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*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Thu, 13 Dec 2007 06:43:48 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/13/t119755491588cml8ocf7q8r6l.htm/, Retrieved Sun, 05 May 2024 09:32:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3558, Retrieved Sun, 05 May 2024 09:32:18 +0000

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Estimated Impact

196

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

-       [Central Tendency] [Central tendency ...] [2007-12-13 13:43:48] [9bb499d88394279c02e6a8b8cf177cf7] [Current]

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Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3558&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]2 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=3558&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3558&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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.19081571428571	0.0163181348947078	72.9749889904336
Geometric Mean	1.18247945904816
Harmonic Mean	1.17348432682254
Quadratic Mean	1.19850552385639
Winsorized Mean ( 1 / 23 )	1.19042571428571	0.0162038398288691	73.4656554778347
Winsorized Mean ( 2 / 23 )	1.19012571428571	0.0160560679996562	74.1231112319156
Winsorized Mean ( 3 / 23 )	1.18983	0.0159619191431644	74.5417884483856
Winsorized Mean ( 4 / 23 )	1.19100714285714	0.0153923468280662	77.3765791637097
Winsorized Mean ( 5 / 23 )	1.19371428571429	0.0147103427348821	81.1479587680628
Winsorized Mean ( 6 / 23 )	1.19484571428571	0.0141507590656990	84.4368636861313
Winsorized Mean ( 7 / 23 )	1.19503571428571	0.0140677657527476	84.9485081916655
Winsorized Mean ( 8 / 23 )	1.19317285714286	0.0137869456846055	86.5436685135527
Winsorized Mean ( 9 / 23 )	1.19422714285714	0.0134208883454513	88.9827194830883
Winsorized Mean ( 10 / 23 )	1.19537	0.0131130409935826	91.158870058059
Winsorized Mean ( 11 / 23 )	1.19673714285714	0.0123749110328155	96.7067269965552
Winsorized Mean ( 12 / 23 )	1.20349142857143	0.0107618268983423	111.829658657380
Winsorized Mean ( 13 / 23 )	1.20518142857143	0.0100819331456750	119.538724484444
Winsorized Mean ( 14 / 23 )	1.20556142857143	0.00991595015443538	121.578004104043
Winsorized Mean ( 15 / 23 )	1.20626857142857	0.00973265374046085	123.940356206637
Winsorized Mean ( 16 / 23 )	1.21170857142857	0.00839736075634996	144.296357699328
Winsorized Mean ( 17 / 23 )	1.21234	0.00786500133265932	154.143648388942
Winsorized Mean ( 18 / 23 )	1.21439714285714	0.00698481018930769	173.862583226118
Winsorized Mean ( 19 / 23 )	1.21898428571429	0.00594790727702127	204.943390833214
Winsorized Mean ( 20 / 23 )	1.22007	0.00543739995029442	224.38481832368
Winsorized Mean ( 21 / 23 )	1.21995	0.00517521316111134	235.729420609609
Winsorized Mean ( 22 / 23 )	1.21995	0.00508715499692441	239.809874229812
Winsorized Mean ( 23 / 23 )	1.22159285714286	0.00454777096968007	268.613539531168
Trimmed Mean ( 1 / 23 )	1.19212352941176	0.0157441295995226	75.7186049489782
Trimmed Mean ( 2 / 23 )	1.19392424242424	0.0151915422519737	78.5913781906593
Trimmed Mean ( 3 / 23 )	1.1960015625	0.0146192297143662	81.8101627697048
Trimmed Mean ( 4 / 23 )	1.19832419354839	0.0139647627647992	85.8105657597698
Trimmed Mean ( 5 / 23 )	1.20045833333333	0.0133893790212387	89.6575062539586
Trimmed Mean ( 6 / 23 )	1.20208620689655	0.0129185517891267	93.0511582504417
Trimmed Mean ( 7 / 23 )	1.20359464285714	0.0125065612441440	96.2370566426248
Trimmed Mean ( 8 / 23 )	1.20517962962963	0.0120149703904955	100.306500179392
Trimmed Mean ( 9 / 23 )	1.2072	0.0114645354529670	105.298640747591
Trimmed Mean ( 10 / 23 )	1.209218	0.0108631508527213	111.313744639483
Trimmed Mean ( 11 / 23 )	1.2112375	0.0101722926351769	119.072223287345
Trimmed Mean ( 12 / 23 )	1.21324347826087	0.00947658933539024	128.025330139613
Trimmed Mean ( 13 / 23 )	1.21453636363636	0.00902617645662328	134.557126095752
Trimmed Mean ( 14 / 23 )	1.21573571428571	0.00861167792968127	141.172919402330
Trimmed Mean ( 15 / 23 )	1.2170075	0.00809883925483405	150.269373388735
Trimmed Mean ( 16 / 23 )	1.21832631578947	0.00745007917531751	163.531995717019
Trimmed Mean ( 17 / 23 )	1.21913055555556	0.00698148096746802	174.623487657763
Trimmed Mean ( 18 / 23 )	1.21995294117647	0.00648860544563535	188.014659143297
Trimmed Mean ( 19 / 23 )	1.220628125	0.00607719533275007	200.853857440129
Trimmed Mean ( 20 / 23 )	1.22083	0.00582903582256017	209.439440271582
Trimmed Mean ( 21 / 23 )	1.220925	0.00562217506959962	217.162394426637
Trimmed Mean ( 22 / 23 )	1.22105	0.00538810441906699	226.619587341152
Trimmed Mean ( 23 / 23 )	1.22119583333333	0.00504370923709501	242.122568119469
Median	1.2197
Midrange	1.14635
Midmean - Weighted Average at Xnp	1.21716
Midmean - Weighted Average at X(n+1)p	1.21913055555556
Midmean - Empirical Distribution Function	1.21913055555556
Midmean - Empirical Distribution Function - Averaging	1.21913055555556
Midmean - Empirical Distribution Function - Interpolation	1.21995294117647
Midmean - Closest Observation	1.21913055555556
Midmean - True Basic - Statistics Graphics Toolkit	1.21913055555556
Midmean - MS Excel (old versions)	1.21913055555556
Number of observations	70

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.19081571428571 & 0.0163181348947078 & 72.9749889904336 \tabularnewline
Geometric Mean & 1.18247945904816 &  &  \tabularnewline
Harmonic Mean & 1.17348432682254 &  &  \tabularnewline
Quadratic Mean & 1.19850552385639 &  &  \tabularnewline
Winsorized Mean ( 1 / 23 ) & 1.19042571428571 & 0.0162038398288691 & 73.4656554778347 \tabularnewline
Winsorized Mean ( 2 / 23 ) & 1.19012571428571 & 0.0160560679996562 & 74.1231112319156 \tabularnewline
Winsorized Mean ( 3 / 23 ) & 1.18983 & 0.0159619191431644 & 74.5417884483856 \tabularnewline
Winsorized Mean ( 4 / 23 ) & 1.19100714285714 & 0.0153923468280662 & 77.3765791637097 \tabularnewline
Winsorized Mean ( 5 / 23 ) & 1.19371428571429 & 0.0147103427348821 & 81.1479587680628 \tabularnewline
Winsorized Mean ( 6 / 23 ) & 1.19484571428571 & 0.0141507590656990 & 84.4368636861313 \tabularnewline
Winsorized Mean ( 7 / 23 ) & 1.19503571428571 & 0.0140677657527476 & 84.9485081916655 \tabularnewline
Winsorized Mean ( 8 / 23 ) & 1.19317285714286 & 0.0137869456846055 & 86.5436685135527 \tabularnewline
Winsorized Mean ( 9 / 23 ) & 1.19422714285714 & 0.0134208883454513 & 88.9827194830883 \tabularnewline
Winsorized Mean ( 10 / 23 ) & 1.19537 & 0.0131130409935826 & 91.158870058059 \tabularnewline
Winsorized Mean ( 11 / 23 ) & 1.19673714285714 & 0.0123749110328155 & 96.7067269965552 \tabularnewline
Winsorized Mean ( 12 / 23 ) & 1.20349142857143 & 0.0107618268983423 & 111.829658657380 \tabularnewline
Winsorized Mean ( 13 / 23 ) & 1.20518142857143 & 0.0100819331456750 & 119.538724484444 \tabularnewline
Winsorized Mean ( 14 / 23 ) & 1.20556142857143 & 0.00991595015443538 & 121.578004104043 \tabularnewline
Winsorized Mean ( 15 / 23 ) & 1.20626857142857 & 0.00973265374046085 & 123.940356206637 \tabularnewline
Winsorized Mean ( 16 / 23 ) & 1.21170857142857 & 0.00839736075634996 & 144.296357699328 \tabularnewline
Winsorized Mean ( 17 / 23 ) & 1.21234 & 0.00786500133265932 & 154.143648388942 \tabularnewline
Winsorized Mean ( 18 / 23 ) & 1.21439714285714 & 0.00698481018930769 & 173.862583226118 \tabularnewline
Winsorized Mean ( 19 / 23 ) & 1.21898428571429 & 0.00594790727702127 & 204.943390833214 \tabularnewline
Winsorized Mean ( 20 / 23 ) & 1.22007 & 0.00543739995029442 & 224.38481832368 \tabularnewline
Winsorized Mean ( 21 / 23 ) & 1.21995 & 0.00517521316111134 & 235.729420609609 \tabularnewline
Winsorized Mean ( 22 / 23 ) & 1.21995 & 0.00508715499692441 & 239.809874229812 \tabularnewline
Winsorized Mean ( 23 / 23 ) & 1.22159285714286 & 0.00454777096968007 & 268.613539531168 \tabularnewline
Trimmed Mean ( 1 / 23 ) & 1.19212352941176 & 0.0157441295995226 & 75.7186049489782 \tabularnewline
Trimmed Mean ( 2 / 23 ) & 1.19392424242424 & 0.0151915422519737 & 78.5913781906593 \tabularnewline
Trimmed Mean ( 3 / 23 ) & 1.1960015625 & 0.0146192297143662 & 81.8101627697048 \tabularnewline
Trimmed Mean ( 4 / 23 ) & 1.19832419354839 & 0.0139647627647992 & 85.8105657597698 \tabularnewline
Trimmed Mean ( 5 / 23 ) & 1.20045833333333 & 0.0133893790212387 & 89.6575062539586 \tabularnewline
Trimmed Mean ( 6 / 23 ) & 1.20208620689655 & 0.0129185517891267 & 93.0511582504417 \tabularnewline
Trimmed Mean ( 7 / 23 ) & 1.20359464285714 & 0.0125065612441440 & 96.2370566426248 \tabularnewline
Trimmed Mean ( 8 / 23 ) & 1.20517962962963 & 0.0120149703904955 & 100.306500179392 \tabularnewline
Trimmed Mean ( 9 / 23 ) & 1.2072 & 0.0114645354529670 & 105.298640747591 \tabularnewline
Trimmed Mean ( 10 / 23 ) & 1.209218 & 0.0108631508527213 & 111.313744639483 \tabularnewline
Trimmed Mean ( 11 / 23 ) & 1.2112375 & 0.0101722926351769 & 119.072223287345 \tabularnewline
Trimmed Mean ( 12 / 23 ) & 1.21324347826087 & 0.00947658933539024 & 128.025330139613 \tabularnewline
Trimmed Mean ( 13 / 23 ) & 1.21453636363636 & 0.00902617645662328 & 134.557126095752 \tabularnewline
Trimmed Mean ( 14 / 23 ) & 1.21573571428571 & 0.00861167792968127 & 141.172919402330 \tabularnewline
Trimmed Mean ( 15 / 23 ) & 1.2170075 & 0.00809883925483405 & 150.269373388735 \tabularnewline
Trimmed Mean ( 16 / 23 ) & 1.21832631578947 & 0.00745007917531751 & 163.531995717019 \tabularnewline
Trimmed Mean ( 17 / 23 ) & 1.21913055555556 & 0.00698148096746802 & 174.623487657763 \tabularnewline
Trimmed Mean ( 18 / 23 ) & 1.21995294117647 & 0.00648860544563535 & 188.014659143297 \tabularnewline
Trimmed Mean ( 19 / 23 ) & 1.220628125 & 0.00607719533275007 & 200.853857440129 \tabularnewline
Trimmed Mean ( 20 / 23 ) & 1.22083 & 0.00582903582256017 & 209.439440271582 \tabularnewline
Trimmed Mean ( 21 / 23 ) & 1.220925 & 0.00562217506959962 & 217.162394426637 \tabularnewline
Trimmed Mean ( 22 / 23 ) & 1.22105 & 0.00538810441906699 & 226.619587341152 \tabularnewline
Trimmed Mean ( 23 / 23 ) & 1.22119583333333 & 0.00504370923709501 & 242.122568119469 \tabularnewline
Median & 1.2197 &  &  \tabularnewline
Midrange & 1.14635 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.21716 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.21913055555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.21913055555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.21913055555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.21995294117647 &  &  \tabularnewline
Midmean - Closest Observation & 1.21913055555556 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.21913055555556 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.21913055555556 &  &  \tabularnewline
Number of observations & 70 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3558&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]1.19081571428571[/C][C]0.0163181348947078[/C][C]72.9749889904336[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.18247945904816[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.17348432682254[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.19850552385639[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 23 )[/C][C]1.19042571428571[/C][C]0.0162038398288691[/C][C]73.4656554778347[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 23 )[/C][C]1.19012571428571[/C][C]0.0160560679996562[/C][C]74.1231112319156[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 23 )[/C][C]1.18983[/C][C]0.0159619191431644[/C][C]74.5417884483856[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 23 )[/C][C]1.19100714285714[/C][C]0.0153923468280662[/C][C]77.3765791637097[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 23 )[/C][C]1.19371428571429[/C][C]0.0147103427348821[/C][C]81.1479587680628[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 23 )[/C][C]1.19484571428571[/C][C]0.0141507590656990[/C][C]84.4368636861313[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 23 )[/C][C]1.19503571428571[/C][C]0.0140677657527476[/C][C]84.9485081916655[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 23 )[/C][C]1.19317285714286[/C][C]0.0137869456846055[/C][C]86.5436685135527[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 23 )[/C][C]1.19422714285714[/C][C]0.0134208883454513[/C][C]88.9827194830883[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 23 )[/C][C]1.19537[/C][C]0.0131130409935826[/C][C]91.158870058059[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 23 )[/C][C]1.19673714285714[/C][C]0.0123749110328155[/C][C]96.7067269965552[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 23 )[/C][C]1.20349142857143[/C][C]0.0107618268983423[/C][C]111.829658657380[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 23 )[/C][C]1.20518142857143[/C][C]0.0100819331456750[/C][C]119.538724484444[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 23 )[/C][C]1.20556142857143[/C][C]0.00991595015443538[/C][C]121.578004104043[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 23 )[/C][C]1.20626857142857[/C][C]0.00973265374046085[/C][C]123.940356206637[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 23 )[/C][C]1.21170857142857[/C][C]0.00839736075634996[/C][C]144.296357699328[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 23 )[/C][C]1.21234[/C][C]0.00786500133265932[/C][C]154.143648388942[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 23 )[/C][C]1.21439714285714[/C][C]0.00698481018930769[/C][C]173.862583226118[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 23 )[/C][C]1.21898428571429[/C][C]0.00594790727702127[/C][C]204.943390833214[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 23 )[/C][C]1.22007[/C][C]0.00543739995029442[/C][C]224.38481832368[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 23 )[/C][C]1.21995[/C][C]0.00517521316111134[/C][C]235.729420609609[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 23 )[/C][C]1.21995[/C][C]0.00508715499692441[/C][C]239.809874229812[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 23 )[/C][C]1.22159285714286[/C][C]0.00454777096968007[/C][C]268.613539531168[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 23 )[/C][C]1.19212352941176[/C][C]0.0157441295995226[/C][C]75.7186049489782[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 23 )[/C][C]1.19392424242424[/C][C]0.0151915422519737[/C][C]78.5913781906593[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 23 )[/C][C]1.1960015625[/C][C]0.0146192297143662[/C][C]81.8101627697048[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 23 )[/C][C]1.19832419354839[/C][C]0.0139647627647992[/C][C]85.8105657597698[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 23 )[/C][C]1.20045833333333[/C][C]0.0133893790212387[/C][C]89.6575062539586[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 23 )[/C][C]1.20208620689655[/C][C]0.0129185517891267[/C][C]93.0511582504417[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 23 )[/C][C]1.20359464285714[/C][C]0.0125065612441440[/C][C]96.2370566426248[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 23 )[/C][C]1.20517962962963[/C][C]0.0120149703904955[/C][C]100.306500179392[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 23 )[/C][C]1.2072[/C][C]0.0114645354529670[/C][C]105.298640747591[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 23 )[/C][C]1.209218[/C][C]0.0108631508527213[/C][C]111.313744639483[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 23 )[/C][C]1.2112375[/C][C]0.0101722926351769[/C][C]119.072223287345[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 23 )[/C][C]1.21324347826087[/C][C]0.00947658933539024[/C][C]128.025330139613[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 23 )[/C][C]1.21453636363636[/C][C]0.00902617645662328[/C][C]134.557126095752[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 23 )[/C][C]1.21573571428571[/C][C]0.00861167792968127[/C][C]141.172919402330[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 23 )[/C][C]1.2170075[/C][C]0.00809883925483405[/C][C]150.269373388735[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 23 )[/C][C]1.21832631578947[/C][C]0.00745007917531751[/C][C]163.531995717019[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 23 )[/C][C]1.21913055555556[/C][C]0.00698148096746802[/C][C]174.623487657763[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 23 )[/C][C]1.21995294117647[/C][C]0.00648860544563535[/C][C]188.014659143297[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 23 )[/C][C]1.220628125[/C][C]0.00607719533275007[/C][C]200.853857440129[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 23 )[/C][C]1.22083[/C][C]0.00582903582256017[/C][C]209.439440271582[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 23 )[/C][C]1.220925[/C][C]0.00562217506959962[/C][C]217.162394426637[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 23 )[/C][C]1.22105[/C][C]0.00538810441906699[/C][C]226.619587341152[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 23 )[/C][C]1.22119583333333[/C][C]0.00504370923709501[/C][C]242.122568119469[/C][/ROW]
[ROW][C]Median[/C][C]1.2197[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.14635[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.21716[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.21913055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.21913055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.21913055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.21995294117647[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.21913055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.21913055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.21913055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]70[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3558&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3558&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	1.19081571428571	0.0163181348947078	72.9749889904336
Geometric Mean	1.18247945904816
Harmonic Mean	1.17348432682254
Quadratic Mean	1.19850552385639
Winsorized Mean ( 1 / 23 )	1.19042571428571	0.0162038398288691	73.4656554778347
Winsorized Mean ( 2 / 23 )	1.19012571428571	0.0160560679996562	74.1231112319156
Winsorized Mean ( 3 / 23 )	1.18983	0.0159619191431644	74.5417884483856
Winsorized Mean ( 4 / 23 )	1.19100714285714	0.0153923468280662	77.3765791637097
Winsorized Mean ( 5 / 23 )	1.19371428571429	0.0147103427348821	81.1479587680628
Winsorized Mean ( 6 / 23 )	1.19484571428571	0.0141507590656990	84.4368636861313
Winsorized Mean ( 7 / 23 )	1.19503571428571	0.0140677657527476	84.9485081916655
Winsorized Mean ( 8 / 23 )	1.19317285714286	0.0137869456846055	86.5436685135527
Winsorized Mean ( 9 / 23 )	1.19422714285714	0.0134208883454513	88.9827194830883
Winsorized Mean ( 10 / 23 )	1.19537	0.0131130409935826	91.158870058059
Winsorized Mean ( 11 / 23 )	1.19673714285714	0.0123749110328155	96.7067269965552
Winsorized Mean ( 12 / 23 )	1.20349142857143	0.0107618268983423	111.829658657380
Winsorized Mean ( 13 / 23 )	1.20518142857143	0.0100819331456750	119.538724484444
Winsorized Mean ( 14 / 23 )	1.20556142857143	0.00991595015443538	121.578004104043
Winsorized Mean ( 15 / 23 )	1.20626857142857	0.00973265374046085	123.940356206637
Winsorized Mean ( 16 / 23 )	1.21170857142857	0.00839736075634996	144.296357699328
Winsorized Mean ( 17 / 23 )	1.21234	0.00786500133265932	154.143648388942
Winsorized Mean ( 18 / 23 )	1.21439714285714	0.00698481018930769	173.862583226118
Winsorized Mean ( 19 / 23 )	1.21898428571429	0.00594790727702127	204.943390833214
Winsorized Mean ( 20 / 23 )	1.22007	0.00543739995029442	224.38481832368
Winsorized Mean ( 21 / 23 )	1.21995	0.00517521316111134	235.729420609609
Winsorized Mean ( 22 / 23 )	1.21995	0.00508715499692441	239.809874229812
Winsorized Mean ( 23 / 23 )	1.22159285714286	0.00454777096968007	268.613539531168
Trimmed Mean ( 1 / 23 )	1.19212352941176	0.0157441295995226	75.7186049489782
Trimmed Mean ( 2 / 23 )	1.19392424242424	0.0151915422519737	78.5913781906593
Trimmed Mean ( 3 / 23 )	1.1960015625	0.0146192297143662	81.8101627697048
Trimmed Mean ( 4 / 23 )	1.19832419354839	0.0139647627647992	85.8105657597698
Trimmed Mean ( 5 / 23 )	1.20045833333333	0.0133893790212387	89.6575062539586
Trimmed Mean ( 6 / 23 )	1.20208620689655	0.0129185517891267	93.0511582504417
Trimmed Mean ( 7 / 23 )	1.20359464285714	0.0125065612441440	96.2370566426248
Trimmed Mean ( 8 / 23 )	1.20517962962963	0.0120149703904955	100.306500179392
Trimmed Mean ( 9 / 23 )	1.2072	0.0114645354529670	105.298640747591
Trimmed Mean ( 10 / 23 )	1.209218	0.0108631508527213	111.313744639483
Trimmed Mean ( 11 / 23 )	1.2112375	0.0101722926351769	119.072223287345
Trimmed Mean ( 12 / 23 )	1.21324347826087	0.00947658933539024	128.025330139613
Trimmed Mean ( 13 / 23 )	1.21453636363636	0.00902617645662328	134.557126095752
Trimmed Mean ( 14 / 23 )	1.21573571428571	0.00861167792968127	141.172919402330
Trimmed Mean ( 15 / 23 )	1.2170075	0.00809883925483405	150.269373388735
Trimmed Mean ( 16 / 23 )	1.21832631578947	0.00745007917531751	163.531995717019
Trimmed Mean ( 17 / 23 )	1.21913055555556	0.00698148096746802	174.623487657763
Trimmed Mean ( 18 / 23 )	1.21995294117647	0.00648860544563535	188.014659143297
Trimmed Mean ( 19 / 23 )	1.220628125	0.00607719533275007	200.853857440129
Trimmed Mean ( 20 / 23 )	1.22083	0.00582903582256017	209.439440271582
Trimmed Mean ( 21 / 23 )	1.220925	0.00562217506959962	217.162394426637
Trimmed Mean ( 22 / 23 )	1.22105	0.00538810441906699	226.619587341152
Trimmed Mean ( 23 / 23 )	1.22119583333333	0.00504370923709501	242.122568119469
Median	1.2197
Midrange	1.14635
Midmean - Weighted Average at Xnp	1.21716
Midmean - Weighted Average at X(n+1)p	1.21913055555556
Midmean - Empirical Distribution Function	1.21913055555556
Midmean - Empirical Distribution Function - Averaging	1.21913055555556
Midmean - Empirical Distribution Function - Interpolation	1.21995294117647
Midmean - Closest Observation	1.21913055555556
Midmean - True Basic - Statistics Graphics Toolkit	1.21913055555556
Midmean - MS Excel (old versions)	1.21913055555556
Number of observations	70

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