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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 16 Oct 2012 04:45:48 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/16/t135037720073hirgcc8ch283v.htm/, Retrieved Tue, 30 Apr 2024 12:59:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=178315, Retrieved Tue, 30 Apr 2024 12:59:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact85
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Gemiddelde consum...] [2012-09-28 06:28:32] [28c6e8aa27b151407c47740a049ee208]
- RMPD    [Central Tendency] [] [2012-10-16 08:45:48] [5f317879e17cb2eb817d39090eb03de3] [Current]
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Dataseries X:
15.13
15.25
15.33
15.36
15.4
15.4
15.41
15.47
15.54
15.55
15.59
15.65
15.75
15.86
15.89
15.94
15.93
15.95
15.99
15.99
16.06
16.08
16.07
16.11
16.15
16.18
16.3
16.42
16.49
16.5
16.58
16.64
16.66
16.81
16.91
16.92
16.95
17.11
17.16
17.16
17.27
17.34
17.39
17.43
17.45
17.5
17.56
17.65
17.62
17.7
17.72
17.71
17.74
17.75
17.78
17.8
17.86
17.88
17.89
17.94
17.98
18.1
18.14
18.19
18.23
18.24
18.27
18.3
18.34
18.36
18.36
18.4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=178315&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=178315&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=178315&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean16.88236111111110.119573527031721141.188116886712
Geometric Mean16.8521139547277
Harmonic Mean16.8217326341888
Quadratic Mean16.9123996671082
Winsorized Mean ( 1 / 24 )16.88347222222220.119142436507425141.708300729355
Winsorized Mean ( 2 / 24 )16.88569444444440.118722797953337142.227901763916
Winsorized Mean ( 3 / 24 )16.88611111111110.118348963385454142.680684545705
Winsorized Mean ( 4 / 24 )16.88611111111110.11756887162734143.627397944545
Winsorized Mean ( 5 / 24 )16.88402777777780.117218957624998144.038371607027
Winsorized Mean ( 6 / 24 )16.88236111111110.116657526981964144.717289555789
Winsorized Mean ( 7 / 24 )16.88722222222220.11547551248492146.240721160925
Winsorized Mean ( 8 / 24 )16.89055555555560.113428379243799148.90943226167
Winsorized Mean ( 9 / 24 )16.88555555555560.112222512743856150.464957009974
Winsorized Mean ( 10 / 24 )16.88555555555560.110430210240138152.907030773886
Winsorized Mean ( 11 / 24 )16.87638888888890.106163408156662158.966155871569
Winsorized Mean ( 12 / 24 )16.88638888888890.102535215820684164.688675531929
Winsorized Mean ( 13 / 24 )16.89722222222220.0982101604275141172.051671116998
Winsorized Mean ( 14 / 24 )16.90111111111110.0970718712239787174.109254287623
Winsorized Mean ( 15 / 24 )16.90527777777780.0952697702142467177.446400256456
Winsorized Mean ( 16 / 24 )16.89416666666670.0930942507079089181.473791756201
Winsorized Mean ( 17 / 24 )16.89180555555560.0921095418460857183.388226854734
Winsorized Mean ( 18 / 24 )16.89430555555560.0896657037814351188.414352902826
Winsorized Mean ( 19 / 24 )16.89166666666670.089311836107302189.131333571202
Winsorized Mean ( 20 / 24 )16.90555555555560.0858370113822672196.949489309084
Winsorized Mean ( 21 / 24 )16.90555555555560.0850436896116213198.786713426476
Winsorized Mean ( 22 / 24 )16.90555555555560.0842147956309619200.743294915035
Winsorized Mean ( 23 / 24 )16.89916666666670.0807870977589816209.181504664065
Winsorized Mean ( 24 / 24 )16.90250.0776545735008732217.662646744302
Trimmed Mean ( 1 / 24 )16.88571428571430.118405306563097142.609438511238
Trimmed Mean ( 2 / 24 )16.88808823529410.11746728335227143.768441333991
Trimmed Mean ( 3 / 24 )16.88939393939390.11654703399187144.914832758182
Trimmed Mean ( 4 / 24 )16.8906250.115543675819256146.183898687989
Trimmed Mean ( 5 / 24 )16.8919354838710.114542946785757147.472506670061
Trimmed Mean ( 6 / 24 )16.89383333333330.113365339033419149.021151238768
Trimmed Mean ( 7 / 24 )16.89620689655170.112013909879198150.840256489337
Trimmed Mean ( 8 / 24 )16.89785714285710.110588072172656152.799997421741
Trimmed Mean ( 9 / 24 )16.89907407407410.109241162674781154.695113639388
Trimmed Mean ( 10 / 24 )16.90115384615380.107757077592162156.844953703377
Trimmed Mean ( 11 / 24 )16.90340.106209884623969159.150911987578
Trimmed Mean ( 12 / 24 )16.90708333333330.105072146074089160.909279624038
Trimmed Mean ( 13 / 24 )16.90978260869570.104258360398989162.191142695734
Trimmed Mean ( 14 / 24 )16.91136363636360.103933011698029162.714072844329
Trimmed Mean ( 15 / 24 )16.9126190476190.103526696789657163.364809001698
Trimmed Mean ( 16 / 24 )16.91350.103133315515554163.996473064509
Trimmed Mean ( 17 / 24 )16.91578947368420.10280257120157164.546365679089
Trimmed Mean ( 18 / 24 )16.91861111111110.102272707943632165.426451017957
Trimmed Mean ( 19 / 24 )16.92147058823530.101790680641247166.237915707368
Trimmed Mean ( 20 / 24 )16.9250.100840220150494167.839776378326
Trimmed Mean ( 21 / 24 )16.92733333333330.10004014519852169.205405487394
Trimmed Mean ( 22 / 24 )16.930.0986630200956343171.594179699645
Trimmed Mean ( 23 / 24 )16.93307692307690.0964249715993165175.608834954502
Trimmed Mean ( 24 / 24 )16.93750.0937508454068162180.665037488489
Median16.935
Midrange16.765
Midmean - Weighted Average at Xnp16.8924324324324
Midmean - Weighted Average at X(n+1)p16.9186111111111
Midmean - Empirical Distribution Function16.8924324324324
Midmean - Empirical Distribution Function - Averaging16.9186111111111
Midmean - Empirical Distribution Function - Interpolation16.9186111111111
Midmean - Closest Observation16.8924324324324
Midmean - True Basic - Statistics Graphics Toolkit16.9186111111111
Midmean - MS Excel (old versions)16.9157894736842
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 16.8823611111111 & 0.119573527031721 & 141.188116886712 \tabularnewline
Geometric Mean & 16.8521139547277 &  &  \tabularnewline
Harmonic Mean & 16.8217326341888 &  &  \tabularnewline
Quadratic Mean & 16.9123996671082 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 16.8834722222222 & 0.119142436507425 & 141.708300729355 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 16.8856944444444 & 0.118722797953337 & 142.227901763916 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 16.8861111111111 & 0.118348963385454 & 142.680684545705 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 16.8861111111111 & 0.11756887162734 & 143.627397944545 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 16.8840277777778 & 0.117218957624998 & 144.038371607027 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 16.8823611111111 & 0.116657526981964 & 144.717289555789 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 16.8872222222222 & 0.11547551248492 & 146.240721160925 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 16.8905555555556 & 0.113428379243799 & 148.90943226167 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 16.8855555555556 & 0.112222512743856 & 150.464957009974 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 16.8855555555556 & 0.110430210240138 & 152.907030773886 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 16.8763888888889 & 0.106163408156662 & 158.966155871569 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 16.8863888888889 & 0.102535215820684 & 164.688675531929 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 16.8972222222222 & 0.0982101604275141 & 172.051671116998 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 16.9011111111111 & 0.0970718712239787 & 174.109254287623 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 16.9052777777778 & 0.0952697702142467 & 177.446400256456 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 16.8941666666667 & 0.0930942507079089 & 181.473791756201 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 16.8918055555556 & 0.0921095418460857 & 183.388226854734 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 16.8943055555556 & 0.0896657037814351 & 188.414352902826 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 16.8916666666667 & 0.089311836107302 & 189.131333571202 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 16.9055555555556 & 0.0858370113822672 & 196.949489309084 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 16.9055555555556 & 0.0850436896116213 & 198.786713426476 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 16.9055555555556 & 0.0842147956309619 & 200.743294915035 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 16.8991666666667 & 0.0807870977589816 & 209.181504664065 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 16.9025 & 0.0776545735008732 & 217.662646744302 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 16.8857142857143 & 0.118405306563097 & 142.609438511238 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 16.8880882352941 & 0.11746728335227 & 143.768441333991 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 16.8893939393939 & 0.11654703399187 & 144.914832758182 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 16.890625 & 0.115543675819256 & 146.183898687989 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 16.891935483871 & 0.114542946785757 & 147.472506670061 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 16.8938333333333 & 0.113365339033419 & 149.021151238768 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 16.8962068965517 & 0.112013909879198 & 150.840256489337 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 16.8978571428571 & 0.110588072172656 & 152.799997421741 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 16.8990740740741 & 0.109241162674781 & 154.695113639388 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 16.9011538461538 & 0.107757077592162 & 156.844953703377 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 16.9034 & 0.106209884623969 & 159.150911987578 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 16.9070833333333 & 0.105072146074089 & 160.909279624038 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 16.9097826086957 & 0.104258360398989 & 162.191142695734 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 16.9113636363636 & 0.103933011698029 & 162.714072844329 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 16.912619047619 & 0.103526696789657 & 163.364809001698 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 16.9135 & 0.103133315515554 & 163.996473064509 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 16.9157894736842 & 0.10280257120157 & 164.546365679089 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 16.9186111111111 & 0.102272707943632 & 165.426451017957 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 16.9214705882353 & 0.101790680641247 & 166.237915707368 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 16.925 & 0.100840220150494 & 167.839776378326 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 16.9273333333333 & 0.10004014519852 & 169.205405487394 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 16.93 & 0.0986630200956343 & 171.594179699645 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 16.9330769230769 & 0.0964249715993165 & 175.608834954502 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 16.9375 & 0.0937508454068162 & 180.665037488489 \tabularnewline
Median & 16.935 &  &  \tabularnewline
Midrange & 16.765 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 16.8924324324324 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 16.9186111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 16.8924324324324 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 16.9186111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 16.9186111111111 &  &  \tabularnewline
Midmean - Closest Observation & 16.8924324324324 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 16.9186111111111 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 16.9157894736842 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=178315&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]16.8823611111111[/C][C]0.119573527031721[/C][C]141.188116886712[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]16.8521139547277[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]16.8217326341888[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]16.9123996671082[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]16.8834722222222[/C][C]0.119142436507425[/C][C]141.708300729355[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]16.8856944444444[/C][C]0.118722797953337[/C][C]142.227901763916[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]16.8861111111111[/C][C]0.118348963385454[/C][C]142.680684545705[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]16.8861111111111[/C][C]0.11756887162734[/C][C]143.627397944545[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]16.8840277777778[/C][C]0.117218957624998[/C][C]144.038371607027[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]16.8823611111111[/C][C]0.116657526981964[/C][C]144.717289555789[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]16.8872222222222[/C][C]0.11547551248492[/C][C]146.240721160925[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]16.8905555555556[/C][C]0.113428379243799[/C][C]148.90943226167[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]16.8855555555556[/C][C]0.112222512743856[/C][C]150.464957009974[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]16.8855555555556[/C][C]0.110430210240138[/C][C]152.907030773886[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]16.8763888888889[/C][C]0.106163408156662[/C][C]158.966155871569[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]16.8863888888889[/C][C]0.102535215820684[/C][C]164.688675531929[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]16.8972222222222[/C][C]0.0982101604275141[/C][C]172.051671116998[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]16.9011111111111[/C][C]0.0970718712239787[/C][C]174.109254287623[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]16.9052777777778[/C][C]0.0952697702142467[/C][C]177.446400256456[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]16.8941666666667[/C][C]0.0930942507079089[/C][C]181.473791756201[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]16.8918055555556[/C][C]0.0921095418460857[/C][C]183.388226854734[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]16.8943055555556[/C][C]0.0896657037814351[/C][C]188.414352902826[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]16.8916666666667[/C][C]0.089311836107302[/C][C]189.131333571202[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]16.9055555555556[/C][C]0.0858370113822672[/C][C]196.949489309084[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]16.9055555555556[/C][C]0.0850436896116213[/C][C]198.786713426476[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]16.9055555555556[/C][C]0.0842147956309619[/C][C]200.743294915035[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]16.8991666666667[/C][C]0.0807870977589816[/C][C]209.181504664065[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]16.9025[/C][C]0.0776545735008732[/C][C]217.662646744302[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]16.8857142857143[/C][C]0.118405306563097[/C][C]142.609438511238[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]16.8880882352941[/C][C]0.11746728335227[/C][C]143.768441333991[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]16.8893939393939[/C][C]0.11654703399187[/C][C]144.914832758182[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]16.890625[/C][C]0.115543675819256[/C][C]146.183898687989[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]16.891935483871[/C][C]0.114542946785757[/C][C]147.472506670061[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]16.8938333333333[/C][C]0.113365339033419[/C][C]149.021151238768[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]16.8962068965517[/C][C]0.112013909879198[/C][C]150.840256489337[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]16.8978571428571[/C][C]0.110588072172656[/C][C]152.799997421741[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]16.8990740740741[/C][C]0.109241162674781[/C][C]154.695113639388[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]16.9011538461538[/C][C]0.107757077592162[/C][C]156.844953703377[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]16.9034[/C][C]0.106209884623969[/C][C]159.150911987578[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]16.9070833333333[/C][C]0.105072146074089[/C][C]160.909279624038[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]16.9097826086957[/C][C]0.104258360398989[/C][C]162.191142695734[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]16.9113636363636[/C][C]0.103933011698029[/C][C]162.714072844329[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]16.912619047619[/C][C]0.103526696789657[/C][C]163.364809001698[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]16.9135[/C][C]0.103133315515554[/C][C]163.996473064509[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]16.9157894736842[/C][C]0.10280257120157[/C][C]164.546365679089[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]16.9186111111111[/C][C]0.102272707943632[/C][C]165.426451017957[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]16.9214705882353[/C][C]0.101790680641247[/C][C]166.237915707368[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]16.925[/C][C]0.100840220150494[/C][C]167.839776378326[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]16.9273333333333[/C][C]0.10004014519852[/C][C]169.205405487394[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]16.93[/C][C]0.0986630200956343[/C][C]171.594179699645[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]16.9330769230769[/C][C]0.0964249715993165[/C][C]175.608834954502[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]16.9375[/C][C]0.0937508454068162[/C][C]180.665037488489[/C][/ROW]
[ROW][C]Median[/C][C]16.935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]16.765[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]16.8924324324324[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]16.9186111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]16.8924324324324[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]16.9186111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]16.9186111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]16.8924324324324[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]16.9186111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]16.9157894736842[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=178315&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=178315&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 Mean16.88236111111110.119573527031721141.188116886712
Geometric Mean16.8521139547277
Harmonic Mean16.8217326341888
Quadratic Mean16.9123996671082
Winsorized Mean ( 1 / 24 )16.88347222222220.119142436507425141.708300729355
Winsorized Mean ( 2 / 24 )16.88569444444440.118722797953337142.227901763916
Winsorized Mean ( 3 / 24 )16.88611111111110.118348963385454142.680684545705
Winsorized Mean ( 4 / 24 )16.88611111111110.11756887162734143.627397944545
Winsorized Mean ( 5 / 24 )16.88402777777780.117218957624998144.038371607027
Winsorized Mean ( 6 / 24 )16.88236111111110.116657526981964144.717289555789
Winsorized Mean ( 7 / 24 )16.88722222222220.11547551248492146.240721160925
Winsorized Mean ( 8 / 24 )16.89055555555560.113428379243799148.90943226167
Winsorized Mean ( 9 / 24 )16.88555555555560.112222512743856150.464957009974
Winsorized Mean ( 10 / 24 )16.88555555555560.110430210240138152.907030773886
Winsorized Mean ( 11 / 24 )16.87638888888890.106163408156662158.966155871569
Winsorized Mean ( 12 / 24 )16.88638888888890.102535215820684164.688675531929
Winsorized Mean ( 13 / 24 )16.89722222222220.0982101604275141172.051671116998
Winsorized Mean ( 14 / 24 )16.90111111111110.0970718712239787174.109254287623
Winsorized Mean ( 15 / 24 )16.90527777777780.0952697702142467177.446400256456
Winsorized Mean ( 16 / 24 )16.89416666666670.0930942507079089181.473791756201
Winsorized Mean ( 17 / 24 )16.89180555555560.0921095418460857183.388226854734
Winsorized Mean ( 18 / 24 )16.89430555555560.0896657037814351188.414352902826
Winsorized Mean ( 19 / 24 )16.89166666666670.089311836107302189.131333571202
Winsorized Mean ( 20 / 24 )16.90555555555560.0858370113822672196.949489309084
Winsorized Mean ( 21 / 24 )16.90555555555560.0850436896116213198.786713426476
Winsorized Mean ( 22 / 24 )16.90555555555560.0842147956309619200.743294915035
Winsorized Mean ( 23 / 24 )16.89916666666670.0807870977589816209.181504664065
Winsorized Mean ( 24 / 24 )16.90250.0776545735008732217.662646744302
Trimmed Mean ( 1 / 24 )16.88571428571430.118405306563097142.609438511238
Trimmed Mean ( 2 / 24 )16.88808823529410.11746728335227143.768441333991
Trimmed Mean ( 3 / 24 )16.88939393939390.11654703399187144.914832758182
Trimmed Mean ( 4 / 24 )16.8906250.115543675819256146.183898687989
Trimmed Mean ( 5 / 24 )16.8919354838710.114542946785757147.472506670061
Trimmed Mean ( 6 / 24 )16.89383333333330.113365339033419149.021151238768
Trimmed Mean ( 7 / 24 )16.89620689655170.112013909879198150.840256489337
Trimmed Mean ( 8 / 24 )16.89785714285710.110588072172656152.799997421741
Trimmed Mean ( 9 / 24 )16.89907407407410.109241162674781154.695113639388
Trimmed Mean ( 10 / 24 )16.90115384615380.107757077592162156.844953703377
Trimmed Mean ( 11 / 24 )16.90340.106209884623969159.150911987578
Trimmed Mean ( 12 / 24 )16.90708333333330.105072146074089160.909279624038
Trimmed Mean ( 13 / 24 )16.90978260869570.104258360398989162.191142695734
Trimmed Mean ( 14 / 24 )16.91136363636360.103933011698029162.714072844329
Trimmed Mean ( 15 / 24 )16.9126190476190.103526696789657163.364809001698
Trimmed Mean ( 16 / 24 )16.91350.103133315515554163.996473064509
Trimmed Mean ( 17 / 24 )16.91578947368420.10280257120157164.546365679089
Trimmed Mean ( 18 / 24 )16.91861111111110.102272707943632165.426451017957
Trimmed Mean ( 19 / 24 )16.92147058823530.101790680641247166.237915707368
Trimmed Mean ( 20 / 24 )16.9250.100840220150494167.839776378326
Trimmed Mean ( 21 / 24 )16.92733333333330.10004014519852169.205405487394
Trimmed Mean ( 22 / 24 )16.930.0986630200956343171.594179699645
Trimmed Mean ( 23 / 24 )16.93307692307690.0964249715993165175.608834954502
Trimmed Mean ( 24 / 24 )16.93750.0937508454068162180.665037488489
Median16.935
Midrange16.765
Midmean - Weighted Average at Xnp16.8924324324324
Midmean - Weighted Average at X(n+1)p16.9186111111111
Midmean - Empirical Distribution Function16.8924324324324
Midmean - Empirical Distribution Function - Averaging16.9186111111111
Midmean - Empirical Distribution Function - Interpolation16.9186111111111
Midmean - Closest Observation16.8924324324324
Midmean - True Basic - Statistics Graphics Toolkit16.9186111111111
Midmean - MS Excel (old versions)16.9157894736842
Number of observations72



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')