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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 19 Oct 2009 15:33:34 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/19/t125598832690yfanvx3q7f34s.htm/, Retrieved Mon, 29 Apr 2024 21:14:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48266, Retrieved Mon, 29 Apr 2024 21:14:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact149
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [central tendency ...] [2009-10-19 21:33:34] [30a48cc4afddc7f052994dfe2358176d] [Current]
-    D          [Central Tendency] [central tendency ...] [2009-10-19 21:52:05] [0a7d38ad9c7f1a2c46637c75a8a0e083]
-    D          [Central Tendency] [centrl tendency Y...] [2009-10-19 22:00:27] [0a7d38ad9c7f1a2c46637c75a8a0e083]
- RMP           [Univariate Explorative Data Analysis] [WS 3 verb 1] [2009-10-22 22:26:37] [6e4e01d7eb22a9f33d58ebb35753a195]
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Dataseries X:
11.1
10.9
10
9.2
9.2
9.5
9.6
9.5
9.1
8.9
9
10.1
10.3
10.2
9.6
9.2
9.3
9.4
9.4
9.2
9
9
9
9.8
10
9.8
9.3
9
9
9.1
9.1
9.1
9.2
8.8
8.3
8.4
8.1
7.7
7.9
7.9
8
7.9
7.6
7.1
6.8
6.5
6.9
8.2
8.7
8.3
7.9
7.5
7.8
8.3
8.4
8.2
7.7
7.2
7.3
8.1
8.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48266&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48266&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48266&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean8.739344262295080.12701444968623168.8059058153166
Geometric Mean8.6829375143686
Harmonic Mean8.62542147954256
Quadratic Mean8.79454935517766
Winsorized Mean ( 1 / 20 )8.740983606557380.12467174493281170.1119857692544
Winsorized Mean ( 2 / 20 )8.724590163934430.11879761312262773.4407866842289
Winsorized Mean ( 3 / 20 )8.729508196721310.11531245891897575.7030790823318
Winsorized Mean ( 4 / 20 )8.729508196721310.11243320451282377.6417272330409
Winsorized Mean ( 5 / 20 )8.729508196721310.10897797096027280.1034201664816
Winsorized Mean ( 6 / 20 )8.749180327868850.10487106189013983.4279749835499
Winsorized Mean ( 7 / 20 )8.737704918032790.098268171456758188.9169380940168
Winsorized Mean ( 8 / 20 )8.750819672131150.095803274948291291.3415504517388
Winsorized Mean ( 9 / 20 )8.721311475409840.090720092968961796.1342872344022
Winsorized Mean ( 10 / 20 )8.737704918032790.087720492973848699.6084794078584
Winsorized Mean ( 11 / 20 )8.737704918032790.0816885975156738106.963581010878
Winsorized Mean ( 12 / 20 )8.737704918032790.0816885975156738106.963581010878
Winsorized Mean ( 13 / 20 )8.716393442622950.0784821976217896111.062046002175
Winsorized Mean ( 14 / 20 )8.716393442622950.0784821976217896111.062046002175
Winsorized Mean ( 15 / 20 )8.716393442622950.0707948752378242123.121813737811
Winsorized Mean ( 16 / 20 )8.742622950819670.0664665993770635131.534079263225
Winsorized Mean ( 17 / 20 )8.714754098360650.0627178635874295138.951705301826
Winsorized Mean ( 18 / 20 )8.744262295081970.0579958821867776150.773847476288
Winsorized Mean ( 19 / 20 )8.744262295081970.0579958821867776150.773847476288
Winsorized Mean ( 20 / 20 )8.777049180327870.0529662972862257165.710076596395
Trimmed Mean ( 1 / 20 )8.737288135593220.11899880174351573.4233287022939
Trimmed Mean ( 2 / 20 )8.733333333333330.11198072396480877.9896130701739
Trimmed Mean ( 3 / 20 )8.738181818181820.10732407605134881.4186540399486
Trimmed Mean ( 4 / 20 )8.741509433962260.10326435288454184.6517621016432
Trimmed Mean ( 5 / 20 )8.745098039215690.099343481209119388.0289067060892
Trimmed Mean ( 6 / 20 )8.748979591836730.095614840351300691.5023186745062
Trimmed Mean ( 7 / 20 )8.748936170212770.092196565361384394.8943828429989
Trimmed Mean ( 8 / 20 )8.751111111111110.089759624127203197.494961640096
Trimmed Mean ( 9 / 20 )8.751162790697680.0872473154510423100.302946233438
Trimmed Mean ( 10 / 20 )8.756097560975610.0852577712993041102.701459673824
Trimmed Mean ( 11 / 20 )8.758974358974360.0833442326517054105.093946879060
Trimmed Mean ( 12 / 20 )8.762162162162160.0822315772837469106.554713549122
Trimmed Mean ( 13 / 20 )8.765714285714290.080538404341218108.838936621794
Trimmed Mean ( 14 / 20 )8.772727272727270.0788497717268567111.258752950064
Trimmed Mean ( 15 / 20 )8.780645161290320.0762592289269396115.142065882972
Trimmed Mean ( 16 / 20 )8.78965517241380.0746658941776957117.719813968818
Trimmed Mean ( 17 / 20 )8.79629629629630.0734733475876811119.720913570721
Trimmed Mean ( 18 / 20 )8.8080.072323348005099121.786397379986
Trimmed Mean ( 19 / 20 )8.817391304347830.0718617947588988122.699291521048
Trimmed Mean ( 20 / 20 )8.828571428571430.0704214716792356125.367607606738
Median9
Midrange8.8
Midmean - Weighted Average at Xnp8.78064516129032
Midmean - Weighted Average at X(n+1)p8.78064516129032
Midmean - Empirical Distribution Function8.78064516129032
Midmean - Empirical Distribution Function - Averaging8.78064516129032
Midmean - Empirical Distribution Function - Interpolation8.78064516129032
Midmean - Closest Observation8.68
Midmean - True Basic - Statistics Graphics Toolkit8.78064516129032
Midmean - MS Excel (old versions)8.78064516129032
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.73934426229508 & 0.127014449686231 & 68.8059058153166 \tabularnewline
Geometric Mean & 8.6829375143686 &  &  \tabularnewline
Harmonic Mean & 8.62542147954256 &  &  \tabularnewline
Quadratic Mean & 8.79454935517766 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 8.74098360655738 & 0.124671744932811 & 70.1119857692544 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 8.72459016393443 & 0.118797613122627 & 73.4407866842289 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 8.72950819672131 & 0.115312458918975 & 75.7030790823318 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 8.72950819672131 & 0.112433204512823 & 77.6417272330409 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 8.72950819672131 & 0.108977970960272 & 80.1034201664816 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 8.74918032786885 & 0.104871061890139 & 83.4279749835499 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 8.73770491803279 & 0.0982681714567581 & 88.9169380940168 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 8.75081967213115 & 0.0958032749482912 & 91.3415504517388 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 8.72131147540984 & 0.0907200929689617 & 96.1342872344022 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 8.73770491803279 & 0.0877204929738486 & 99.6084794078584 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 8.73770491803279 & 0.0816885975156738 & 106.963581010878 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 8.73770491803279 & 0.0816885975156738 & 106.963581010878 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 8.71639344262295 & 0.0784821976217896 & 111.062046002175 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 8.71639344262295 & 0.0784821976217896 & 111.062046002175 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 8.71639344262295 & 0.0707948752378242 & 123.121813737811 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 8.74262295081967 & 0.0664665993770635 & 131.534079263225 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 8.71475409836065 & 0.0627178635874295 & 138.951705301826 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 8.74426229508197 & 0.0579958821867776 & 150.773847476288 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 8.74426229508197 & 0.0579958821867776 & 150.773847476288 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 8.77704918032787 & 0.0529662972862257 & 165.710076596395 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 8.73728813559322 & 0.118998801743515 & 73.4233287022939 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 8.73333333333333 & 0.111980723964808 & 77.9896130701739 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 8.73818181818182 & 0.107324076051348 & 81.4186540399486 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 8.74150943396226 & 0.103264352884541 & 84.6517621016432 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 8.74509803921569 & 0.0993434812091193 & 88.0289067060892 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 8.74897959183673 & 0.0956148403513006 & 91.5023186745062 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 8.74893617021277 & 0.0921965653613843 & 94.8943828429989 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 8.75111111111111 & 0.0897596241272031 & 97.494961640096 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 8.75116279069768 & 0.0872473154510423 & 100.302946233438 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 8.75609756097561 & 0.0852577712993041 & 102.701459673824 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 8.75897435897436 & 0.0833442326517054 & 105.093946879060 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 8.76216216216216 & 0.0822315772837469 & 106.554713549122 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 8.76571428571429 & 0.080538404341218 & 108.838936621794 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 8.77272727272727 & 0.0788497717268567 & 111.258752950064 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 8.78064516129032 & 0.0762592289269396 & 115.142065882972 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 8.7896551724138 & 0.0746658941776957 & 117.719813968818 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 8.7962962962963 & 0.0734733475876811 & 119.720913570721 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 8.808 & 0.072323348005099 & 121.786397379986 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 8.81739130434783 & 0.0718617947588988 & 122.699291521048 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 8.82857142857143 & 0.0704214716792356 & 125.367607606738 \tabularnewline
Median & 9 &  &  \tabularnewline
Midrange & 8.8 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.78064516129032 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.78064516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.78064516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.78064516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.78064516129032 &  &  \tabularnewline
Midmean - Closest Observation & 8.68 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.78064516129032 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.78064516129032 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48266&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]8.73934426229508[/C][C]0.127014449686231[/C][C]68.8059058153166[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8.6829375143686[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8.62542147954256[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.79454935517766[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]8.74098360655738[/C][C]0.124671744932811[/C][C]70.1119857692544[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]8.72459016393443[/C][C]0.118797613122627[/C][C]73.4407866842289[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]8.72950819672131[/C][C]0.115312458918975[/C][C]75.7030790823318[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]8.72950819672131[/C][C]0.112433204512823[/C][C]77.6417272330409[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]8.72950819672131[/C][C]0.108977970960272[/C][C]80.1034201664816[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]8.74918032786885[/C][C]0.104871061890139[/C][C]83.4279749835499[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]8.73770491803279[/C][C]0.0982681714567581[/C][C]88.9169380940168[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]8.75081967213115[/C][C]0.0958032749482912[/C][C]91.3415504517388[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]8.72131147540984[/C][C]0.0907200929689617[/C][C]96.1342872344022[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]8.73770491803279[/C][C]0.0877204929738486[/C][C]99.6084794078584[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]8.73770491803279[/C][C]0.0816885975156738[/C][C]106.963581010878[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]8.73770491803279[/C][C]0.0816885975156738[/C][C]106.963581010878[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]8.71639344262295[/C][C]0.0784821976217896[/C][C]111.062046002175[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]8.71639344262295[/C][C]0.0784821976217896[/C][C]111.062046002175[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]8.71639344262295[/C][C]0.0707948752378242[/C][C]123.121813737811[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]8.74262295081967[/C][C]0.0664665993770635[/C][C]131.534079263225[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]8.71475409836065[/C][C]0.0627178635874295[/C][C]138.951705301826[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]8.74426229508197[/C][C]0.0579958821867776[/C][C]150.773847476288[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]8.74426229508197[/C][C]0.0579958821867776[/C][C]150.773847476288[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]8.77704918032787[/C][C]0.0529662972862257[/C][C]165.710076596395[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]8.73728813559322[/C][C]0.118998801743515[/C][C]73.4233287022939[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]8.73333333333333[/C][C]0.111980723964808[/C][C]77.9896130701739[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]8.73818181818182[/C][C]0.107324076051348[/C][C]81.4186540399486[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]8.74150943396226[/C][C]0.103264352884541[/C][C]84.6517621016432[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]8.74509803921569[/C][C]0.0993434812091193[/C][C]88.0289067060892[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]8.74897959183673[/C][C]0.0956148403513006[/C][C]91.5023186745062[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]8.74893617021277[/C][C]0.0921965653613843[/C][C]94.8943828429989[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]8.75111111111111[/C][C]0.0897596241272031[/C][C]97.494961640096[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]8.75116279069768[/C][C]0.0872473154510423[/C][C]100.302946233438[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]8.75609756097561[/C][C]0.0852577712993041[/C][C]102.701459673824[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]8.75897435897436[/C][C]0.0833442326517054[/C][C]105.093946879060[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]8.76216216216216[/C][C]0.0822315772837469[/C][C]106.554713549122[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]8.76571428571429[/C][C]0.080538404341218[/C][C]108.838936621794[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]8.77272727272727[/C][C]0.0788497717268567[/C][C]111.258752950064[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]8.78064516129032[/C][C]0.0762592289269396[/C][C]115.142065882972[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]8.7896551724138[/C][C]0.0746658941776957[/C][C]117.719813968818[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]8.7962962962963[/C][C]0.0734733475876811[/C][C]119.720913570721[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]8.808[/C][C]0.072323348005099[/C][C]121.786397379986[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]8.81739130434783[/C][C]0.0718617947588988[/C][C]122.699291521048[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]8.82857142857143[/C][C]0.0704214716792356[/C][C]125.367607606738[/C][/ROW]
[ROW][C]Median[/C][C]9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.78064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.78064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.78064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.78064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.78064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.68[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.78064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.78064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48266&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48266&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
MeasureValueS.E.Value/S.E.
Arithmetic Mean8.739344262295080.12701444968623168.8059058153166
Geometric Mean8.6829375143686
Harmonic Mean8.62542147954256
Quadratic Mean8.79454935517766
Winsorized Mean ( 1 / 20 )8.740983606557380.12467174493281170.1119857692544
Winsorized Mean ( 2 / 20 )8.724590163934430.11879761312262773.4407866842289
Winsorized Mean ( 3 / 20 )8.729508196721310.11531245891897575.7030790823318
Winsorized Mean ( 4 / 20 )8.729508196721310.11243320451282377.6417272330409
Winsorized Mean ( 5 / 20 )8.729508196721310.10897797096027280.1034201664816
Winsorized Mean ( 6 / 20 )8.749180327868850.10487106189013983.4279749835499
Winsorized Mean ( 7 / 20 )8.737704918032790.098268171456758188.9169380940168
Winsorized Mean ( 8 / 20 )8.750819672131150.095803274948291291.3415504517388
Winsorized Mean ( 9 / 20 )8.721311475409840.090720092968961796.1342872344022
Winsorized Mean ( 10 / 20 )8.737704918032790.087720492973848699.6084794078584
Winsorized Mean ( 11 / 20 )8.737704918032790.0816885975156738106.963581010878
Winsorized Mean ( 12 / 20 )8.737704918032790.0816885975156738106.963581010878
Winsorized Mean ( 13 / 20 )8.716393442622950.0784821976217896111.062046002175
Winsorized Mean ( 14 / 20 )8.716393442622950.0784821976217896111.062046002175
Winsorized Mean ( 15 / 20 )8.716393442622950.0707948752378242123.121813737811
Winsorized Mean ( 16 / 20 )8.742622950819670.0664665993770635131.534079263225
Winsorized Mean ( 17 / 20 )8.714754098360650.0627178635874295138.951705301826
Winsorized Mean ( 18 / 20 )8.744262295081970.0579958821867776150.773847476288
Winsorized Mean ( 19 / 20 )8.744262295081970.0579958821867776150.773847476288
Winsorized Mean ( 20 / 20 )8.777049180327870.0529662972862257165.710076596395
Trimmed Mean ( 1 / 20 )8.737288135593220.11899880174351573.4233287022939
Trimmed Mean ( 2 / 20 )8.733333333333330.11198072396480877.9896130701739
Trimmed Mean ( 3 / 20 )8.738181818181820.10732407605134881.4186540399486
Trimmed Mean ( 4 / 20 )8.741509433962260.10326435288454184.6517621016432
Trimmed Mean ( 5 / 20 )8.745098039215690.099343481209119388.0289067060892
Trimmed Mean ( 6 / 20 )8.748979591836730.095614840351300691.5023186745062
Trimmed Mean ( 7 / 20 )8.748936170212770.092196565361384394.8943828429989
Trimmed Mean ( 8 / 20 )8.751111111111110.089759624127203197.494961640096
Trimmed Mean ( 9 / 20 )8.751162790697680.0872473154510423100.302946233438
Trimmed Mean ( 10 / 20 )8.756097560975610.0852577712993041102.701459673824
Trimmed Mean ( 11 / 20 )8.758974358974360.0833442326517054105.093946879060
Trimmed Mean ( 12 / 20 )8.762162162162160.0822315772837469106.554713549122
Trimmed Mean ( 13 / 20 )8.765714285714290.080538404341218108.838936621794
Trimmed Mean ( 14 / 20 )8.772727272727270.0788497717268567111.258752950064
Trimmed Mean ( 15 / 20 )8.780645161290320.0762592289269396115.142065882972
Trimmed Mean ( 16 / 20 )8.78965517241380.0746658941776957117.719813968818
Trimmed Mean ( 17 / 20 )8.79629629629630.0734733475876811119.720913570721
Trimmed Mean ( 18 / 20 )8.8080.072323348005099121.786397379986
Trimmed Mean ( 19 / 20 )8.817391304347830.0718617947588988122.699291521048
Trimmed Mean ( 20 / 20 )8.828571428571430.0704214716792356125.367607606738
Median9
Midrange8.8
Midmean - Weighted Average at Xnp8.78064516129032
Midmean - Weighted Average at X(n+1)p8.78064516129032
Midmean - Empirical Distribution Function8.78064516129032
Midmean - Empirical Distribution Function - Averaging8.78064516129032
Midmean - Empirical Distribution Function - Interpolation8.78064516129032
Midmean - Closest Observation8.68
Midmean - True Basic - Statistics Graphics Toolkit8.78064516129032
Midmean - MS Excel (old versions)8.78064516129032
Number of observations61



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')