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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 05 Mar 2013 14:07:48 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Mar/05/t1362510517iw62flhpm5eiaxg.htm/, Retrieved Sat, 04 May 2024 17:11:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207471, Retrieved Sat, 04 May 2024 17:11:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact59
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-03-05 19:07:48] [8f84a338303fe8d74ac0d8ad91c8b331] [Current]
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Dataseries X:
20,5
20,2
19,4
19,2
18,8
18,8
22,6
23,3
23
21,4
19,9
18,8
18,6
18,4
18,6
19,9
19,2
18,4
21,1
20,5
19,1
18,1
17
17,1
17,4
16,8
15,3
14,3
13,4
15,3
22,1
23,7
22,2
19,5
16,6
17,3
19,8
21,2
21,5
20,6
19,1
19,6
23,4
24,3
24,1
22,8
22,5
23,8
24,9
25,2
24,3
22,8
20,7
19,8
22,5
22,6
22,5
21,8
21,2
20,6
19,9
18,7
17,6
16,4
15,9
16,8
22,8
24
22,2
17,9
16
16




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207471&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207471&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207471&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean20.02222222222220.32551405248545261.5095479575864
Geometric Mean19.8278870816173
Harmonic Mean19.6270142014312
Quadratic Mean20.2092181936858
Winsorized Mean ( 1 / 24 )20.03055555555560.32123976688480562.3539101332321
Winsorized Mean ( 2 / 24 )20.04166666666670.31137630520461864.36477770361
Winsorized Mean ( 3 / 24 )20.04166666666670.31137630520461864.36477770361
Winsorized Mean ( 4 / 24 )20.06388888888890.30245025429091666.3378145802124
Winsorized Mean ( 5 / 24 )20.06388888888890.29981936107994566.9199241056984
Winsorized Mean ( 6 / 24 )20.04722222222220.29679411345803767.5458889283418
Winsorized Mean ( 7 / 24 )20.07638888888890.28783018771884869.7508105317273
Winsorized Mean ( 8 / 24 )20.06527777777780.27810812711719172.1491960187218
Winsorized Mean ( 9 / 24 )20.07777777777780.27168993982962573.8995996332011
Winsorized Mean ( 10 / 24 )20.03611111111110.26492466194832375.6294675012906
Winsorized Mean ( 11 / 24 )20.03611111111110.25499168076548578.5755482334275
Winsorized Mean ( 12 / 24 )20.05277777777780.25221997303430779.5051142720176
Winsorized Mean ( 13 / 24 )20.08888888888890.24636286611002981.5418703560499
Winsorized Mean ( 14 / 24 )20.06944444444440.23733687165104684.5610052278447
Winsorized Mean ( 15 / 24 )20.11111111111110.23084314698851987.1202432191383
Winsorized Mean ( 16 / 24 )20.15555555555560.21748571166069992.6753091118022
Winsorized Mean ( 17 / 24 )20.20277777777780.21071615926158295.8767369743967
Winsorized Mean ( 18 / 24 )20.27777777777780.200490617155466101.140781875362
Winsorized Mean ( 19 / 24 )20.19861111111110.18838009988502107.222637228877
Winsorized Mean ( 20 / 24 )20.25416666666670.181067274738481111.859896803109
Winsorized Mean ( 21 / 24 )20.2250.17667984271886114.47259454596
Winsorized Mean ( 22 / 24 )20.16388888888890.15922722166868126.635939995524
Winsorized Mean ( 23 / 24 )20.10.141462847027769142.086777004102
Winsorized Mean ( 24 / 24 )20.06666666666670.136852044205156146.630375769796
Trimmed Mean ( 1 / 24 )20.04285714285710.3122652919244664.1853502812784
Trimmed Mean ( 2 / 24 )20.05588235294120.30158625374863666.5013146443246
Trimmed Mean ( 3 / 24 )20.06363636363640.29516410325295467.9745136434898
Trimmed Mean ( 4 / 24 )20.0718750.2874307089550469.8320477758682
Trimmed Mean ( 5 / 24 )20.07419354838710.28139878269368271.337172663746
Trimmed Mean ( 6 / 24 )20.07666666666670.27487405093873973.0395124534368
Trimmed Mean ( 7 / 24 )20.08275862068970.26773611096026375.009525419118
Trimmed Mean ( 8 / 24 )20.08392857142860.26132500521150776.854216668525
Trimmed Mean ( 9 / 24 )20.0870370370370.25575208416654178.5410492450052
Trimmed Mean ( 10 / 24 )20.08846153846150.25024352914207480.275648314792
Trimmed Mean ( 11 / 24 )20.0960.2447649434682682.1032608479162
Trimmed Mean ( 12 / 24 )20.10416666666670.23993864340800383.7887819198869
Trimmed Mean ( 13 / 24 )20.11086956521740.23424724253749785.8531752492162
Trimmed Mean ( 14 / 24 )20.11363636363640.22811366619511888.1737455678435
Trimmed Mean ( 15 / 24 )20.11904761904760.22204932159832890.6062107023305
Trimmed Mean ( 16 / 24 )20.120.21543634909833793.3918537155312
Trimmed Mean ( 17 / 24 )20.11578947368420.20967109363876195.9397364919622
Trimmed Mean ( 18 / 24 )20.10555555555560.20326479892801298.9131205284399
Trimmed Mean ( 19 / 24 )20.08529411764710.196680670500901102.121342511668
Trimmed Mean ( 20 / 24 )20.0718750.190724128112714105.240355264007
Trimmed Mean ( 21 / 24 )20.050.183750830790209109.11515291537
Trimmed Mean ( 22 / 24 )20.02857142857140.174639245913259114.685398026279
Trimmed Mean ( 23 / 24 )20.01153846153850.167086060098651119.767851667119
Trimmed Mean ( 24 / 24 )200.161850709525516123.570666193755
Median19.9
Midrange19.3
Midmean - Weighted Average at Xnp20.1769230769231
Midmean - Weighted Average at X(n+1)p20.2315789473684
Midmean - Empirical Distribution Function20.1769230769231
Midmean - Empirical Distribution Function - Averaging20.2315789473684
Midmean - Empirical Distribution Function - Interpolation20.2315789473684
Midmean - Closest Observation20.1769230769231
Midmean - True Basic - Statistics Graphics Toolkit20.2315789473684
Midmean - MS Excel (old versions)20.1769230769231
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 20.0222222222222 & 0.325514052485452 & 61.5095479575864 \tabularnewline
Geometric Mean & 19.8278870816173 &  &  \tabularnewline
Harmonic Mean & 19.6270142014312 &  &  \tabularnewline
Quadratic Mean & 20.2092181936858 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 20.0305555555556 & 0.321239766884805 & 62.3539101332321 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 20.0416666666667 & 0.311376305204618 & 64.36477770361 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 20.0416666666667 & 0.311376305204618 & 64.36477770361 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 20.0638888888889 & 0.302450254290916 & 66.3378145802124 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 20.0638888888889 & 0.299819361079945 & 66.9199241056984 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 20.0472222222222 & 0.296794113458037 & 67.5458889283418 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 20.0763888888889 & 0.287830187718848 & 69.7508105317273 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 20.0652777777778 & 0.278108127117191 & 72.1491960187218 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 20.0777777777778 & 0.271689939829625 & 73.8995996332011 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 20.0361111111111 & 0.264924661948323 & 75.6294675012906 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 20.0361111111111 & 0.254991680765485 & 78.5755482334275 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 20.0527777777778 & 0.252219973034307 & 79.5051142720176 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 20.0888888888889 & 0.246362866110029 & 81.5418703560499 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 20.0694444444444 & 0.237336871651046 & 84.5610052278447 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 20.1111111111111 & 0.230843146988519 & 87.1202432191383 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 20.1555555555556 & 0.217485711660699 & 92.6753091118022 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 20.2027777777778 & 0.210716159261582 & 95.8767369743967 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 20.2777777777778 & 0.200490617155466 & 101.140781875362 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 20.1986111111111 & 0.18838009988502 & 107.222637228877 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 20.2541666666667 & 0.181067274738481 & 111.859896803109 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 20.225 & 0.17667984271886 & 114.47259454596 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 20.1638888888889 & 0.15922722166868 & 126.635939995524 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 20.1 & 0.141462847027769 & 142.086777004102 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 20.0666666666667 & 0.136852044205156 & 146.630375769796 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 20.0428571428571 & 0.31226529192446 & 64.1853502812784 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 20.0558823529412 & 0.301586253748636 & 66.5013146443246 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 20.0636363636364 & 0.295164103252954 & 67.9745136434898 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 20.071875 & 0.28743070895504 & 69.8320477758682 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 20.0741935483871 & 0.281398782693682 & 71.337172663746 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 20.0766666666667 & 0.274874050938739 & 73.0395124534368 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 20.0827586206897 & 0.267736110960263 & 75.009525419118 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 20.0839285714286 & 0.261325005211507 & 76.854216668525 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 20.087037037037 & 0.255752084166541 & 78.5410492450052 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 20.0884615384615 & 0.250243529142074 & 80.275648314792 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 20.096 & 0.24476494346826 & 82.1032608479162 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 20.1041666666667 & 0.239938643408003 & 83.7887819198869 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 20.1108695652174 & 0.234247242537497 & 85.8531752492162 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 20.1136363636364 & 0.228113666195118 & 88.1737455678435 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 20.1190476190476 & 0.222049321598328 & 90.6062107023305 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 20.12 & 0.215436349098337 & 93.3918537155312 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 20.1157894736842 & 0.209671093638761 & 95.9397364919622 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 20.1055555555556 & 0.203264798928012 & 98.9131205284399 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 20.0852941176471 & 0.196680670500901 & 102.121342511668 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 20.071875 & 0.190724128112714 & 105.240355264007 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 20.05 & 0.183750830790209 & 109.11515291537 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 20.0285714285714 & 0.174639245913259 & 114.685398026279 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 20.0115384615385 & 0.167086060098651 & 119.767851667119 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 20 & 0.161850709525516 & 123.570666193755 \tabularnewline
Median & 19.9 &  &  \tabularnewline
Midrange & 19.3 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 20.1769230769231 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 20.2315789473684 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 20.1769230769231 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 20.2315789473684 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 20.2315789473684 &  &  \tabularnewline
Midmean - Closest Observation & 20.1769230769231 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 20.2315789473684 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 20.1769230769231 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207471&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]20.0222222222222[/C][C]0.325514052485452[/C][C]61.5095479575864[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]19.8278870816173[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]19.6270142014312[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]20.2092181936858[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]20.0305555555556[/C][C]0.321239766884805[/C][C]62.3539101332321[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]20.0416666666667[/C][C]0.311376305204618[/C][C]64.36477770361[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]20.0416666666667[/C][C]0.311376305204618[/C][C]64.36477770361[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]20.0638888888889[/C][C]0.302450254290916[/C][C]66.3378145802124[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]20.0638888888889[/C][C]0.299819361079945[/C][C]66.9199241056984[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]20.0472222222222[/C][C]0.296794113458037[/C][C]67.5458889283418[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]20.0763888888889[/C][C]0.287830187718848[/C][C]69.7508105317273[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]20.0652777777778[/C][C]0.278108127117191[/C][C]72.1491960187218[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]20.0777777777778[/C][C]0.271689939829625[/C][C]73.8995996332011[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]20.0361111111111[/C][C]0.264924661948323[/C][C]75.6294675012906[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]20.0361111111111[/C][C]0.254991680765485[/C][C]78.5755482334275[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]20.0527777777778[/C][C]0.252219973034307[/C][C]79.5051142720176[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]20.0888888888889[/C][C]0.246362866110029[/C][C]81.5418703560499[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]20.0694444444444[/C][C]0.237336871651046[/C][C]84.5610052278447[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]20.1111111111111[/C][C]0.230843146988519[/C][C]87.1202432191383[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]20.1555555555556[/C][C]0.217485711660699[/C][C]92.6753091118022[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]20.2027777777778[/C][C]0.210716159261582[/C][C]95.8767369743967[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]20.2777777777778[/C][C]0.200490617155466[/C][C]101.140781875362[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]20.1986111111111[/C][C]0.18838009988502[/C][C]107.222637228877[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]20.2541666666667[/C][C]0.181067274738481[/C][C]111.859896803109[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]20.225[/C][C]0.17667984271886[/C][C]114.47259454596[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]20.1638888888889[/C][C]0.15922722166868[/C][C]126.635939995524[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]20.1[/C][C]0.141462847027769[/C][C]142.086777004102[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]20.0666666666667[/C][C]0.136852044205156[/C][C]146.630375769796[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]20.0428571428571[/C][C]0.31226529192446[/C][C]64.1853502812784[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]20.0558823529412[/C][C]0.301586253748636[/C][C]66.5013146443246[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]20.0636363636364[/C][C]0.295164103252954[/C][C]67.9745136434898[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]20.071875[/C][C]0.28743070895504[/C][C]69.8320477758682[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]20.0741935483871[/C][C]0.281398782693682[/C][C]71.337172663746[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]20.0766666666667[/C][C]0.274874050938739[/C][C]73.0395124534368[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]20.0827586206897[/C][C]0.267736110960263[/C][C]75.009525419118[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]20.0839285714286[/C][C]0.261325005211507[/C][C]76.854216668525[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]20.087037037037[/C][C]0.255752084166541[/C][C]78.5410492450052[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]20.0884615384615[/C][C]0.250243529142074[/C][C]80.275648314792[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]20.096[/C][C]0.24476494346826[/C][C]82.1032608479162[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]20.1041666666667[/C][C]0.239938643408003[/C][C]83.7887819198869[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]20.1108695652174[/C][C]0.234247242537497[/C][C]85.8531752492162[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]20.1136363636364[/C][C]0.228113666195118[/C][C]88.1737455678435[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]20.1190476190476[/C][C]0.222049321598328[/C][C]90.6062107023305[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]20.12[/C][C]0.215436349098337[/C][C]93.3918537155312[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]20.1157894736842[/C][C]0.209671093638761[/C][C]95.9397364919622[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]20.1055555555556[/C][C]0.203264798928012[/C][C]98.9131205284399[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]20.0852941176471[/C][C]0.196680670500901[/C][C]102.121342511668[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]20.071875[/C][C]0.190724128112714[/C][C]105.240355264007[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]20.05[/C][C]0.183750830790209[/C][C]109.11515291537[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]20.0285714285714[/C][C]0.174639245913259[/C][C]114.685398026279[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]20.0115384615385[/C][C]0.167086060098651[/C][C]119.767851667119[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]20[/C][C]0.161850709525516[/C][C]123.570666193755[/C][/ROW]
[ROW][C]Median[/C][C]19.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]19.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]20.1769230769231[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]20.2315789473684[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]20.1769230769231[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]20.2315789473684[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]20.2315789473684[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]20.1769230769231[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]20.2315789473684[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]20.1769230769231[/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=207471&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207471&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 Mean20.02222222222220.32551405248545261.5095479575864
Geometric Mean19.8278870816173
Harmonic Mean19.6270142014312
Quadratic Mean20.2092181936858
Winsorized Mean ( 1 / 24 )20.03055555555560.32123976688480562.3539101332321
Winsorized Mean ( 2 / 24 )20.04166666666670.31137630520461864.36477770361
Winsorized Mean ( 3 / 24 )20.04166666666670.31137630520461864.36477770361
Winsorized Mean ( 4 / 24 )20.06388888888890.30245025429091666.3378145802124
Winsorized Mean ( 5 / 24 )20.06388888888890.29981936107994566.9199241056984
Winsorized Mean ( 6 / 24 )20.04722222222220.29679411345803767.5458889283418
Winsorized Mean ( 7 / 24 )20.07638888888890.28783018771884869.7508105317273
Winsorized Mean ( 8 / 24 )20.06527777777780.27810812711719172.1491960187218
Winsorized Mean ( 9 / 24 )20.07777777777780.27168993982962573.8995996332011
Winsorized Mean ( 10 / 24 )20.03611111111110.26492466194832375.6294675012906
Winsorized Mean ( 11 / 24 )20.03611111111110.25499168076548578.5755482334275
Winsorized Mean ( 12 / 24 )20.05277777777780.25221997303430779.5051142720176
Winsorized Mean ( 13 / 24 )20.08888888888890.24636286611002981.5418703560499
Winsorized Mean ( 14 / 24 )20.06944444444440.23733687165104684.5610052278447
Winsorized Mean ( 15 / 24 )20.11111111111110.23084314698851987.1202432191383
Winsorized Mean ( 16 / 24 )20.15555555555560.21748571166069992.6753091118022
Winsorized Mean ( 17 / 24 )20.20277777777780.21071615926158295.8767369743967
Winsorized Mean ( 18 / 24 )20.27777777777780.200490617155466101.140781875362
Winsorized Mean ( 19 / 24 )20.19861111111110.18838009988502107.222637228877
Winsorized Mean ( 20 / 24 )20.25416666666670.181067274738481111.859896803109
Winsorized Mean ( 21 / 24 )20.2250.17667984271886114.47259454596
Winsorized Mean ( 22 / 24 )20.16388888888890.15922722166868126.635939995524
Winsorized Mean ( 23 / 24 )20.10.141462847027769142.086777004102
Winsorized Mean ( 24 / 24 )20.06666666666670.136852044205156146.630375769796
Trimmed Mean ( 1 / 24 )20.04285714285710.3122652919244664.1853502812784
Trimmed Mean ( 2 / 24 )20.05588235294120.30158625374863666.5013146443246
Trimmed Mean ( 3 / 24 )20.06363636363640.29516410325295467.9745136434898
Trimmed Mean ( 4 / 24 )20.0718750.2874307089550469.8320477758682
Trimmed Mean ( 5 / 24 )20.07419354838710.28139878269368271.337172663746
Trimmed Mean ( 6 / 24 )20.07666666666670.27487405093873973.0395124534368
Trimmed Mean ( 7 / 24 )20.08275862068970.26773611096026375.009525419118
Trimmed Mean ( 8 / 24 )20.08392857142860.26132500521150776.854216668525
Trimmed Mean ( 9 / 24 )20.0870370370370.25575208416654178.5410492450052
Trimmed Mean ( 10 / 24 )20.08846153846150.25024352914207480.275648314792
Trimmed Mean ( 11 / 24 )20.0960.2447649434682682.1032608479162
Trimmed Mean ( 12 / 24 )20.10416666666670.23993864340800383.7887819198869
Trimmed Mean ( 13 / 24 )20.11086956521740.23424724253749785.8531752492162
Trimmed Mean ( 14 / 24 )20.11363636363640.22811366619511888.1737455678435
Trimmed Mean ( 15 / 24 )20.11904761904760.22204932159832890.6062107023305
Trimmed Mean ( 16 / 24 )20.120.21543634909833793.3918537155312
Trimmed Mean ( 17 / 24 )20.11578947368420.20967109363876195.9397364919622
Trimmed Mean ( 18 / 24 )20.10555555555560.20326479892801298.9131205284399
Trimmed Mean ( 19 / 24 )20.08529411764710.196680670500901102.121342511668
Trimmed Mean ( 20 / 24 )20.0718750.190724128112714105.240355264007
Trimmed Mean ( 21 / 24 )20.050.183750830790209109.11515291537
Trimmed Mean ( 22 / 24 )20.02857142857140.174639245913259114.685398026279
Trimmed Mean ( 23 / 24 )20.01153846153850.167086060098651119.767851667119
Trimmed Mean ( 24 / 24 )200.161850709525516123.570666193755
Median19.9
Midrange19.3
Midmean - Weighted Average at Xnp20.1769230769231
Midmean - Weighted Average at X(n+1)p20.2315789473684
Midmean - Empirical Distribution Function20.1769230769231
Midmean - Empirical Distribution Function - Averaging20.2315789473684
Midmean - Empirical Distribution Function - Interpolation20.2315789473684
Midmean - Closest Observation20.1769230769231
Midmean - True Basic - Statistics Graphics Toolkit20.2315789473684
Midmean - MS Excel (old versions)20.1769230769231
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')