Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 05 Jun 2009 03:22:44 -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/Jun/05/t12441937984x231x52y1um3ib.htm/, Retrieved Fri, 10 May 2024 00:03:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41768, Retrieved Fri, 10 May 2024 00:03:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact154
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [opgave 5 - oef 2/...] [2009-06-05 09:22:44] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
20.050
19.260
19.280
19.100
18.955
18.265
17.760
18.760
19.280
18.920
18.950
18.490
18.470
18.570
18.900
18.485
18.635
18.865
18.860
18.400
18.515
18.950
18.830
18.840
19.200
19.340
20.780
20.270
20.270
20.270
20.250
20.310
19.660
19.760
19.750
19.470
19.320
19.360
19.600
20.140
19.660
19.790
19.670
19.590
19.340
19.330
19.430
19.520
19.400
19.910
19.800
19.830
20.100
20.260
20.310
20.450
19.990
20.095
20.365
19.740
20.100
19.910
20.060
20.440
20.740
21.480
21.050
21.850
22.490
21.660
21.650
21.680
23.020
23.100
22.650
22.440
22.910
22.980
22.535




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41768&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41768&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41768&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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean19.98056962025320.140988707141953141.717517844433
Geometric Mean19.9431335192693
Harmonic Mean19.9070126490824
Quadratic Mean20.0193314564204
Winsorized Mean ( 1 / 26 )19.98594936708860.139552510709369143.214545302672
Winsorized Mean ( 2 / 26 )19.98835443037970.138750384776229144.059812609645
Winsorized Mean ( 3 / 26 )19.98835443037970.137638181769485145.223906429221
Winsorized Mean ( 4 / 26 )19.97594936708860.134054264735514149.013904231250
Winsorized Mean ( 5 / 26 )19.96898734177220.132172334334918151.082958792055
Winsorized Mean ( 6 / 26 )19.96746835443040.131054194244577152.360391588586
Winsorized Mean ( 7 / 26 )19.96791139240510.129280384371126154.454300933102
Winsorized Mean ( 8 / 26 )19.91474683544300.114505445584912173.91964839502
Winsorized Mean ( 9 / 26 )19.90962025316460.108387601772736183.689092917753
Winsorized Mean ( 10 / 26 )19.91594936708860.106676355499701186.695067278939
Winsorized Mean ( 11 / 26 )19.91594936708860.106203404963374187.526467479616
Winsorized Mean ( 12 / 26 )19.89316455696200.100486813166586197.967911709801
Winsorized Mean ( 13 / 26 )19.82322784810130.0867419422224803228.531058219305
Winsorized Mean ( 14 / 26 )19.7815822784810.0775425642610736255.106114518983
Winsorized Mean ( 15 / 26 )19.77778481012660.0757446933812892261.111160759048
Winsorized Mean ( 16 / 26 )19.72512658227850.0658762360060941299.427043470634
Winsorized Mean ( 17 / 26 )19.72297468354430.0655736130311596300.776086170092
Winsorized Mean ( 18 / 26 )19.70702531645570.0630585730369616312.519366794178
Winsorized Mean ( 19 / 26 )19.72867088607590.0561151523949517351.574753770976
Winsorized Mean ( 20 / 26 )19.75398734177220.0525837903973402375.666858408354
Winsorized Mean ( 21 / 26 )19.75930379746840.0490333145710368402.977118115116
Winsorized Mean ( 22 / 26 )19.76487341772150.0483113897755755409.114155265182
Winsorized Mean ( 23 / 26 )19.76487341772150.0483113897755755409.114155265182
Winsorized Mean ( 24 / 26 )19.77398734177220.0463585874273645426.544216273941
Winsorized Mean ( 25 / 26 )19.77398734177220.0455374144642538434.236057852921
Winsorized Mean ( 26 / 26 )19.74107594936710.0403969141063093488.677820722051
Trimmed Mean ( 1 / 26 )19.96889610389610.135733514681013147.118389668351
Trimmed Mean ( 2 / 26 )19.95093333333330.131229895700353152.030398461101
Trimmed Mean ( 3 / 26 )19.93068493150680.126394478758152157.686357247004
Trimmed Mean ( 4 / 26 )19.90929577464790.121132453892683164.359716449619
Trimmed Mean ( 5 / 26 )19.89021739130430.116205982177908171.163454914507
Trimmed Mean ( 6 / 26 )19.87164179104480.110895953822361179.191765849963
Trimmed Mean ( 7 / 26 )19.85223076923080.104766913379431189.489507029118
Trimmed Mean ( 8 / 26 )19.83150793650790.0977117637373596202.959266908877
Trimmed Mean ( 9 / 26 )19.81803278688520.093176875010533212.692610528578
Trimmed Mean ( 10 / 26 )19.8044067796610.089119588547709222.222825558255
Trimmed Mean ( 11 / 26 )19.78894736842110.084463953327364234.288670952014
Trimmed Mean ( 12 / 26 )19.77236363636360.0786953652652635251.251945647824
Trimmed Mean ( 13 / 26 )19.75735849056600.0728656889873159271.147624693500
Trimmed Mean ( 14 / 26 )19.74950980392160.0690619578182193285.967997836161
Trimmed Mean ( 15 / 26 )19.74581632653060.0664263867630352297.258624000888
Trimmed Mean ( 16 / 26 )19.74223404255320.0634614410362378311.090226130856
Trimmed Mean ( 17 / 26 )19.74411111111110.0618666472555989319.139827143684
Trimmed Mean ( 18 / 26 )19.74639534883720.0598230885728514330.079837399075
Trimmed Mean ( 19 / 26 )19.75060975609760.0576660368197652342.499863790327
Trimmed Mean ( 20 / 26 )19.75294871794870.0564179619936488350.118083318437
Trimmed Mean ( 21 / 26 )19.75294871794870.0554880545204527355.985606067119
Trimmed Mean ( 22 / 26 )19.75214285714290.0549313114679764359.578941942026
Trimmed Mean ( 23 / 26 )19.75075757575760.0541777907627984364.554502826269
Trimmed Mean ( 24 / 26 )19.74919354838710.0529587467641335372.916557794421
Trimmed Mean ( 25 / 26 )19.74637931034480.0516112890473187382.598064780765
Trimmed Mean ( 26 / 26 )19.74314814814810.0497237010820625397.057091859768
Median19.75
Midrange20.43
Midmean - Weighted Average at Xnp19.7506097560976
Midmean - Weighted Average at X(n+1)p19.7506097560976
Midmean - Empirical Distribution Function19.7506097560976
Midmean - Empirical Distribution Function - Averaging19.7506097560976
Midmean - Empirical Distribution Function - Interpolation19.766875
Midmean - Closest Observation19.7506097560976
Midmean - True Basic - Statistics Graphics Toolkit19.7506097560976
Midmean - MS Excel (old versions)19.7506097560976
Number of observations79

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 19.9805696202532 & 0.140988707141953 & 141.717517844433 \tabularnewline
Geometric Mean & 19.9431335192693 &  &  \tabularnewline
Harmonic Mean & 19.9070126490824 &  &  \tabularnewline
Quadratic Mean & 20.0193314564204 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 19.9859493670886 & 0.139552510709369 & 143.214545302672 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 19.9883544303797 & 0.138750384776229 & 144.059812609645 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 19.9883544303797 & 0.137638181769485 & 145.223906429221 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 19.9759493670886 & 0.134054264735514 & 149.013904231250 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 19.9689873417722 & 0.132172334334918 & 151.082958792055 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 19.9674683544304 & 0.131054194244577 & 152.360391588586 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 19.9679113924051 & 0.129280384371126 & 154.454300933102 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 19.9147468354430 & 0.114505445584912 & 173.91964839502 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 19.9096202531646 & 0.108387601772736 & 183.689092917753 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 19.9159493670886 & 0.106676355499701 & 186.695067278939 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 19.9159493670886 & 0.106203404963374 & 187.526467479616 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 19.8931645569620 & 0.100486813166586 & 197.967911709801 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 19.8232278481013 & 0.0867419422224803 & 228.531058219305 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 19.781582278481 & 0.0775425642610736 & 255.106114518983 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 19.7777848101266 & 0.0757446933812892 & 261.111160759048 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 19.7251265822785 & 0.0658762360060941 & 299.427043470634 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 19.7229746835443 & 0.0655736130311596 & 300.776086170092 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 19.7070253164557 & 0.0630585730369616 & 312.519366794178 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 19.7286708860759 & 0.0561151523949517 & 351.574753770976 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 19.7539873417722 & 0.0525837903973402 & 375.666858408354 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 19.7593037974684 & 0.0490333145710368 & 402.977118115116 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 19.7648734177215 & 0.0483113897755755 & 409.114155265182 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 19.7648734177215 & 0.0483113897755755 & 409.114155265182 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 19.7739873417722 & 0.0463585874273645 & 426.544216273941 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 19.7739873417722 & 0.0455374144642538 & 434.236057852921 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 19.7410759493671 & 0.0403969141063093 & 488.677820722051 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 19.9688961038961 & 0.135733514681013 & 147.118389668351 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 19.9509333333333 & 0.131229895700353 & 152.030398461101 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 19.9306849315068 & 0.126394478758152 & 157.686357247004 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 19.9092957746479 & 0.121132453892683 & 164.359716449619 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 19.8902173913043 & 0.116205982177908 & 171.163454914507 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 19.8716417910448 & 0.110895953822361 & 179.191765849963 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 19.8522307692308 & 0.104766913379431 & 189.489507029118 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 19.8315079365079 & 0.0977117637373596 & 202.959266908877 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 19.8180327868852 & 0.093176875010533 & 212.692610528578 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 19.804406779661 & 0.089119588547709 & 222.222825558255 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 19.7889473684211 & 0.084463953327364 & 234.288670952014 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 19.7723636363636 & 0.0786953652652635 & 251.251945647824 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 19.7573584905660 & 0.0728656889873159 & 271.147624693500 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 19.7495098039216 & 0.0690619578182193 & 285.967997836161 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 19.7458163265306 & 0.0664263867630352 & 297.258624000888 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 19.7422340425532 & 0.0634614410362378 & 311.090226130856 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 19.7441111111111 & 0.0618666472555989 & 319.139827143684 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 19.7463953488372 & 0.0598230885728514 & 330.079837399075 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 19.7506097560976 & 0.0576660368197652 & 342.499863790327 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 19.7529487179487 & 0.0564179619936488 & 350.118083318437 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 19.7529487179487 & 0.0554880545204527 & 355.985606067119 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 19.7521428571429 & 0.0549313114679764 & 359.578941942026 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 19.7507575757576 & 0.0541777907627984 & 364.554502826269 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 19.7491935483871 & 0.0529587467641335 & 372.916557794421 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 19.7463793103448 & 0.0516112890473187 & 382.598064780765 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 19.7431481481481 & 0.0497237010820625 & 397.057091859768 \tabularnewline
Median & 19.75 &  &  \tabularnewline
Midrange & 20.43 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 19.7506097560976 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 19.7506097560976 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 19.7506097560976 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 19.7506097560976 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 19.766875 &  &  \tabularnewline
Midmean - Closest Observation & 19.7506097560976 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 19.7506097560976 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 19.7506097560976 &  &  \tabularnewline
Number of observations & 79 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41768&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]19.9805696202532[/C][C]0.140988707141953[/C][C]141.717517844433[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]19.9431335192693[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]19.9070126490824[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]20.0193314564204[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]19.9859493670886[/C][C]0.139552510709369[/C][C]143.214545302672[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]19.9883544303797[/C][C]0.138750384776229[/C][C]144.059812609645[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]19.9883544303797[/C][C]0.137638181769485[/C][C]145.223906429221[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]19.9759493670886[/C][C]0.134054264735514[/C][C]149.013904231250[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]19.9689873417722[/C][C]0.132172334334918[/C][C]151.082958792055[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]19.9674683544304[/C][C]0.131054194244577[/C][C]152.360391588586[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]19.9679113924051[/C][C]0.129280384371126[/C][C]154.454300933102[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]19.9147468354430[/C][C]0.114505445584912[/C][C]173.91964839502[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]19.9096202531646[/C][C]0.108387601772736[/C][C]183.689092917753[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]19.9159493670886[/C][C]0.106676355499701[/C][C]186.695067278939[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]19.9159493670886[/C][C]0.106203404963374[/C][C]187.526467479616[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]19.8931645569620[/C][C]0.100486813166586[/C][C]197.967911709801[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]19.8232278481013[/C][C]0.0867419422224803[/C][C]228.531058219305[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]19.781582278481[/C][C]0.0775425642610736[/C][C]255.106114518983[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]19.7777848101266[/C][C]0.0757446933812892[/C][C]261.111160759048[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]19.7251265822785[/C][C]0.0658762360060941[/C][C]299.427043470634[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]19.7229746835443[/C][C]0.0655736130311596[/C][C]300.776086170092[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]19.7070253164557[/C][C]0.0630585730369616[/C][C]312.519366794178[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]19.7286708860759[/C][C]0.0561151523949517[/C][C]351.574753770976[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]19.7539873417722[/C][C]0.0525837903973402[/C][C]375.666858408354[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]19.7593037974684[/C][C]0.0490333145710368[/C][C]402.977118115116[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]19.7648734177215[/C][C]0.0483113897755755[/C][C]409.114155265182[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]19.7648734177215[/C][C]0.0483113897755755[/C][C]409.114155265182[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]19.7739873417722[/C][C]0.0463585874273645[/C][C]426.544216273941[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]19.7739873417722[/C][C]0.0455374144642538[/C][C]434.236057852921[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]19.7410759493671[/C][C]0.0403969141063093[/C][C]488.677820722051[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]19.9688961038961[/C][C]0.135733514681013[/C][C]147.118389668351[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]19.9509333333333[/C][C]0.131229895700353[/C][C]152.030398461101[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]19.9306849315068[/C][C]0.126394478758152[/C][C]157.686357247004[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]19.9092957746479[/C][C]0.121132453892683[/C][C]164.359716449619[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]19.8902173913043[/C][C]0.116205982177908[/C][C]171.163454914507[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]19.8716417910448[/C][C]0.110895953822361[/C][C]179.191765849963[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]19.8522307692308[/C][C]0.104766913379431[/C][C]189.489507029118[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]19.8315079365079[/C][C]0.0977117637373596[/C][C]202.959266908877[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]19.8180327868852[/C][C]0.093176875010533[/C][C]212.692610528578[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]19.804406779661[/C][C]0.089119588547709[/C][C]222.222825558255[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]19.7889473684211[/C][C]0.084463953327364[/C][C]234.288670952014[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]19.7723636363636[/C][C]0.0786953652652635[/C][C]251.251945647824[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]19.7573584905660[/C][C]0.0728656889873159[/C][C]271.147624693500[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]19.7495098039216[/C][C]0.0690619578182193[/C][C]285.967997836161[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]19.7458163265306[/C][C]0.0664263867630352[/C][C]297.258624000888[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]19.7422340425532[/C][C]0.0634614410362378[/C][C]311.090226130856[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]19.7441111111111[/C][C]0.0618666472555989[/C][C]319.139827143684[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]19.7463953488372[/C][C]0.0598230885728514[/C][C]330.079837399075[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]19.7506097560976[/C][C]0.0576660368197652[/C][C]342.499863790327[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]19.7529487179487[/C][C]0.0564179619936488[/C][C]350.118083318437[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]19.7529487179487[/C][C]0.0554880545204527[/C][C]355.985606067119[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]19.7521428571429[/C][C]0.0549313114679764[/C][C]359.578941942026[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]19.7507575757576[/C][C]0.0541777907627984[/C][C]364.554502826269[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]19.7491935483871[/C][C]0.0529587467641335[/C][C]372.916557794421[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]19.7463793103448[/C][C]0.0516112890473187[/C][C]382.598064780765[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]19.7431481481481[/C][C]0.0497237010820625[/C][C]397.057091859768[/C][/ROW]
[ROW][C]Median[/C][C]19.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]20.43[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]19.7506097560976[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]19.7506097560976[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]19.7506097560976[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]19.7506097560976[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]19.766875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]19.7506097560976[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]19.7506097560976[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]19.7506097560976[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]79[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41768&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41768&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 Mean19.98056962025320.140988707141953141.717517844433
Geometric Mean19.9431335192693
Harmonic Mean19.9070126490824
Quadratic Mean20.0193314564204
Winsorized Mean ( 1 / 26 )19.98594936708860.139552510709369143.214545302672
Winsorized Mean ( 2 / 26 )19.98835443037970.138750384776229144.059812609645
Winsorized Mean ( 3 / 26 )19.98835443037970.137638181769485145.223906429221
Winsorized Mean ( 4 / 26 )19.97594936708860.134054264735514149.013904231250
Winsorized Mean ( 5 / 26 )19.96898734177220.132172334334918151.082958792055
Winsorized Mean ( 6 / 26 )19.96746835443040.131054194244577152.360391588586
Winsorized Mean ( 7 / 26 )19.96791139240510.129280384371126154.454300933102
Winsorized Mean ( 8 / 26 )19.91474683544300.114505445584912173.91964839502
Winsorized Mean ( 9 / 26 )19.90962025316460.108387601772736183.689092917753
Winsorized Mean ( 10 / 26 )19.91594936708860.106676355499701186.695067278939
Winsorized Mean ( 11 / 26 )19.91594936708860.106203404963374187.526467479616
Winsorized Mean ( 12 / 26 )19.89316455696200.100486813166586197.967911709801
Winsorized Mean ( 13 / 26 )19.82322784810130.0867419422224803228.531058219305
Winsorized Mean ( 14 / 26 )19.7815822784810.0775425642610736255.106114518983
Winsorized Mean ( 15 / 26 )19.77778481012660.0757446933812892261.111160759048
Winsorized Mean ( 16 / 26 )19.72512658227850.0658762360060941299.427043470634
Winsorized Mean ( 17 / 26 )19.72297468354430.0655736130311596300.776086170092
Winsorized Mean ( 18 / 26 )19.70702531645570.0630585730369616312.519366794178
Winsorized Mean ( 19 / 26 )19.72867088607590.0561151523949517351.574753770976
Winsorized Mean ( 20 / 26 )19.75398734177220.0525837903973402375.666858408354
Winsorized Mean ( 21 / 26 )19.75930379746840.0490333145710368402.977118115116
Winsorized Mean ( 22 / 26 )19.76487341772150.0483113897755755409.114155265182
Winsorized Mean ( 23 / 26 )19.76487341772150.0483113897755755409.114155265182
Winsorized Mean ( 24 / 26 )19.77398734177220.0463585874273645426.544216273941
Winsorized Mean ( 25 / 26 )19.77398734177220.0455374144642538434.236057852921
Winsorized Mean ( 26 / 26 )19.74107594936710.0403969141063093488.677820722051
Trimmed Mean ( 1 / 26 )19.96889610389610.135733514681013147.118389668351
Trimmed Mean ( 2 / 26 )19.95093333333330.131229895700353152.030398461101
Trimmed Mean ( 3 / 26 )19.93068493150680.126394478758152157.686357247004
Trimmed Mean ( 4 / 26 )19.90929577464790.121132453892683164.359716449619
Trimmed Mean ( 5 / 26 )19.89021739130430.116205982177908171.163454914507
Trimmed Mean ( 6 / 26 )19.87164179104480.110895953822361179.191765849963
Trimmed Mean ( 7 / 26 )19.85223076923080.104766913379431189.489507029118
Trimmed Mean ( 8 / 26 )19.83150793650790.0977117637373596202.959266908877
Trimmed Mean ( 9 / 26 )19.81803278688520.093176875010533212.692610528578
Trimmed Mean ( 10 / 26 )19.8044067796610.089119588547709222.222825558255
Trimmed Mean ( 11 / 26 )19.78894736842110.084463953327364234.288670952014
Trimmed Mean ( 12 / 26 )19.77236363636360.0786953652652635251.251945647824
Trimmed Mean ( 13 / 26 )19.75735849056600.0728656889873159271.147624693500
Trimmed Mean ( 14 / 26 )19.74950980392160.0690619578182193285.967997836161
Trimmed Mean ( 15 / 26 )19.74581632653060.0664263867630352297.258624000888
Trimmed Mean ( 16 / 26 )19.74223404255320.0634614410362378311.090226130856
Trimmed Mean ( 17 / 26 )19.74411111111110.0618666472555989319.139827143684
Trimmed Mean ( 18 / 26 )19.74639534883720.0598230885728514330.079837399075
Trimmed Mean ( 19 / 26 )19.75060975609760.0576660368197652342.499863790327
Trimmed Mean ( 20 / 26 )19.75294871794870.0564179619936488350.118083318437
Trimmed Mean ( 21 / 26 )19.75294871794870.0554880545204527355.985606067119
Trimmed Mean ( 22 / 26 )19.75214285714290.0549313114679764359.578941942026
Trimmed Mean ( 23 / 26 )19.75075757575760.0541777907627984364.554502826269
Trimmed Mean ( 24 / 26 )19.74919354838710.0529587467641335372.916557794421
Trimmed Mean ( 25 / 26 )19.74637931034480.0516112890473187382.598064780765
Trimmed Mean ( 26 / 26 )19.74314814814810.0497237010820625397.057091859768
Median19.75
Midrange20.43
Midmean - Weighted Average at Xnp19.7506097560976
Midmean - Weighted Average at X(n+1)p19.7506097560976
Midmean - Empirical Distribution Function19.7506097560976
Midmean - Empirical Distribution Function - Averaging19.7506097560976
Midmean - Empirical Distribution Function - Interpolation19.766875
Midmean - Closest Observation19.7506097560976
Midmean - True Basic - Statistics Graphics Toolkit19.7506097560976
Midmean - MS Excel (old versions)19.7506097560976
Number of observations79



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')