Mean ( 7 / 24 )	0.644444444444444	0.0180915435256262	35.6213080178374
Winsorized Mean ( 8 / 24 )	0.644444444444444	0.0180915435256262	35.6213080178374
Winsorized Mean ( 9 / 24 )	0.640694444444444	0.0170005596760593	37.6866677716905
Winsorized Mean ( 10 / 24 )	0.639305555555555	0.0167746809602458	38.111339170661
Winsorized Mean ( 11 / 24 )	0.639305555555556	0.0167746809602458	38.111339170661
Winsorized Mean ( 12 / 24 )	0.640972222222222	0.0153953630528748	41.6341089210322
Winsorized Mean ( 13 / 24 )	0.65	0.0140073197944763	46.40430928523
Winsorized Mean ( 14 / 24 )	0.644166666666667	0.0131110431419155	49.1316106349531
Winsorized Mean ( 15 / 24 )	0.642083333333333	0.0128125059639667	50.1137978112243
Winsorized Mean ( 16 / 24 )	0.644305555555556	0.0124954238711081	51.5633212767851
Winsorized Mean ( 17 / 24 )	0.644305555555556	0.0124954238711081	51.5633212767851
Winsorized Mean ( 18 / 24 )	0.641805555555556	0.0121469329785732	52.8368401050436
Winsorized Mean ( 19 / 24 )	0.641805555555556	0.0121469329785732	52.8368401050436
Winsorized Mean ( 20 / 24 )	0.644583333333333	0.0117600845746057	54.8111137504253
Winsorized Mean ( 21 / 24 )	0.6475	0.0113655817085768	56.9702472431639
Winsorized Mean ( 22 / 24 )	0.653611111111111	0.0105766920413049	61.7973094573029
Winsorized Mean ( 23 / 24 )	0.650416666666667	0.0101291300817411	64.2124902551223
Winsorized Mean ( 24 / 24 )	0.65375	0.00971712083912673	67.2781589138653
Trimmed Mean ( 1 / 24 )	0.649	0.0206540567955015	31.4223983416834
Trimmed Mean ( 2 / 24 )	0.647794117647059	0.0200184787200461	32.3598074911842
Trimmed Mean ( 3 / 24 )	0.646515151515151	0.0192571754849196	33.5726883738189
Trimmed Mean ( 4 / 24 )	0.64578125	0.0185335451548522	34.8439138116504
Trimmed Mean ( 5 / 24 )	0.645	0.0177498780356451	36.338277857725
Trimmed Mean ( 6 / 24 )	0.643666666666667	0.0172042674161326	37.4131981965763
Trimmed Mean ( 7 / 24 )	0.643103448275862	0.0167905983267092	38.3014015202105
Trimmed Mean ( 8 / 24 )	0.642857142857143	0.0163776738388288	39.2520420899477
Trimmed Mean ( 9 / 24 )	0.642592592592593	0.0158636423689299	40.5072541127855
Trimmed Mean ( 10 / 24 )	0.642884615384615	0.0154869101017395	41.5114836440101
Trimmed Mean ( 11 / 24 )	0.6434	0.0150607206375541	42.7203993410297
Trimmed Mean ( 12 / 24 )	0.643958333333333	0.0145156420378392	44.3630623884682
Trimmed Mean ( 13 / 24 )	0.644347826086957	0.0141409474086706	45.5661001675088
Trimmed Mean ( 14 / 24 )	0.643636363636364	0.0139543612386350	46.1243873961315
Trimmed Mean ( 15 / 24 )	0.643571428571429	0.0138844636498690	46.3519113737967
Trimmed Mean ( 16 / 24 )	0.64375	0.0138243908383437	46.5662471155312
Trimmed Mean ( 17 / 24 )	0.643684210526316	0.0137774479828655	46.7201336072428
Trimmed Mean ( 18 / 24 )	0.643611111111111	0.0136751006367428	47.0644515318469
Trimmed Mean ( 19 / 24 )	0.643823529411765	0.0135763156585135	47.4225515674447
Trimmed Mean ( 20 / 24 )	0.6440625	0.0133942947577113	48.0848384816382
Trimmed Mean ( 21 / 24 )	0.644	0.0131970041880811	48.798953976360
Trimmed Mean ( 22 / 24 )	0.643571428571429	0.0129734597388812	49.6067696300515
Trimmed Mean ( 23 / 24 )	0.642307692307692	0.0128099443619484	50.141333495222
Trimmed Mean ( 24 / 24 )	0.64125	0.0126449924212446	50.7117741662422
Median	0.615
Midrange	0.71
Midmean - Weighted Average at Xnp	0.637105263157895
Midmean - Weighted Average at X(n+1)p	0.637105263157895
Midmean - Empirical Distribution Function	0.637105263157895
Midmean - Empirical Distribution Function - Averaging	0.637105263157895
Midmean - Empirical Distribution Function - Interpolation	0.637105263157895
Midmean - Closest Observation	0.637105263157895
Midmean - True Basic - Statistics Graphics Toolkit	0.637105263157895
Midmean - MS Excel (old versions)	0.646829268292683
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.650694444444444 & 0.0214701510499289 & 30.3069337021082 \tabularnewline
Geometric Mean & 0.625084470460239 &  &  \tabularnewline
Harmonic Mean & 0.59914984335744 &  &  \tabularnewline
Quadratic Mean & 0.675375410008718 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 0.650138888888889 & 0.0211878226456759 & 30.6845540365882 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 0.650138888888889 & 0.0211878226456759 & 30.6845540365882 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 0.648472222222222 & 0.0207843647241947 & 31.200002060556 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 0.648472222222222 & 0.0205458186027905 & 31.5622480057401 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 0.650555555555556 & 0.0193172679819973 & 33.6774100852067 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 0.646388888888889 & 0.0184580749359880 & 35.0193013697552 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 0.644444444444444 & 0.0180915435256262 & 35.6213080178374 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 0.644444444444444 & 0.0180915435256262 & 35.6213080178374 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 0.640694444444444 & 0.0170005596760593 & 37.6866677716905 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 0.639305555555555 & 0.0167746809602458 & 38.111339170661 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 0.639305555555556 & 0.0167746809602458 & 38.111339170661 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 0.640972222222222 & 0.0153953630528748 & 41.6341089210322 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 0.65 & 0.0140073197944763 & 46.40430928523 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 0.644166666666667 & 0.0131110431419155 & 49.1316106349531 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 0.642083333333333 & 0.0128125059639667 & 50.1137978112243 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 0.644305555555556 & 0.0124954238711081 & 51.5633212767851 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 0.644305555555556 & 0.0124954238711081 & 51.5633212767851 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 0.641805555555556 & 0.0121469329785732 & 52.8368401050436 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 0.641805555555556 & 0.0121469329785732 & 52.8368401050436 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 0.644583333333333 & 0.0117600845746057 & 54.8111137504253 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 0.6475 & 0.0113655817085768 & 56.9702472431639 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 0.653611111111111 & 0.0105766920413049 & 61.7973094573029 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 0.650416666666667 & 0.0101291300817411 & 64.2124902551223 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 0.65375 & 0.00971712083912673 & 67.2781589138653 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 0.649 & 0.0206540567955015 & 31.4223983416834 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 0.647794117647059 & 0.0200184787200461 & 32.3598074911842 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 0.646515151515151 & 0.0192571754849196 & 33.5726883738189 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 0.64578125 & 0.0185335451548522 & 34.8439138116504 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 0.645 & 0.0177498780356451 & 36.338277857725 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 0.643666666666667 & 0.0172042674161326 & 37.4131981965763 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 0.643103448275862 & 0.0167905983267092 & 38.3014015202105 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 0.642857142857143 & 0.0163776738388288 & 39.2520420899477 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 0.642592592592593 & 0.0158636423689299 & 40.5072541127855 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 0.642884615384615 & 0.0154869101017395 & 41.5114836440101 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 0.6434 & 0.0150607206375541 & 42.7203993410297 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 0.643958333333333 & 0.0145156420378392 & 44.3630623884682 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 0.644347826086957 & 0.0141409474086706 & 45.5661001675088 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 0.643636363636364 & 0.0139543612386350 & 46.1243873961315 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 0.643571428571429 & 0.0138844636498690 & 46.3519113737967 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 0.64375 & 0.0138243908383437 & 46.5662471155312 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 0.643684210526316 & 0.0137774479828655 & 46.7201336072428 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 0.643611111111111 & 0.0136751006367428 & 47.0644515318469 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 0.643823529411765 & 0.0135763156585135 & 47.4225515674447 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 0.6440625 & 0.0133942947577113 & 48.0848384816382 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 0.644 & 0.0131970041880811 & 48.798953976360 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 0.643571428571429 & 0.0129734597388812 & 49.6067696300515 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 0.642307692307692 & 0.0128099443619484 & 50.141333495222 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 0.64125 & 0.0126449924212446 & 50.7117741662422 \tabularnewline
Median & 0.615 &  &  \tabularnewline
Midrange & 0.71 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.637105263157895 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.637105263157895 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.637105263157895 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.637105263157895 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.637105263157895 &  &  \tabularnewline
Midmean - Closest Observation & 0.637105263157895 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.637105263157895 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.646829268292683 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4899&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]0.650694444444444[/C][C]0.0214701510499289[/C][C]30.3069337021082[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.625084470460239[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.59914984335744[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.675375410008718[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]0.650138888888889[/C][C]0.0211878226456759[/C][C]30.6845540365882[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]0.650138888888889[/C][C]0.0211878226456759[/C][C]30.6845540365882[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]0.648472222222222[/C][C]0.0207843647241947[/C][C]31.200002060556[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]0.648472222222222[/C][C]0.0205458186027905[/C][C]31.5622480057401[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]0.650555555555556[/C][C]0.0193172679819973[/C][C]33.6774100852067[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]0.646388888888889[/C][C]0.0184580749359880[/C][C]35.0193013697552[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]0.644444444444444[/C][C]0.0180915435256262[/C][C]35.6213080178374[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]0.644444444444444[/C][C]0.0180915435256262[/C][C]35.6213080178374[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]0.640694444444444[/C][C]0.0170005596760593[/C][C]37.6866677716905[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]0.639305555555555[/C][C]0.0167746809602458[/C][C]38.111339170661[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]0.639305555555556[/C][C]0.0167746809602458[/C][C]38.111339170661[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]0.640972222222222[/C][C]0.0153953630528748[/C][C]41.6341089210322[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]0.65[/C][C]0.0140073197944763[/C][C]46.40430928523[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]0.644166666666667[/C][C]0.0131110431419155[/C][C]49.1316106349531[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]0.642083333333333[/C][C]0.0128125059639667[/C][C]50.1137978112243[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]0.644305555555556[/C][C]0.0124954238711081[/C][C]51.5633212767851[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]0.644305555555556[/C][C]0.0124954238711081[/C][C]51.5633212767851[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]0.641805555555556[/C][C]0.0121469329785732[/C][C]52.8368401050436[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]0.641805555555556[/C][C]0.0121469329785732[/C][C]52.8368401050436[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]0.644583333333333[/C][C]0.0117600845746057[/C][C]54.8111137504253[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]0.6475[/C][C]0.0113655817085768[/C][C]56.9702472431639[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]0.653611111111111[/C][C]0.0105766920413049[/C][C]61.7973094573029[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]0.650416666666667[/C][C]0.0101291300817411[/C][C]64.2124902551223[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]0.65375[/C][C]0.00971712083912673[/C][C]67.2781589138653[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]0.649[/C][C]0.0206540567955015[/C][C]31.4223983416834[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]0.647794117647059[/C][C]0.0200184787200461[/C][C]32.3598074911842[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]0.646515151515151[/C][C]0.0192571754849196[/C][C]33.5726883738189[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]0.64578125[/C][C]0.0185335451548522[/C][C]34.8439138116504[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]0.645[/C][C]0.0177498780356451[/C][C]36.338277857725[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]0.643666666666667[/C][C]0.0172042674161326[/C][C]37.4131981965763[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]0.643103448275862[/C][C]0.0167905983267092[/C][C]38.3014015202105[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]0.642857142857143[/C][C]0.0163776738388288[/C][C]39.2520420899477[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]0.642592592592593[/C][C]0.0158636423689299[/C][C]40.5072541127855[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]0.642884615384615[/C][C]0.0154869101017395[/C][C]41.5114836440101[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]0.6434[/C][C]0.0150607206375541[/C][C]42.7203993410297[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]0.643958333333333[/C][C]0.0145156420378392[/C][C]44.3630623884682[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]0.644347826086957[/C][C]0.0141409474086706[/C][C]45.5661001675088[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]0.643636363636364[/C][C]0.0139543612386350[/C][C]46.1243873961315[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]0.643571428571429[/C][C]0.0138844636498690[/C][C]46.3519113737967[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]0.64375[/C][C]0.0138243908383437[/C][C]46.5662471155312[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]0.643684210526316[/C][C]0.0137774479828655[/C][C]46.7201336072428[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]0.643611111111111[/C][C]0.0136751006367428[/C][C]47.0644515318469[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]0.643823529411765[/C][C]0.0135763156585135[/C][C]47.4225515674447[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]0.6440625[/C][C]0.0133942947577113[/C][C]48.0848384816382[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]0.644[/C][C]0.0131970041880811[/C][C]48.798953976360[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]0.643571428571429[/C][C]0.0129734597388812[/C][C]49.6067696300515[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]0.642307692307692[/C][C]0.0128099443619484[/C][C]50.141333495222[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]0.64125[/C][C]0.0126449924212446[/C][C]50.7117741662422[/C][/ROW]
[ROW][C]Median[/C][C]0.615[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.71[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.637105263157895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.637105263157895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.637105263157895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.637105263157895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.637105263157895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.637105263157895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.637105263157895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.646829268292683[/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=4899&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4899&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	0.650694444444444	0.0214701510499289	30.3069337021082
Geometric Mean	0.625084470460239
Harmonic Mean	0.59914984335744
Quadratic Mean	0.675375410008718
Winsorized Mean ( 1 / 24 )	0.650138888888889	0.0211878226456759	30.6845540365882
Winsorized Mean ( 2 / 24 )	0.650138888888889	0.0211878226456759	30.6845540365882
Winsorized Mean ( 3 / 24 )	0.648472222222222	0.0207843647241947	31.200002060556
Winsorized Mean ( 4 / 24 )	0.648472222222222	0.0205458186027905	31.5622480057401
Winsorized Mean ( 5 / 24 )	0.650555555555556	0.0193172679819973	33.6774100852067
Winsorized Mean ( 6 / 24 )	0.646388888888889	0.0184580749359880	35.0193013697552
Winsorized Mean ( 7 / 24 )	0.644444444444444	0.0180915435256262	35.6213080178374
Winsorized Mean ( 8 / 24 )	0.644444444444444	0.0180915435256262	35.6213080178374
Winsorized Mean ( 9 / 24 )	0.640694444444444	0.0170005596760593	37.6866677716905
Winsorized Mean ( 10 / 24 )	0.639305555555555	0.0167746809602458	38.111339170661
Winsorized Mean ( 11 / 24 )	0.639305555555556	0.0167746809602458	38.111339170661
Winsorized Mean ( 12 / 24 )	0.640972222222222	0.0153953630528748	41.6341089210322
Winsorized Mean ( 13 / 24 )	0.65	0.0140073197944763	46.40430928523
Winsorized Mean ( 14 / 24 )	0.644166666666667	0.0131110431419155	49.1316106349531
Winsorized Mean ( 15 / 24 )	0.642083333333333	0.0128125059639667	50.1137978112243
Winsorized Mean ( 16 / 24 )	0.644305555555556	0.0124954238711081	51.5633212767851
Winsorized Mean ( 17 / 24 )	0.644305555555556	0.0124954238711081	51.5633212767851
Winsorized Mean ( 18 / 24 )	0.641805555555556	0.0121469329785732	52.8368401050436
Winsorized Mean ( 19 / 24 )	0.641805555555556	0.0121469329785732	52.8368401050436
Winsorized Mean ( 20 / 24 )	0.644583333333333	0.0117600845746057	54.8111137504253
Winsorized Mean ( 21 / 24 )	0.6475	0.0113655817085768	56.9702472431639
Winsorized Mean ( 22 / 24 )	0.653611111111111	0.0105766920413049	61.7973094573029
Winsorized Mean ( 23 / 24 )	0.650416666666667	0.0101291300817411	64.2124902551223
Winsorized Mean ( 24 / 24 )	0.65375	0.00971712083912673	67.2781589138653
Trimmed Mean ( 1 / 24 )	0.649	0.0206540567955015	31.4223983416834
Trimmed Mean ( 2 / 24 )	0.647794117647059	0.0200184787200461	32.3598074911842
Trimmed Mean ( 3 / 24 )	0.646515151515151	0.0192571754849196	33.5726883738189
Trimmed Mean ( 4 / 24 )	0.64578125	0.0185335451548522	34.8439138116504
Trimmed Mean ( 5 / 24 )	0.645	0.0177498780356451	36.338277857725
Trimmed Mean ( 6 / 24 )	0.643666666666667	0.0172042674161326	37.4131981965763
Trimmed Mean ( 7 / 24 )	0.643103448275862	0.0167905983267092	38.3014015202105
Trimmed Mean ( 8 / 24 )	0.642857142857143	0.0163776738388288	39.2520420899477
Trimmed Mean ( 9 / 24 )	0.642592592592593	0.0158636423689299	40.5072541127855
Trimmed Mean ( 10 / 24 )	0.642884615384615	0.0154869101017395	41.5114836440101
Trimmed Mean ( 11 / 24 )	0.6434	0.0150607206375541	42.7203993410297
Trimmed Mean ( 12 / 24 )	0.643958333333333	0.0145156420378392	44.3630623884682
Trimmed Mean ( 13 / 24 )	0.644347826086957	0.0141409474086706	45.5661001675088
Trimmed Mean ( 14 / 24 )	0.643636363636364	0.0139543612386350	46.1243873961315
Trimmed Mean ( 15 / 24 )	0.643571428571429	0.0138844636498690	46.3519113737967
Trimmed Mean ( 16 / 24 )	0.64375	0.0138243908383437	46.5662471155312
Trimmed Mean ( 17 / 24 )	0.643684210526316	0.0137774479828655	46.7201336072428
Trimmed Mean ( 18 / 24 )	0.643611111111111	0.0136751006367428	47.0644515318469
Trimmed Mean ( 19 / 24 )	0.643823529411765	0.0135763156585135	47.4225515674447
Trimmed Mean ( 20 / 24 )	0.6440625	0.0133942947577113	48.0848384816382
Trimmed Mean ( 21 / 24 )	0.644	0.0131970041880811	48.798953976360
Trimmed Mean ( 22 / 24 )	0.643571428571429	0.0129734597388812	49.6067696300515
Trimmed Mean ( 23 / 24 )	0.642307692307692	0.0128099443619484	50.141333495222
Trimmed Mean ( 24 / 24 )	0.64125	0.0126449924212446	50.7117741662422
Median	0.615
Midrange	0.71
Midmean - Weighted Average at Xnp	0.637105263157895
Midmean - Weighted Average at X(n+1)p	0.637105263157895
Midmean - Empirical Distribution Function	0.637105263157895
Midmean - Empirical Distribution Function - Averaging	0.637105263157895
Midmean - Empirical Distribution Function - Interpolation	0.637105263157895
Midmean - Closest Observation	0.637105263157895
Midmean - True Basic - Statistics Graphics Toolkit	0.637105263157895
Midmean - MS Excel (old versions)	0.646829268292683
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