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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 computationSun, 20 Dec 2009 03:50:56 -0700
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/Dec/20/t12613063068gwxd7vr6ch5l66.htm/, Retrieved Sat, 27 Apr 2024 08:32:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69827, Retrieved Sat, 27 Apr 2024 08:32:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper central ten...] [2009-12-20 10:50:56] [ba02bcb7e07025bbb7f8a074d38ad767] [Current]
-    D    [Central Tendency] [Paper central ten...] [2009-12-20 10:53:40] [62d3ced7fb1c10c35a82e9cb1d0d0e2b]
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Dataseries X:
13.4
13.5
14.8
14.3
14.3
14
13.2
12.2
14.3
15.7
14.2
14.6
14.5
14.3
15.3
14.4
13.7
14.2
13.5
11.9
14.6
15.6
14.1
14.9
14.2
14.6
17.2
15.4
14.3
17.5
14.5
14.4
16.6
16.7
16.6
16.9
15.7
16.4
18.4
16.9
16.5
18.3
15.1
15.7
18.1
16.8
18.9
19
18.1
17.8
21.5
17.1
18.7
19
16.4
16.9
18.6
19.3
19.4
17.6
18.6
18.1
20.4
18.1
19.6
19.9
19.2
17.8
19.2
22
21.1
19.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69827&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69827&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69827&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean16.50138888888890.27522570802561059.9558413611326
Geometric Mean16.3396792170603
Harmonic Mean16.1797717283663
Quadratic Mean16.6635538759827
Winsorized Mean ( 1 / 24 )16.49861111111110.27239657593947660.5683498561192
Winsorized Mean ( 2 / 24 )16.51527777777780.26404713770842562.5467025361769
Winsorized Mean ( 3 / 24 )16.49444444444440.25589213733577264.4585824956437
Winsorized Mean ( 4 / 24 )16.47222222222220.24927298218771566.0810573117701
Winsorized Mean ( 5 / 24 )16.45138888888890.24537181597196267.0467748046855
Winsorized Mean ( 6 / 24 )16.45972222222220.24112298988861668.262765942914
Winsorized Mean ( 7 / 24 )16.47916666666670.23488699293973170.157851060297
Winsorized Mean ( 8 / 24 )16.47916666666670.23132889467538971.2369576217056
Winsorized Mean ( 9 / 24 )16.47916666666670.22741434181653972.4631812357763
Winsorized Mean ( 10 / 24 )16.47916666666670.22741434181653972.4631812357763
Winsorized Mean ( 11 / 24 )16.44861111111110.22236980379162073.9696255096077
Winsorized Mean ( 12 / 24 )16.46527777777780.22002773799228774.8327366722962
Winsorized Mean ( 13 / 24 )16.44722222222220.21712638320601375.7495334255019
Winsorized Mean ( 14 / 24 )16.40833333333330.21105730926321277.74349720753
Winsorized Mean ( 15 / 24 )16.38750.20790272399552078.8229210520258
Winsorized Mean ( 16 / 24 )16.38750.20790272399552078.8229210520258
Winsorized Mean ( 17 / 24 )16.36388888888890.19761197134515582.808186050162
Winsorized Mean ( 18 / 24 )16.33888888888890.19401808834606184.2132247986382
Winsorized Mean ( 19 / 24 )16.31250.18292675253188789.175037408246
Winsorized Mean ( 20 / 24 )16.31250.18292675253188789.175037408246
Winsorized Mean ( 21 / 24 )16.34166666666670.17889145256184691.3496225372595
Winsorized Mean ( 22 / 24 )16.34166666666670.17889145256184691.3496225372595
Winsorized Mean ( 23 / 24 )16.24583333333330.16592484558331497.9107937465337
Winsorized Mean ( 24 / 24 )16.31250.156733797174824104.077743881907
Trimmed Mean ( 1 / 24 )16.48857142857140.26367794253496762.5329948726554
Trimmed Mean ( 2 / 24 )16.47794117647060.25329128994163165.0553012709904
Trimmed Mean ( 3 / 24 )16.45757575757580.24625929259439966.8302730191067
Trimmed Mean ( 4 / 24 )16.443750.24155246685975268.0752724812676
Trimmed Mean ( 5 / 24 )16.43548387096770.2382300410972468.9899720256487
Trimmed Mean ( 6 / 24 )16.43166666666670.23530832840381169.8303658783738
Trimmed Mean ( 7 / 24 )16.42586206896550.23277385623771770.5657513882953
Trimmed Mean ( 8 / 24 )16.41607142857140.23103067747208371.0558078615126
Trimmed Mean ( 9 / 24 )16.40555555555560.22947417586975271.4919467228733
Trimmed Mean ( 10 / 24 )16.39423076923080.22813780634586271.8610870851311
Trimmed Mean ( 11 / 24 )16.3820.22617836559057672.429562205142
Trimmed Mean ( 12 / 24 )16.37291666666670.22451167622207872.9267935734051
Trimmed Mean ( 13 / 24 )16.36086956521740.222534332386173.5206535988841
Trimmed Mean ( 14 / 24 )16.350.22028474749482474.2221156296088
Trimmed Mean ( 15 / 24 )16.34285714285710.21832811185632174.8545709661619
Trimmed Mean ( 16 / 24 )16.33750.2160450896670275.6207883510808
Trimmed Mean ( 17 / 24 )16.33157894736840.21258770303481876.8227828525603
Trimmed Mean ( 18 / 24 )16.32777777777780.20993616229668277.7749654902395
Trimmed Mean ( 19 / 24 )16.32647058823530.20667595963507078.9954991236676
Trimmed Mean ( 20 / 24 )16.3281250.20439892086507379.8836164637994
Trimmed Mean ( 21 / 24 )16.330.20046784361048881.4594485873227
Trimmed Mean ( 22 / 24 )16.32857142857140.19530583416440683.6051390806186
Trimmed Mean ( 23 / 24 )16.32692307692310.18692307692307787.3456790123457
Trimmed Mean ( 24 / 24 )16.33750.17833900505676791.6092359873802
Median16.55
Midrange16.95
Midmean - Weighted Average at Xnp16.2756756756757
Midmean - Weighted Average at X(n+1)p16.2756756756757
Midmean - Empirical Distribution Function16.2756756756757
Midmean - Empirical Distribution Function - Averaging16.2756756756757
Midmean - Empirical Distribution Function - Interpolation16.2756756756757
Midmean - Closest Observation16.2756756756757
Midmean - True Basic - Statistics Graphics Toolkit16.2756756756757
Midmean - MS Excel (old versions)16.3315789473684
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 16.5013888888889 & 0.275225708025610 & 59.9558413611326 \tabularnewline
Geometric Mean & 16.3396792170603 &  &  \tabularnewline
Harmonic Mean & 16.1797717283663 &  &  \tabularnewline
Quadratic Mean & 16.6635538759827 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 16.4986111111111 & 0.272396575939476 & 60.5683498561192 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 16.5152777777778 & 0.264047137708425 & 62.5467025361769 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 16.4944444444444 & 0.255892137335772 & 64.4585824956437 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 16.4722222222222 & 0.249272982187715 & 66.0810573117701 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 16.4513888888889 & 0.245371815971962 & 67.0467748046855 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 16.4597222222222 & 0.241122989888616 & 68.262765942914 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 16.4791666666667 & 0.234886992939731 & 70.157851060297 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 16.4791666666667 & 0.231328894675389 & 71.2369576217056 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 16.4791666666667 & 0.227414341816539 & 72.4631812357763 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 16.4791666666667 & 0.227414341816539 & 72.4631812357763 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 16.4486111111111 & 0.222369803791620 & 73.9696255096077 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 16.4652777777778 & 0.220027737992287 & 74.8327366722962 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 16.4472222222222 & 0.217126383206013 & 75.7495334255019 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 16.4083333333333 & 0.211057309263212 & 77.74349720753 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 16.3875 & 0.207902723995520 & 78.8229210520258 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 16.3875 & 0.207902723995520 & 78.8229210520258 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 16.3638888888889 & 0.197611971345155 & 82.808186050162 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 16.3388888888889 & 0.194018088346061 & 84.2132247986382 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 16.3125 & 0.182926752531887 & 89.175037408246 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 16.3125 & 0.182926752531887 & 89.175037408246 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 16.3416666666667 & 0.178891452561846 & 91.3496225372595 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 16.3416666666667 & 0.178891452561846 & 91.3496225372595 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 16.2458333333333 & 0.165924845583314 & 97.9107937465337 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 16.3125 & 0.156733797174824 & 104.077743881907 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 16.4885714285714 & 0.263677942534967 & 62.5329948726554 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 16.4779411764706 & 0.253291289941631 & 65.0553012709904 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 16.4575757575758 & 0.246259292594399 & 66.8302730191067 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 16.44375 & 0.241552466859752 & 68.0752724812676 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 16.4354838709677 & 0.23823004109724 & 68.9899720256487 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 16.4316666666667 & 0.235308328403811 & 69.8303658783738 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 16.4258620689655 & 0.232773856237717 & 70.5657513882953 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 16.4160714285714 & 0.231030677472083 & 71.0558078615126 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 16.4055555555556 & 0.229474175869752 & 71.4919467228733 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 16.3942307692308 & 0.228137806345862 & 71.8610870851311 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 16.382 & 0.226178365590576 & 72.429562205142 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 16.3729166666667 & 0.224511676222078 & 72.9267935734051 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 16.3608695652174 & 0.2225343323861 & 73.5206535988841 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 16.35 & 0.220284747494824 & 74.2221156296088 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 16.3428571428571 & 0.218328111856321 & 74.8545709661619 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 16.3375 & 0.21604508966702 & 75.6207883510808 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 16.3315789473684 & 0.212587703034818 & 76.8227828525603 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 16.3277777777778 & 0.209936162296682 & 77.7749654902395 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 16.3264705882353 & 0.206675959635070 & 78.9954991236676 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 16.328125 & 0.204398920865073 & 79.8836164637994 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 16.33 & 0.200467843610488 & 81.4594485873227 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 16.3285714285714 & 0.195305834164406 & 83.6051390806186 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 16.3269230769231 & 0.186923076923077 & 87.3456790123457 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 16.3375 & 0.178339005056767 & 91.6092359873802 \tabularnewline
Median & 16.55 &  &  \tabularnewline
Midrange & 16.95 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 16.2756756756757 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 16.2756756756757 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 16.2756756756757 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 16.2756756756757 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 16.2756756756757 &  &  \tabularnewline
Midmean - Closest Observation & 16.2756756756757 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 16.2756756756757 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 16.3315789473684 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69827&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]16.5013888888889[/C][C]0.275225708025610[/C][C]59.9558413611326[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]16.3396792170603[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]16.1797717283663[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]16.6635538759827[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]16.4986111111111[/C][C]0.272396575939476[/C][C]60.5683498561192[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]16.5152777777778[/C][C]0.264047137708425[/C][C]62.5467025361769[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]16.4944444444444[/C][C]0.255892137335772[/C][C]64.4585824956437[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]16.4722222222222[/C][C]0.249272982187715[/C][C]66.0810573117701[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]16.4513888888889[/C][C]0.245371815971962[/C][C]67.0467748046855[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]16.4597222222222[/C][C]0.241122989888616[/C][C]68.262765942914[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]16.4791666666667[/C][C]0.234886992939731[/C][C]70.157851060297[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]16.4791666666667[/C][C]0.231328894675389[/C][C]71.2369576217056[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]16.4791666666667[/C][C]0.227414341816539[/C][C]72.4631812357763[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]16.4791666666667[/C][C]0.227414341816539[/C][C]72.4631812357763[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]16.4486111111111[/C][C]0.222369803791620[/C][C]73.9696255096077[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]16.4652777777778[/C][C]0.220027737992287[/C][C]74.8327366722962[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]16.4472222222222[/C][C]0.217126383206013[/C][C]75.7495334255019[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]16.4083333333333[/C][C]0.211057309263212[/C][C]77.74349720753[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]16.3875[/C][C]0.207902723995520[/C][C]78.8229210520258[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]16.3875[/C][C]0.207902723995520[/C][C]78.8229210520258[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]16.3638888888889[/C][C]0.197611971345155[/C][C]82.808186050162[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]16.3388888888889[/C][C]0.194018088346061[/C][C]84.2132247986382[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]16.3125[/C][C]0.182926752531887[/C][C]89.175037408246[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]16.3125[/C][C]0.182926752531887[/C][C]89.175037408246[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]16.3416666666667[/C][C]0.178891452561846[/C][C]91.3496225372595[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]16.3416666666667[/C][C]0.178891452561846[/C][C]91.3496225372595[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]16.2458333333333[/C][C]0.165924845583314[/C][C]97.9107937465337[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]16.3125[/C][C]0.156733797174824[/C][C]104.077743881907[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]16.4885714285714[/C][C]0.263677942534967[/C][C]62.5329948726554[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]16.4779411764706[/C][C]0.253291289941631[/C][C]65.0553012709904[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]16.4575757575758[/C][C]0.246259292594399[/C][C]66.8302730191067[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]16.44375[/C][C]0.241552466859752[/C][C]68.0752724812676[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]16.4354838709677[/C][C]0.23823004109724[/C][C]68.9899720256487[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]16.4316666666667[/C][C]0.235308328403811[/C][C]69.8303658783738[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]16.4258620689655[/C][C]0.232773856237717[/C][C]70.5657513882953[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]16.4160714285714[/C][C]0.231030677472083[/C][C]71.0558078615126[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]16.4055555555556[/C][C]0.229474175869752[/C][C]71.4919467228733[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]16.3942307692308[/C][C]0.228137806345862[/C][C]71.8610870851311[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]16.382[/C][C]0.226178365590576[/C][C]72.429562205142[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]16.3729166666667[/C][C]0.224511676222078[/C][C]72.9267935734051[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]16.3608695652174[/C][C]0.2225343323861[/C][C]73.5206535988841[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]16.35[/C][C]0.220284747494824[/C][C]74.2221156296088[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]16.3428571428571[/C][C]0.218328111856321[/C][C]74.8545709661619[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]16.3375[/C][C]0.21604508966702[/C][C]75.6207883510808[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]16.3315789473684[/C][C]0.212587703034818[/C][C]76.8227828525603[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]16.3277777777778[/C][C]0.209936162296682[/C][C]77.7749654902395[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]16.3264705882353[/C][C]0.206675959635070[/C][C]78.9954991236676[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]16.328125[/C][C]0.204398920865073[/C][C]79.8836164637994[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]16.33[/C][C]0.200467843610488[/C][C]81.4594485873227[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]16.3285714285714[/C][C]0.195305834164406[/C][C]83.6051390806186[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]16.3269230769231[/C][C]0.186923076923077[/C][C]87.3456790123457[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]16.3375[/C][C]0.178339005056767[/C][C]91.6092359873802[/C][/ROW]
[ROW][C]Median[/C][C]16.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]16.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]16.2756756756757[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]16.2756756756757[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]16.2756756756757[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]16.2756756756757[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]16.2756756756757[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]16.2756756756757[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]16.2756756756757[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]16.3315789473684[/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=69827&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69827&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 Mean16.50138888888890.27522570802561059.9558413611326
Geometric Mean16.3396792170603
Harmonic Mean16.1797717283663
Quadratic Mean16.6635538759827
Winsorized Mean ( 1 / 24 )16.49861111111110.27239657593947660.5683498561192
Winsorized Mean ( 2 / 24 )16.51527777777780.26404713770842562.5467025361769
Winsorized Mean ( 3 / 24 )16.49444444444440.25589213733577264.4585824956437
Winsorized Mean ( 4 / 24 )16.47222222222220.24927298218771566.0810573117701
Winsorized Mean ( 5 / 24 )16.45138888888890.24537181597196267.0467748046855
Winsorized Mean ( 6 / 24 )16.45972222222220.24112298988861668.262765942914
Winsorized Mean ( 7 / 24 )16.47916666666670.23488699293973170.157851060297
Winsorized Mean ( 8 / 24 )16.47916666666670.23132889467538971.2369576217056
Winsorized Mean ( 9 / 24 )16.47916666666670.22741434181653972.4631812357763
Winsorized Mean ( 10 / 24 )16.47916666666670.22741434181653972.4631812357763
Winsorized Mean ( 11 / 24 )16.44861111111110.22236980379162073.9696255096077
Winsorized Mean ( 12 / 24 )16.46527777777780.22002773799228774.8327366722962
Winsorized Mean ( 13 / 24 )16.44722222222220.21712638320601375.7495334255019
Winsorized Mean ( 14 / 24 )16.40833333333330.21105730926321277.74349720753
Winsorized Mean ( 15 / 24 )16.38750.20790272399552078.8229210520258
Winsorized Mean ( 16 / 24 )16.38750.20790272399552078.8229210520258
Winsorized Mean ( 17 / 24 )16.36388888888890.19761197134515582.808186050162
Winsorized Mean ( 18 / 24 )16.33888888888890.19401808834606184.2132247986382
Winsorized Mean ( 19 / 24 )16.31250.18292675253188789.175037408246
Winsorized Mean ( 20 / 24 )16.31250.18292675253188789.175037408246
Winsorized Mean ( 21 / 24 )16.34166666666670.17889145256184691.3496225372595
Winsorized Mean ( 22 / 24 )16.34166666666670.17889145256184691.3496225372595
Winsorized Mean ( 23 / 24 )16.24583333333330.16592484558331497.9107937465337
Winsorized Mean ( 24 / 24 )16.31250.156733797174824104.077743881907
Trimmed Mean ( 1 / 24 )16.48857142857140.26367794253496762.5329948726554
Trimmed Mean ( 2 / 24 )16.47794117647060.25329128994163165.0553012709904
Trimmed Mean ( 3 / 24 )16.45757575757580.24625929259439966.8302730191067
Trimmed Mean ( 4 / 24 )16.443750.24155246685975268.0752724812676
Trimmed Mean ( 5 / 24 )16.43548387096770.2382300410972468.9899720256487
Trimmed Mean ( 6 / 24 )16.43166666666670.23530832840381169.8303658783738
Trimmed Mean ( 7 / 24 )16.42586206896550.23277385623771770.5657513882953
Trimmed Mean ( 8 / 24 )16.41607142857140.23103067747208371.0558078615126
Trimmed Mean ( 9 / 24 )16.40555555555560.22947417586975271.4919467228733
Trimmed Mean ( 10 / 24 )16.39423076923080.22813780634586271.8610870851311
Trimmed Mean ( 11 / 24 )16.3820.22617836559057672.429562205142
Trimmed Mean ( 12 / 24 )16.37291666666670.22451167622207872.9267935734051
Trimmed Mean ( 13 / 24 )16.36086956521740.222534332386173.5206535988841
Trimmed Mean ( 14 / 24 )16.350.22028474749482474.2221156296088
Trimmed Mean ( 15 / 24 )16.34285714285710.21832811185632174.8545709661619
Trimmed Mean ( 16 / 24 )16.33750.2160450896670275.6207883510808
Trimmed Mean ( 17 / 24 )16.33157894736840.21258770303481876.8227828525603
Trimmed Mean ( 18 / 24 )16.32777777777780.20993616229668277.7749654902395
Trimmed Mean ( 19 / 24 )16.32647058823530.20667595963507078.9954991236676
Trimmed Mean ( 20 / 24 )16.3281250.20439892086507379.8836164637994
Trimmed Mean ( 21 / 24 )16.330.20046784361048881.4594485873227
Trimmed Mean ( 22 / 24 )16.32857142857140.19530583416440683.6051390806186
Trimmed Mean ( 23 / 24 )16.32692307692310.18692307692307787.3456790123457
Trimmed Mean ( 24 / 24 )16.33750.17833900505676791.6092359873802
Median16.55
Midrange16.95
Midmean - Weighted Average at Xnp16.2756756756757
Midmean - Weighted Average at X(n+1)p16.2756756756757
Midmean - Empirical Distribution Function16.2756756756757
Midmean - Empirical Distribution Function - Averaging16.2756756756757
Midmean - Empirical Distribution Function - Interpolation16.2756756756757
Midmean - Closest Observation16.2756756756757
Midmean - True Basic - Statistics Graphics Toolkit16.2756756756757
Midmean - MS Excel (old versions)16.3315789473684
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')