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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 computationMon, 27 Oct 2008 12:27:00 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/27/t1225132063dqs4f8kn34xwi5t.htm/, Retrieved Wed, 29 May 2024 00:09:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=19375, Retrieved Wed, 29 May 2024 00:09:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsQ6 2
Estimated Impact138
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Q6 Distributions] [2007-10-22 19:20:42] [b731da8b544846036771bbf9bf2f34ce]
-   PD  [Central Tendency] [Q6 1] [2008-10-27 18:16:38] [fe7291e888d31b8c4db0b24d6c0f75c6]
-    D      [Central Tendency] [Q6 2] [2008-10-27 18:27:00] [783db4b4a0f63b73ca8b14666b7f4329] [Current]
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Dataseries X:
0,135240492
0,919087137
0,925417076
0,925612053
1,066666667
0,851108765
1,030693069
0,989031079
0,913000978
0,792723264
0,978170478
0,987513007
0,909433962
0,883608147
0,82745098
0,8252149
1,023255814
0,815418024
1,026192703
0,914742451
0,807276303
0,739130435
0,98973306
0,972164948
0,853889943
0,856864654
0,775739042
0,789473684
0,931350114
0,73971079
0,885245902
0,842435094
0,818458418
0,72755418
0,923238696
0,922680412
0,883762201
0,818270165
0,771047228
0,825852783
0,924485126
0,755165289
0,874671341
0,815956482
0,799807507
0,712598425
0,832980973
0,910323253
0,869149952
0,779182879
0,750254842
0,75856014
0,920889988
0,743991641
0,816254417
0,769593957
0,784007353
0,683284457
0,850505051
0,900695134
0,868398268




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=19375&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=19375&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=19375&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 Mean0.8481018946393440.016349368265597851.8736798181928
Geometric Mean0.830062517364542
Harmonic Mean0.783188534586578
Quadratic Mean0.857505063688777
Winsorized Mean ( 1 / 20 )0.8564964908196720.011435116390120174.9005485908027
Winsorized Mean ( 2 / 20 )0.8573100515409830.011172533329776976.7337206554662
Winsorized Mean ( 3 / 20 )0.8579011433114750.010984034032712778.1043777501478
Winsorized Mean ( 4 / 20 )0.8564620286229510.010323504522166682.9623338454452
Winsorized Mean ( 5 / 20 )0.8564520592786890.010302146226615383.133362742034
Winsorized Mean ( 6 / 20 )0.8567238080327870.010191584344544384.0618866576327
Winsorized Mean ( 7 / 20 )0.856370442524590.009835320870955287.0709205892355
Winsorized Mean ( 8 / 20 )0.8562268250819670.009559765072342289.5656764159567
Winsorized Mean ( 9 / 20 )0.8507058439836070.0083693698702011101.645148580722
Winsorized Mean ( 10 / 20 )0.8515740007049180.0078975884478689107.827092577191
Winsorized Mean ( 11 / 20 )0.8518009061803280.0078469482932564108.551869382440
Winsorized Mean ( 12 / 20 )0.8525405515573770.0076619941913619111.268754617241
Winsorized Mean ( 13 / 20 )0.8530088514098360.00749894740920204113.750477882149
Winsorized Mean ( 14 / 20 )0.8539879769836070.00729956820008977116.991574511641
Winsorized Mean ( 15 / 20 )0.8548918885409840.00701869103620872121.802182790307
Winsorized Mean ( 16 / 20 )0.8552713584426230.00681329980402921125.529682098656
Winsorized Mean ( 17 / 20 )0.8560348415409840.00632773287888688135.283024414199
Winsorized Mean ( 18 / 20 )0.8577248712786890.00592837075792166144.681381496353
Winsorized Mean ( 19 / 20 )0.8594267716721310.00544769581332401157.759684299946
Winsorized Mean ( 20 / 20 )0.8593117444590160.00537860842939758159.764696712689
Trimmed Mean ( 1 / 20 )0.8564798036271190.011055378809838277.4717735465505
Trimmed Mean ( 2 / 20 )0.8564619454035090.010588786877361580.8838590598697
Trimmed Mean ( 3 / 20 )0.8559916320.010189737303665184.0052698603046
Trimmed Mean ( 4 / 20 )0.855259052188680.0097849775864556487.4053154063969
Trimmed Mean ( 5 / 20 )0.8548993386470590.0095445225773684689.569628204784
Trimmed Mean ( 6 / 20 )0.854512742897960.0092451638573289692.4280798139188
Trimmed Mean ( 7 / 20 )0.8540344628510640.0088965139161696695.9965297529443
Trimmed Mean ( 8 / 20 )0.8535820985333330.0085554850015468699.7701589540515
Trimmed Mean ( 9 / 20 )0.8531131208604650.00819108389280974104.151432462966
Trimmed Mean ( 10 / 20 )0.8535110717804880.00804346866138197106.112313942160
Trimmed Mean ( 11 / 20 )0.8538140495641030.0079582031801338107.287289635366
Trimmed Mean ( 12 / 20 )0.8541157737567570.00784031672085347108.938937566770
Trimmed Mean ( 13 / 20 )0.8543445560285710.0077123825203516110.775697882478
Trimmed Mean ( 14 / 20 )0.854534481393940.00756194957591531113.004519907884
Trimmed Mean ( 15 / 20 )0.8546112942258060.007388395968792115.669395337718
Trimmed Mean ( 16 / 20 )0.8545719465172410.00720319005418774118.637984016598
Trimmed Mean ( 17 / 20 )0.8544731869629630.00697407248104978122.521409016722
Trimmed Mean ( 18 / 20 )0.85424904360.00677270003937853126.131238447464
Trimmed Mean ( 19 / 20 )0.853736904739130.00657240289048055129.897226169090
Trimmed Mean ( 20 / 20 )0.8528670253333330.00639404053481014133.384676041729
Median0.851108765
Midrange0.6009535795
Midmean - Weighted Average at Xnp0.852402004433333
Midmean - Weighted Average at X(n+1)p0.854611294225806
Midmean - Empirical Distribution Function0.854611294225806
Midmean - Empirical Distribution Function - Averaging0.854611294225806
Midmean - Empirical Distribution Function - Interpolation0.854611294225806
Midmean - Closest Observation0.8524049210625
Midmean - True Basic - Statistics Graphics Toolkit0.854611294225806
Midmean - MS Excel (old versions)0.854611294225806
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.848101894639344 & 0.0163493682655978 & 51.8736798181928 \tabularnewline
Geometric Mean & 0.830062517364542 &  &  \tabularnewline
Harmonic Mean & 0.783188534586578 &  &  \tabularnewline
Quadratic Mean & 0.857505063688777 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 0.856496490819672 & 0.0114351163901201 & 74.9005485908027 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 0.857310051540983 & 0.0111725333297769 & 76.7337206554662 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 0.857901143311475 & 0.0109840340327127 & 78.1043777501478 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 0.856462028622951 & 0.0103235045221666 & 82.9623338454452 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 0.856452059278689 & 0.0103021462266153 & 83.133362742034 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 0.856723808032787 & 0.0101915843445443 & 84.0618866576327 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 0.85637044252459 & 0.0098353208709552 & 87.0709205892355 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.856226825081967 & 0.0095597650723422 & 89.5656764159567 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 0.850705843983607 & 0.0083693698702011 & 101.645148580722 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.851574000704918 & 0.0078975884478689 & 107.827092577191 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.851800906180328 & 0.0078469482932564 & 108.551869382440 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.852540551557377 & 0.0076619941913619 & 111.268754617241 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.853008851409836 & 0.00749894740920204 & 113.750477882149 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.853987976983607 & 0.00729956820008977 & 116.991574511641 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.854891888540984 & 0.00701869103620872 & 121.802182790307 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.855271358442623 & 0.00681329980402921 & 125.529682098656 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.856034841540984 & 0.00632773287888688 & 135.283024414199 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.857724871278689 & 0.00592837075792166 & 144.681381496353 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.859426771672131 & 0.00544769581332401 & 157.759684299946 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 0.859311744459016 & 0.00537860842939758 & 159.764696712689 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 0.856479803627119 & 0.0110553788098382 & 77.4717735465505 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 0.856461945403509 & 0.0105887868773615 & 80.8838590598697 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 0.855991632 & 0.0101897373036651 & 84.0052698603046 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 0.85525905218868 & 0.00978497758645564 & 87.4053154063969 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 0.854899338647059 & 0.00954452257736846 & 89.569628204784 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 0.85451274289796 & 0.00924516385732896 & 92.4280798139188 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.854034462851064 & 0.00889651391616966 & 95.9965297529443 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.853582098533333 & 0.00855548500154686 & 99.7701589540515 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.853113120860465 & 0.00819108389280974 & 104.151432462966 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.853511071780488 & 0.00804346866138197 & 106.112313942160 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.853814049564103 & 0.0079582031801338 & 107.287289635366 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.854115773756757 & 0.00784031672085347 & 108.938937566770 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.854344556028571 & 0.0077123825203516 & 110.775697882478 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.85453448139394 & 0.00756194957591531 & 113.004519907884 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.854611294225806 & 0.007388395968792 & 115.669395337718 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.854571946517241 & 0.00720319005418774 & 118.637984016598 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 0.854473186962963 & 0.00697407248104978 & 122.521409016722 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 0.8542490436 & 0.00677270003937853 & 126.131238447464 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 0.85373690473913 & 0.00657240289048055 & 129.897226169090 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 0.852867025333333 & 0.00639404053481014 & 133.384676041729 \tabularnewline
Median & 0.851108765 &  &  \tabularnewline
Midrange & 0.6009535795 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.852402004433333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.854611294225806 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.854611294225806 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.854611294225806 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.854611294225806 &  &  \tabularnewline
Midmean - Closest Observation & 0.8524049210625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.854611294225806 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.854611294225806 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=19375&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]0.848101894639344[/C][C]0.0163493682655978[/C][C]51.8736798181928[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.830062517364542[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.783188534586578[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.857505063688777[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]0.856496490819672[/C][C]0.0114351163901201[/C][C]74.9005485908027[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]0.857310051540983[/C][C]0.0111725333297769[/C][C]76.7337206554662[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]0.857901143311475[/C][C]0.0109840340327127[/C][C]78.1043777501478[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]0.856462028622951[/C][C]0.0103235045221666[/C][C]82.9623338454452[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]0.856452059278689[/C][C]0.0103021462266153[/C][C]83.133362742034[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]0.856723808032787[/C][C]0.0101915843445443[/C][C]84.0618866576327[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]0.85637044252459[/C][C]0.0098353208709552[/C][C]87.0709205892355[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.856226825081967[/C][C]0.0095597650723422[/C][C]89.5656764159567[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]0.850705843983607[/C][C]0.0083693698702011[/C][C]101.645148580722[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.851574000704918[/C][C]0.0078975884478689[/C][C]107.827092577191[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.851800906180328[/C][C]0.0078469482932564[/C][C]108.551869382440[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.852540551557377[/C][C]0.0076619941913619[/C][C]111.268754617241[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.853008851409836[/C][C]0.00749894740920204[/C][C]113.750477882149[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.853987976983607[/C][C]0.00729956820008977[/C][C]116.991574511641[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.854891888540984[/C][C]0.00701869103620872[/C][C]121.802182790307[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.855271358442623[/C][C]0.00681329980402921[/C][C]125.529682098656[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.856034841540984[/C][C]0.00632773287888688[/C][C]135.283024414199[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.857724871278689[/C][C]0.00592837075792166[/C][C]144.681381496353[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.859426771672131[/C][C]0.00544769581332401[/C][C]157.759684299946[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]0.859311744459016[/C][C]0.00537860842939758[/C][C]159.764696712689[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]0.856479803627119[/C][C]0.0110553788098382[/C][C]77.4717735465505[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]0.856461945403509[/C][C]0.0105887868773615[/C][C]80.8838590598697[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]0.855991632[/C][C]0.0101897373036651[/C][C]84.0052698603046[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]0.85525905218868[/C][C]0.00978497758645564[/C][C]87.4053154063969[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]0.854899338647059[/C][C]0.00954452257736846[/C][C]89.569628204784[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]0.85451274289796[/C][C]0.00924516385732896[/C][C]92.4280798139188[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.854034462851064[/C][C]0.00889651391616966[/C][C]95.9965297529443[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.853582098533333[/C][C]0.00855548500154686[/C][C]99.7701589540515[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.853113120860465[/C][C]0.00819108389280974[/C][C]104.151432462966[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.853511071780488[/C][C]0.00804346866138197[/C][C]106.112313942160[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.853814049564103[/C][C]0.0079582031801338[/C][C]107.287289635366[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.854115773756757[/C][C]0.00784031672085347[/C][C]108.938937566770[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.854344556028571[/C][C]0.0077123825203516[/C][C]110.775697882478[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.85453448139394[/C][C]0.00756194957591531[/C][C]113.004519907884[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.854611294225806[/C][C]0.007388395968792[/C][C]115.669395337718[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.854571946517241[/C][C]0.00720319005418774[/C][C]118.637984016598[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]0.854473186962963[/C][C]0.00697407248104978[/C][C]122.521409016722[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]0.8542490436[/C][C]0.00677270003937853[/C][C]126.131238447464[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]0.85373690473913[/C][C]0.00657240289048055[/C][C]129.897226169090[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]0.852867025333333[/C][C]0.00639404053481014[/C][C]133.384676041729[/C][/ROW]
[ROW][C]Median[/C][C]0.851108765[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.6009535795[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.852402004433333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.854611294225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.854611294225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.854611294225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.854611294225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.8524049210625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.854611294225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.854611294225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=19375&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=19375&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 Mean0.8481018946393440.016349368265597851.8736798181928
Geometric Mean0.830062517364542
Harmonic Mean0.783188534586578
Quadratic Mean0.857505063688777
Winsorized Mean ( 1 / 20 )0.8564964908196720.011435116390120174.9005485908027
Winsorized Mean ( 2 / 20 )0.8573100515409830.011172533329776976.7337206554662
Winsorized Mean ( 3 / 20 )0.8579011433114750.010984034032712778.1043777501478
Winsorized Mean ( 4 / 20 )0.8564620286229510.010323504522166682.9623338454452
Winsorized Mean ( 5 / 20 )0.8564520592786890.010302146226615383.133362742034
Winsorized Mean ( 6 / 20 )0.8567238080327870.010191584344544384.0618866576327
Winsorized Mean ( 7 / 20 )0.856370442524590.009835320870955287.0709205892355
Winsorized Mean ( 8 / 20 )0.8562268250819670.009559765072342289.5656764159567
Winsorized Mean ( 9 / 20 )0.8507058439836070.0083693698702011101.645148580722
Winsorized Mean ( 10 / 20 )0.8515740007049180.0078975884478689107.827092577191
Winsorized Mean ( 11 / 20 )0.8518009061803280.0078469482932564108.551869382440
Winsorized Mean ( 12 / 20 )0.8525405515573770.0076619941913619111.268754617241
Winsorized Mean ( 13 / 20 )0.8530088514098360.00749894740920204113.750477882149
Winsorized Mean ( 14 / 20 )0.8539879769836070.00729956820008977116.991574511641
Winsorized Mean ( 15 / 20 )0.8548918885409840.00701869103620872121.802182790307
Winsorized Mean ( 16 / 20 )0.8552713584426230.00681329980402921125.529682098656
Winsorized Mean ( 17 / 20 )0.8560348415409840.00632773287888688135.283024414199
Winsorized Mean ( 18 / 20 )0.8577248712786890.00592837075792166144.681381496353
Winsorized Mean ( 19 / 20 )0.8594267716721310.00544769581332401157.759684299946
Winsorized Mean ( 20 / 20 )0.8593117444590160.00537860842939758159.764696712689
Trimmed Mean ( 1 / 20 )0.8564798036271190.011055378809838277.4717735465505
Trimmed Mean ( 2 / 20 )0.8564619454035090.010588786877361580.8838590598697
Trimmed Mean ( 3 / 20 )0.8559916320.010189737303665184.0052698603046
Trimmed Mean ( 4 / 20 )0.855259052188680.0097849775864556487.4053154063969
Trimmed Mean ( 5 / 20 )0.8548993386470590.0095445225773684689.569628204784
Trimmed Mean ( 6 / 20 )0.854512742897960.0092451638573289692.4280798139188
Trimmed Mean ( 7 / 20 )0.8540344628510640.0088965139161696695.9965297529443
Trimmed Mean ( 8 / 20 )0.8535820985333330.0085554850015468699.7701589540515
Trimmed Mean ( 9 / 20 )0.8531131208604650.00819108389280974104.151432462966
Trimmed Mean ( 10 / 20 )0.8535110717804880.00804346866138197106.112313942160
Trimmed Mean ( 11 / 20 )0.8538140495641030.0079582031801338107.287289635366
Trimmed Mean ( 12 / 20 )0.8541157737567570.00784031672085347108.938937566770
Trimmed Mean ( 13 / 20 )0.8543445560285710.0077123825203516110.775697882478
Trimmed Mean ( 14 / 20 )0.854534481393940.00756194957591531113.004519907884
Trimmed Mean ( 15 / 20 )0.8546112942258060.007388395968792115.669395337718
Trimmed Mean ( 16 / 20 )0.8545719465172410.00720319005418774118.637984016598
Trimmed Mean ( 17 / 20 )0.8544731869629630.00697407248104978122.521409016722
Trimmed Mean ( 18 / 20 )0.85424904360.00677270003937853126.131238447464
Trimmed Mean ( 19 / 20 )0.853736904739130.00657240289048055129.897226169090
Trimmed Mean ( 20 / 20 )0.8528670253333330.00639404053481014133.384676041729
Median0.851108765
Midrange0.6009535795
Midmean - Weighted Average at Xnp0.852402004433333
Midmean - Weighted Average at X(n+1)p0.854611294225806
Midmean - Empirical Distribution Function0.854611294225806
Midmean - Empirical Distribution Function - Averaging0.854611294225806
Midmean - Empirical Distribution Function - Interpolation0.854611294225806
Midmean - Closest Observation0.8524049210625
Midmean - True Basic - Statistics Graphics Toolkit0.854611294225806
Midmean - MS Excel (old versions)0.854611294225806
Number of observations61



Parameters (Session):
par1 = 0 ; par2 = 0 ;
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')