Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 08 Oct 2014 18:15:40 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/08/t1412788552z1s4znfo09nmdb5.htm/, Retrieved Sun, 12 May 2024 09:32:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=239791, Retrieved Sun, 12 May 2024 09:32:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact54
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-08 17:15:40] [823d84bc2f1aa2ddbab319cc794dd4cf] [Current]
Feedback Forum

Post a new message
Dataseries X:
104.31
104.76
105.68
106.22
106.69
107.17
107.46
107.16
107.35
107.65
107.75
108.22
108.68
109.35
109.54
109.46
108.86
108.63
107.55
106.8
106.07
106.44
106.38
107.07
106.54
107.83
108.06
108.49
107.9
108.02
108.46
108.31
107.69
107.71
107.74
108.15
107.39
109.16
109.65
110.4
110.26
110.5
110.31
109.85
109.4
109.75
109.79
110.27
109.19
111.78
111.58
111.71
111.59
112.14
111.73
111.32
111.29
112.45
112.61
114.3
113.32
114.85
115.35
114.9
115.49
115.55
115.44
114.81
113.83
113.64
113.26
114.68




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=239791&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=239791&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=239791&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 Mean109.7734722222220.341096865973015321.824921812406
Geometric Mean109.736144479014
Harmonic Mean109.699117492877
Quadratic Mean109.811091633921
Winsorized Mean ( 1 / 24 )109.7788888888890.339543071610509323.313588370952
Winsorized Mean ( 2 / 24 )109.8030555555560.334330646482171328.426534363223
Winsorized Mean ( 3 / 24 )109.8155555555560.330735587012918332.034289225931
Winsorized Mean ( 4 / 24 )109.7988888888890.323699610767114339.199941046219
Winsorized Mean ( 5 / 24 )109.8065277777780.321230466345728341.830988283649
Winsorized Mean ( 6 / 24 )109.8081944444440.319748184761708343.420853276396
Winsorized Mean ( 7 / 24 )109.8052777777780.315550973304802347.97952491724
Winsorized Mean ( 8 / 24 )109.7797222222220.304127640574534360.965948424928
Winsorized Mean ( 9 / 24 )109.7347222222220.290168652878883378.175661407595
Winsorized Mean ( 10 / 24 )109.7458333333330.279758919101611392.287165269869
Winsorized Mean ( 11 / 24 )109.7106944444440.268488664573125408.623189432878
Winsorized Mean ( 12 / 24 )109.7023611111110.266378328053017411.829152592613
Winsorized Mean ( 13 / 24 )109.61750.240692934691988455.424668531613
Winsorized Mean ( 14 / 24 )109.5941666666670.234266055796137467.81923353863
Winsorized Mean ( 15 / 24 )109.5441666666670.221451566185214494.664221859907
Winsorized Mean ( 16 / 24 )109.4841666666670.205905643910149531.720085897412
Winsorized Mean ( 17 / 24 )109.4959722222220.200964775886701544.851562862706
Winsorized Mean ( 18 / 24 )109.5009722222220.198894161083416550.548953401892
Winsorized Mean ( 19 / 24 )109.4745833333330.1932986185342566.349538157533
Winsorized Mean ( 20 / 24 )109.4801388888890.191802206928826570.797076018602
Winsorized Mean ( 21 / 24 )109.4072222222220.179896425406701608.167849777336
Winsorized Mean ( 22 / 24 )109.42250.175373372095261623.940217905846
Winsorized Mean ( 23 / 24 )109.19250.136242578870702801.45649697094
Winsorized Mean ( 24 / 24 )109.1991666666670.126459205877523863.512987519682
Trimmed Mean ( 1 / 24 )109.7690.331739573954535330.889072688819
Trimmed Mean ( 2 / 24 )109.7585294117650.322454798045437340.384233936252
Trimmed Mean ( 3 / 24 )109.7342424242420.314663846284874348.734828356789
Trimmed Mean ( 4 / 24 )109.703750.30689186057519357.467121462227
Trimmed Mean ( 5 / 24 )109.6761290322580.30007907955082365.490753958687
Trimmed Mean ( 6 / 24 )109.6448333333330.292499117934511374.855261470847
Trimmed Mean ( 7 / 24 )109.6110344827590.283574932365135386.532877107847
Trimmed Mean ( 8 / 24 )109.5753571428570.273656216727517400.412453454192
Trimmed Mean ( 9 / 24 )109.5412962962960.264313523027799414.436972582653
Trimmed Mean ( 10 / 24 )109.5115384615380.256139011885945427.547282451071
Trimmed Mean ( 11 / 24 )109.47780.248200098669585441.086851241512
Trimmed Mean ( 12 / 24 )109.4460416666670.240737036795436454.629013979545
Trimmed Mean ( 13 / 24 )109.4126086956520.231532269384714472.558788398745
Trimmed Mean ( 14 / 24 )109.3868181818180.225794292789167484.453423647679
Trimmed Mean ( 15 / 24 )109.3614285714290.219627118120171497.941372210651
Trimmed Mean ( 16 / 24 )109.33950.214397471162851509.985026441605
Trimmed Mean ( 17 / 24 )109.3223684210530.210901146580119518.358340833022
Trimmed Mean ( 18 / 24 )109.3019444444440.206884224752636528.324209229258
Trimmed Mean ( 19 / 24 )109.2785294117650.201406875440432542.575963073738
Trimmed Mean ( 20 / 24 )109.25531250.19492863891474560.488767111266
Trimmed Mean ( 21 / 24 )109.2283333333330.18560561533651588.496922010136
Trimmed Mean ( 22 / 24 )109.2064285714290.17592177064751620.766993018975
Trimmed Mean ( 23 / 24 )109.1792307692310.162395455674316672.304716384366
Trimmed Mean ( 24 / 24 )109.17750.157890589984955691.475660521652
Median109.27
Midrange109.93
Midmean - Weighted Average at Xnp109.257297297297
Midmean - Weighted Average at X(n+1)p109.301944444444
Midmean - Empirical Distribution Function109.257297297297
Midmean - Empirical Distribution Function - Averaging109.301944444444
Midmean - Empirical Distribution Function - Interpolation109.301944444444
Midmean - Closest Observation109.257297297297
Midmean - True Basic - Statistics Graphics Toolkit109.301944444444
Midmean - MS Excel (old versions)109.322368421053
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 109.773472222222 & 0.341096865973015 & 321.824921812406 \tabularnewline
Geometric Mean & 109.736144479014 &  &  \tabularnewline
Harmonic Mean & 109.699117492877 &  &  \tabularnewline
Quadratic Mean & 109.811091633921 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 109.778888888889 & 0.339543071610509 & 323.313588370952 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 109.803055555556 & 0.334330646482171 & 328.426534363223 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 109.815555555556 & 0.330735587012918 & 332.034289225931 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 109.798888888889 & 0.323699610767114 & 339.199941046219 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 109.806527777778 & 0.321230466345728 & 341.830988283649 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 109.808194444444 & 0.319748184761708 & 343.420853276396 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 109.805277777778 & 0.315550973304802 & 347.97952491724 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 109.779722222222 & 0.304127640574534 & 360.965948424928 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 109.734722222222 & 0.290168652878883 & 378.175661407595 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 109.745833333333 & 0.279758919101611 & 392.287165269869 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 109.710694444444 & 0.268488664573125 & 408.623189432878 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 109.702361111111 & 0.266378328053017 & 411.829152592613 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 109.6175 & 0.240692934691988 & 455.424668531613 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 109.594166666667 & 0.234266055796137 & 467.81923353863 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 109.544166666667 & 0.221451566185214 & 494.664221859907 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 109.484166666667 & 0.205905643910149 & 531.720085897412 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 109.495972222222 & 0.200964775886701 & 544.851562862706 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 109.500972222222 & 0.198894161083416 & 550.548953401892 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 109.474583333333 & 0.1932986185342 & 566.349538157533 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 109.480138888889 & 0.191802206928826 & 570.797076018602 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 109.407222222222 & 0.179896425406701 & 608.167849777336 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 109.4225 & 0.175373372095261 & 623.940217905846 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 109.1925 & 0.136242578870702 & 801.45649697094 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 109.199166666667 & 0.126459205877523 & 863.512987519682 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 109.769 & 0.331739573954535 & 330.889072688819 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 109.758529411765 & 0.322454798045437 & 340.384233936252 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 109.734242424242 & 0.314663846284874 & 348.734828356789 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 109.70375 & 0.30689186057519 & 357.467121462227 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 109.676129032258 & 0.30007907955082 & 365.490753958687 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 109.644833333333 & 0.292499117934511 & 374.855261470847 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 109.611034482759 & 0.283574932365135 & 386.532877107847 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 109.575357142857 & 0.273656216727517 & 400.412453454192 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 109.541296296296 & 0.264313523027799 & 414.436972582653 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 109.511538461538 & 0.256139011885945 & 427.547282451071 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 109.4778 & 0.248200098669585 & 441.086851241512 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 109.446041666667 & 0.240737036795436 & 454.629013979545 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 109.412608695652 & 0.231532269384714 & 472.558788398745 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 109.386818181818 & 0.225794292789167 & 484.453423647679 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 109.361428571429 & 0.219627118120171 & 497.941372210651 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 109.3395 & 0.214397471162851 & 509.985026441605 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 109.322368421053 & 0.210901146580119 & 518.358340833022 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 109.301944444444 & 0.206884224752636 & 528.324209229258 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 109.278529411765 & 0.201406875440432 & 542.575963073738 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 109.2553125 & 0.19492863891474 & 560.488767111266 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 109.228333333333 & 0.18560561533651 & 588.496922010136 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 109.206428571429 & 0.17592177064751 & 620.766993018975 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 109.179230769231 & 0.162395455674316 & 672.304716384366 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 109.1775 & 0.157890589984955 & 691.475660521652 \tabularnewline
Median & 109.27 &  &  \tabularnewline
Midrange & 109.93 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 109.257297297297 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 109.301944444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 109.257297297297 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 109.301944444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 109.301944444444 &  &  \tabularnewline
Midmean - Closest Observation & 109.257297297297 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 109.301944444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 109.322368421053 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=239791&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]109.773472222222[/C][C]0.341096865973015[/C][C]321.824921812406[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]109.736144479014[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]109.699117492877[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]109.811091633921[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]109.778888888889[/C][C]0.339543071610509[/C][C]323.313588370952[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]109.803055555556[/C][C]0.334330646482171[/C][C]328.426534363223[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]109.815555555556[/C][C]0.330735587012918[/C][C]332.034289225931[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]109.798888888889[/C][C]0.323699610767114[/C][C]339.199941046219[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]109.806527777778[/C][C]0.321230466345728[/C][C]341.830988283649[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]109.808194444444[/C][C]0.319748184761708[/C][C]343.420853276396[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]109.805277777778[/C][C]0.315550973304802[/C][C]347.97952491724[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]109.779722222222[/C][C]0.304127640574534[/C][C]360.965948424928[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]109.734722222222[/C][C]0.290168652878883[/C][C]378.175661407595[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]109.745833333333[/C][C]0.279758919101611[/C][C]392.287165269869[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]109.710694444444[/C][C]0.268488664573125[/C][C]408.623189432878[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]109.702361111111[/C][C]0.266378328053017[/C][C]411.829152592613[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]109.6175[/C][C]0.240692934691988[/C][C]455.424668531613[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]109.594166666667[/C][C]0.234266055796137[/C][C]467.81923353863[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]109.544166666667[/C][C]0.221451566185214[/C][C]494.664221859907[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]109.484166666667[/C][C]0.205905643910149[/C][C]531.720085897412[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]109.495972222222[/C][C]0.200964775886701[/C][C]544.851562862706[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]109.500972222222[/C][C]0.198894161083416[/C][C]550.548953401892[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]109.474583333333[/C][C]0.1932986185342[/C][C]566.349538157533[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]109.480138888889[/C][C]0.191802206928826[/C][C]570.797076018602[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]109.407222222222[/C][C]0.179896425406701[/C][C]608.167849777336[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]109.4225[/C][C]0.175373372095261[/C][C]623.940217905846[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]109.1925[/C][C]0.136242578870702[/C][C]801.45649697094[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]109.199166666667[/C][C]0.126459205877523[/C][C]863.512987519682[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]109.769[/C][C]0.331739573954535[/C][C]330.889072688819[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]109.758529411765[/C][C]0.322454798045437[/C][C]340.384233936252[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]109.734242424242[/C][C]0.314663846284874[/C][C]348.734828356789[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]109.70375[/C][C]0.30689186057519[/C][C]357.467121462227[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]109.676129032258[/C][C]0.30007907955082[/C][C]365.490753958687[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]109.644833333333[/C][C]0.292499117934511[/C][C]374.855261470847[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]109.611034482759[/C][C]0.283574932365135[/C][C]386.532877107847[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]109.575357142857[/C][C]0.273656216727517[/C][C]400.412453454192[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]109.541296296296[/C][C]0.264313523027799[/C][C]414.436972582653[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]109.511538461538[/C][C]0.256139011885945[/C][C]427.547282451071[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]109.4778[/C][C]0.248200098669585[/C][C]441.086851241512[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]109.446041666667[/C][C]0.240737036795436[/C][C]454.629013979545[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]109.412608695652[/C][C]0.231532269384714[/C][C]472.558788398745[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]109.386818181818[/C][C]0.225794292789167[/C][C]484.453423647679[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]109.361428571429[/C][C]0.219627118120171[/C][C]497.941372210651[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]109.3395[/C][C]0.214397471162851[/C][C]509.985026441605[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]109.322368421053[/C][C]0.210901146580119[/C][C]518.358340833022[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]109.301944444444[/C][C]0.206884224752636[/C][C]528.324209229258[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]109.278529411765[/C][C]0.201406875440432[/C][C]542.575963073738[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]109.2553125[/C][C]0.19492863891474[/C][C]560.488767111266[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]109.228333333333[/C][C]0.18560561533651[/C][C]588.496922010136[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]109.206428571429[/C][C]0.17592177064751[/C][C]620.766993018975[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]109.179230769231[/C][C]0.162395455674316[/C][C]672.304716384366[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]109.1775[/C][C]0.157890589984955[/C][C]691.475660521652[/C][/ROW]
[ROW][C]Median[/C][C]109.27[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]109.93[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]109.257297297297[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]109.301944444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]109.257297297297[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]109.301944444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]109.301944444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]109.257297297297[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]109.301944444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]109.322368421053[/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=239791&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=239791&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 Mean109.7734722222220.341096865973015321.824921812406
Geometric Mean109.736144479014
Harmonic Mean109.699117492877
Quadratic Mean109.811091633921
Winsorized Mean ( 1 / 24 )109.7788888888890.339543071610509323.313588370952
Winsorized Mean ( 2 / 24 )109.8030555555560.334330646482171328.426534363223
Winsorized Mean ( 3 / 24 )109.8155555555560.330735587012918332.034289225931
Winsorized Mean ( 4 / 24 )109.7988888888890.323699610767114339.199941046219
Winsorized Mean ( 5 / 24 )109.8065277777780.321230466345728341.830988283649
Winsorized Mean ( 6 / 24 )109.8081944444440.319748184761708343.420853276396
Winsorized Mean ( 7 / 24 )109.8052777777780.315550973304802347.97952491724
Winsorized Mean ( 8 / 24 )109.7797222222220.304127640574534360.965948424928
Winsorized Mean ( 9 / 24 )109.7347222222220.290168652878883378.175661407595
Winsorized Mean ( 10 / 24 )109.7458333333330.279758919101611392.287165269869
Winsorized Mean ( 11 / 24 )109.7106944444440.268488664573125408.623189432878
Winsorized Mean ( 12 / 24 )109.7023611111110.266378328053017411.829152592613
Winsorized Mean ( 13 / 24 )109.61750.240692934691988455.424668531613
Winsorized Mean ( 14 / 24 )109.5941666666670.234266055796137467.81923353863
Winsorized Mean ( 15 / 24 )109.5441666666670.221451566185214494.664221859907
Winsorized Mean ( 16 / 24 )109.4841666666670.205905643910149531.720085897412
Winsorized Mean ( 17 / 24 )109.4959722222220.200964775886701544.851562862706
Winsorized Mean ( 18 / 24 )109.5009722222220.198894161083416550.548953401892
Winsorized Mean ( 19 / 24 )109.4745833333330.1932986185342566.349538157533
Winsorized Mean ( 20 / 24 )109.4801388888890.191802206928826570.797076018602
Winsorized Mean ( 21 / 24 )109.4072222222220.179896425406701608.167849777336
Winsorized Mean ( 22 / 24 )109.42250.175373372095261623.940217905846
Winsorized Mean ( 23 / 24 )109.19250.136242578870702801.45649697094
Winsorized Mean ( 24 / 24 )109.1991666666670.126459205877523863.512987519682
Trimmed Mean ( 1 / 24 )109.7690.331739573954535330.889072688819
Trimmed Mean ( 2 / 24 )109.7585294117650.322454798045437340.384233936252
Trimmed Mean ( 3 / 24 )109.7342424242420.314663846284874348.734828356789
Trimmed Mean ( 4 / 24 )109.703750.30689186057519357.467121462227
Trimmed Mean ( 5 / 24 )109.6761290322580.30007907955082365.490753958687
Trimmed Mean ( 6 / 24 )109.6448333333330.292499117934511374.855261470847
Trimmed Mean ( 7 / 24 )109.6110344827590.283574932365135386.532877107847
Trimmed Mean ( 8 / 24 )109.5753571428570.273656216727517400.412453454192
Trimmed Mean ( 9 / 24 )109.5412962962960.264313523027799414.436972582653
Trimmed Mean ( 10 / 24 )109.5115384615380.256139011885945427.547282451071
Trimmed Mean ( 11 / 24 )109.47780.248200098669585441.086851241512
Trimmed Mean ( 12 / 24 )109.4460416666670.240737036795436454.629013979545
Trimmed Mean ( 13 / 24 )109.4126086956520.231532269384714472.558788398745
Trimmed Mean ( 14 / 24 )109.3868181818180.225794292789167484.453423647679
Trimmed Mean ( 15 / 24 )109.3614285714290.219627118120171497.941372210651
Trimmed Mean ( 16 / 24 )109.33950.214397471162851509.985026441605
Trimmed Mean ( 17 / 24 )109.3223684210530.210901146580119518.358340833022
Trimmed Mean ( 18 / 24 )109.3019444444440.206884224752636528.324209229258
Trimmed Mean ( 19 / 24 )109.2785294117650.201406875440432542.575963073738
Trimmed Mean ( 20 / 24 )109.25531250.19492863891474560.488767111266
Trimmed Mean ( 21 / 24 )109.2283333333330.18560561533651588.496922010136
Trimmed Mean ( 22 / 24 )109.2064285714290.17592177064751620.766993018975
Trimmed Mean ( 23 / 24 )109.1792307692310.162395455674316672.304716384366
Trimmed Mean ( 24 / 24 )109.17750.157890589984955691.475660521652
Median109.27
Midrange109.93
Midmean - Weighted Average at Xnp109.257297297297
Midmean - Weighted Average at X(n+1)p109.301944444444
Midmean - Empirical Distribution Function109.257297297297
Midmean - Empirical Distribution Function - Averaging109.301944444444
Midmean - Empirical Distribution Function - Interpolation109.301944444444
Midmean - Closest Observation109.257297297297
Midmean - True Basic - Statistics Graphics Toolkit109.301944444444
Midmean - MS Excel (old versions)109.322368421053
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')