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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 22 Oct 2012 15:04:51 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/22/t1350932706ctsme1022plwwra.htm/, Retrieved Sat, 04 May 2024 04:31:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=182135, Retrieved Sat, 04 May 2024 04:31:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-10-22 19:04:51] [a14baeeafb42bd31c8e1f231a0a4996d] [Current]
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Dataseries X:
6,11
6,13
6,15
6,15
6,16
6,18
6,21
6,22
6,23
6,26
6,28
6,28
6,29
6,32
6,36
6,37
6,38
6,38
6,4
6,41
6,42
6,43
6,44
6,47
6,47
6,48
6,51
6,54
6,56
6,57
6,6
6,62
6,65
6,71
6,76
6,78
6,8
6,83
6,86
6,86
6,87
6,88
6,9
6,92
6,93
6,94
6,96
6,98
6,99
7,01
7,06
7,07
7,08
7,08
7,1
7,11
7,22
7,24
7,25
7,26
7,27
7,3
7,32
7,34
7,35
7,36
7,39
7,41
7,43
7,46
7,47
7,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=182135&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=182135&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=182135&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'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean6.7650.0496001224189514136.390792402867
Geometric Mean6.75212102795677
Harmonic Mean6.73929240194605
Quadratic Mean6.77789769930339
Winsorized Mean ( 1 / 24 )6.764861111111110.0494638678198634136.763690533608
Winsorized Mean ( 2 / 24 )6.765138888888890.0493093906242866137.197779231058
Winsorized Mean ( 3 / 24 )6.763888888888890.0490658254305197137.853359839365
Winsorized Mean ( 4 / 24 )6.763333333333330.0487584509748931138.710996721695
Winsorized Mean ( 5 / 24 )6.763333333333330.0482624540998834140.136540080122
Winsorized Mean ( 6 / 24 )6.763333333333330.0473937325412765142.705226422987
Winsorized Mean ( 7 / 24 )6.763333333333330.047063204596766143.707454502537
Winsorized Mean ( 8 / 24 )6.763333333333330.0466892969944303144.858324470813
Winsorized Mean ( 9 / 24 )6.764583333333330.045664086790154148.137930895662
Winsorized Mean ( 10 / 24 )6.764583333333330.0447641784307389151.115994316746
Winsorized Mean ( 11 / 24 )6.760.0440039299710281153.622642442408
Winsorized Mean ( 12 / 24 )6.760.0434779997610721155.480933740023
Winsorized Mean ( 13 / 24 )6.763611111111110.0423739526188671159.617186811589
Winsorized Mean ( 14 / 24 )6.769444444444440.0409377026277172165.359656500635
Winsorized Mean ( 15 / 24 )6.767361111111110.0399755368541121169.287560434976
Winsorized Mean ( 16 / 24 )6.745138888888890.0359544535906605187.602319470126
Winsorized Mean ( 17 / 24 )6.742777777777780.0356189526741285189.303089270093
Winsorized Mean ( 18 / 24 )6.742777777777780.0342069911027853197.116950670027
Winsorized Mean ( 19 / 24 )6.745416666666670.0338365406444808199.353023039219
Winsorized Mean ( 20 / 24 )6.745416666666670.0330646078201049204.007157845832
Winsorized Mean ( 21 / 24 )6.745416666666670.0322596672436795209.097527749245
Winsorized Mean ( 22 / 24 )6.733194444444450.0297865557610079226.048103663551
Winsorized Mean ( 23 / 24 )6.736388888888890.0276401716816836243.717331660169
Winsorized Mean ( 24 / 24 )6.733055555555560.0272117406603976247.432005162185
Trimmed Mean ( 1 / 24 )6.763857142857140.0490216045907504137.977065404615
Trimmed Mean ( 2 / 24 )6.762794117647060.0484767286603399139.505991937527
Trimmed Mean ( 3 / 24 )6.761515151515150.0479044515327611141.145862966223
Trimmed Mean ( 4 / 24 )6.7606250.047308445733277142.905244406382
Trimmed Mean ( 5 / 24 )6.759838709677420.0466812338712479144.80848403283
Trimmed Mean ( 6 / 24 )6.7590.0460537023791232146.763444649001
Trimmed Mean ( 7 / 24 )6.758103448275860.0455041377406004148.516240145037
Trimmed Mean ( 8 / 24 )6.757142857142860.0448863747915723150.538841430597
Trimmed Mean ( 9 / 24 )6.756111111111110.0441864234650756152.900157589153
Trimmed Mean ( 10 / 24 )6.754807692307690.0435236195515715155.19866596352
Trimmed Mean ( 11 / 24 )6.75340.0428615331084664157.563192686311
Trimmed Mean ( 12 / 24 )6.75250.0421596720013618160.164908298667
Trimmed Mean ( 13 / 24 )6.751521739130430.0413445139054472163.299095850318
Trimmed Mean ( 14 / 24 )6.750.0405016116924114166.660034451536
Trimmed Mean ( 15 / 24 )6.747619047619050.0396790397217665170.054998682782
Trimmed Mean ( 16 / 24 )6.745250.038772822063518173.968507862282
Trimmed Mean ( 17 / 24 )6.745263157894740.0384510493008137175.4246836055
Trimmed Mean ( 18 / 24 )6.745555555555560.0380005105321687177.512234996033
Trimmed Mean ( 19 / 24 )6.745882352941180.0376235164803292179.299623852761
Trimmed Mean ( 20 / 24 )6.74593750.0370778914621943181.939620457608
Trimmed Mean ( 21 / 24 )6.7460.0363969178940183185.345364122402
Trimmed Mean ( 22 / 24 )6.746071428571430.0355245622074394189.898791410262
Trimmed Mean ( 23 / 24 )6.747692307692310.0348769604017309193.471341251327
Trimmed Mean ( 24 / 24 )6.749166666666670.034441278879003195.961557942649
Median6.79
Midrange6.805
Midmean - Weighted Average at Xnp6.72631578947369
Midmean - Weighted Average at X(n+1)p6.74555555555556
Midmean - Empirical Distribution Function6.72631578947369
Midmean - Empirical Distribution Function - Averaging6.74555555555556
Midmean - Empirical Distribution Function - Interpolation6.74555555555556
Midmean - Closest Observation6.72631578947369
Midmean - True Basic - Statistics Graphics Toolkit6.74555555555556
Midmean - MS Excel (old versions)6.73589743589744
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 6.765 & 0.0496001224189514 & 136.390792402867 \tabularnewline
Geometric Mean & 6.75212102795677 &  &  \tabularnewline
Harmonic Mean & 6.73929240194605 &  &  \tabularnewline
Quadratic Mean & 6.77789769930339 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 6.76486111111111 & 0.0494638678198634 & 136.763690533608 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 6.76513888888889 & 0.0493093906242866 & 137.197779231058 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 6.76388888888889 & 0.0490658254305197 & 137.853359839365 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 6.76333333333333 & 0.0487584509748931 & 138.710996721695 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 6.76333333333333 & 0.0482624540998834 & 140.136540080122 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 6.76333333333333 & 0.0473937325412765 & 142.705226422987 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 6.76333333333333 & 0.047063204596766 & 143.707454502537 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 6.76333333333333 & 0.0466892969944303 & 144.858324470813 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 6.76458333333333 & 0.045664086790154 & 148.137930895662 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 6.76458333333333 & 0.0447641784307389 & 151.115994316746 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 6.76 & 0.0440039299710281 & 153.622642442408 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 6.76 & 0.0434779997610721 & 155.480933740023 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 6.76361111111111 & 0.0423739526188671 & 159.617186811589 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 6.76944444444444 & 0.0409377026277172 & 165.359656500635 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 6.76736111111111 & 0.0399755368541121 & 169.287560434976 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 6.74513888888889 & 0.0359544535906605 & 187.602319470126 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 6.74277777777778 & 0.0356189526741285 & 189.303089270093 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 6.74277777777778 & 0.0342069911027853 & 197.116950670027 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 6.74541666666667 & 0.0338365406444808 & 199.353023039219 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 6.74541666666667 & 0.0330646078201049 & 204.007157845832 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 6.74541666666667 & 0.0322596672436795 & 209.097527749245 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 6.73319444444445 & 0.0297865557610079 & 226.048103663551 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 6.73638888888889 & 0.0276401716816836 & 243.717331660169 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 6.73305555555556 & 0.0272117406603976 & 247.432005162185 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 6.76385714285714 & 0.0490216045907504 & 137.977065404615 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 6.76279411764706 & 0.0484767286603399 & 139.505991937527 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 6.76151515151515 & 0.0479044515327611 & 141.145862966223 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 6.760625 & 0.047308445733277 & 142.905244406382 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 6.75983870967742 & 0.0466812338712479 & 144.80848403283 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 6.759 & 0.0460537023791232 & 146.763444649001 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 6.75810344827586 & 0.0455041377406004 & 148.516240145037 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 6.75714285714286 & 0.0448863747915723 & 150.538841430597 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 6.75611111111111 & 0.0441864234650756 & 152.900157589153 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 6.75480769230769 & 0.0435236195515715 & 155.19866596352 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 6.7534 & 0.0428615331084664 & 157.563192686311 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 6.7525 & 0.0421596720013618 & 160.164908298667 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 6.75152173913043 & 0.0413445139054472 & 163.299095850318 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 6.75 & 0.0405016116924114 & 166.660034451536 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 6.74761904761905 & 0.0396790397217665 & 170.054998682782 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 6.74525 & 0.038772822063518 & 173.968507862282 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 6.74526315789474 & 0.0384510493008137 & 175.4246836055 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 6.74555555555556 & 0.0380005105321687 & 177.512234996033 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 6.74588235294118 & 0.0376235164803292 & 179.299623852761 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 6.7459375 & 0.0370778914621943 & 181.939620457608 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 6.746 & 0.0363969178940183 & 185.345364122402 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 6.74607142857143 & 0.0355245622074394 & 189.898791410262 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 6.74769230769231 & 0.0348769604017309 & 193.471341251327 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 6.74916666666667 & 0.034441278879003 & 195.961557942649 \tabularnewline
Median & 6.79 &  &  \tabularnewline
Midrange & 6.805 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 6.72631578947369 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 6.74555555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 6.72631578947369 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 6.74555555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 6.74555555555556 &  &  \tabularnewline
Midmean - Closest Observation & 6.72631578947369 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 6.74555555555556 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 6.73589743589744 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=182135&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]6.765[/C][C]0.0496001224189514[/C][C]136.390792402867[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]6.75212102795677[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]6.73929240194605[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]6.77789769930339[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]6.76486111111111[/C][C]0.0494638678198634[/C][C]136.763690533608[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]6.76513888888889[/C][C]0.0493093906242866[/C][C]137.197779231058[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]6.76388888888889[/C][C]0.0490658254305197[/C][C]137.853359839365[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]6.76333333333333[/C][C]0.0487584509748931[/C][C]138.710996721695[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]6.76333333333333[/C][C]0.0482624540998834[/C][C]140.136540080122[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]6.76333333333333[/C][C]0.0473937325412765[/C][C]142.705226422987[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]6.76333333333333[/C][C]0.047063204596766[/C][C]143.707454502537[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]6.76333333333333[/C][C]0.0466892969944303[/C][C]144.858324470813[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]6.76458333333333[/C][C]0.045664086790154[/C][C]148.137930895662[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]6.76458333333333[/C][C]0.0447641784307389[/C][C]151.115994316746[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]6.76[/C][C]0.0440039299710281[/C][C]153.622642442408[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]6.76[/C][C]0.0434779997610721[/C][C]155.480933740023[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]6.76361111111111[/C][C]0.0423739526188671[/C][C]159.617186811589[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]6.76944444444444[/C][C]0.0409377026277172[/C][C]165.359656500635[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]6.76736111111111[/C][C]0.0399755368541121[/C][C]169.287560434976[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]6.74513888888889[/C][C]0.0359544535906605[/C][C]187.602319470126[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]6.74277777777778[/C][C]0.0356189526741285[/C][C]189.303089270093[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]6.74277777777778[/C][C]0.0342069911027853[/C][C]197.116950670027[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]6.74541666666667[/C][C]0.0338365406444808[/C][C]199.353023039219[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]6.74541666666667[/C][C]0.0330646078201049[/C][C]204.007157845832[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]6.74541666666667[/C][C]0.0322596672436795[/C][C]209.097527749245[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]6.73319444444445[/C][C]0.0297865557610079[/C][C]226.048103663551[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]6.73638888888889[/C][C]0.0276401716816836[/C][C]243.717331660169[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]6.73305555555556[/C][C]0.0272117406603976[/C][C]247.432005162185[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]6.76385714285714[/C][C]0.0490216045907504[/C][C]137.977065404615[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]6.76279411764706[/C][C]0.0484767286603399[/C][C]139.505991937527[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]6.76151515151515[/C][C]0.0479044515327611[/C][C]141.145862966223[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]6.760625[/C][C]0.047308445733277[/C][C]142.905244406382[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]6.75983870967742[/C][C]0.0466812338712479[/C][C]144.80848403283[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]6.759[/C][C]0.0460537023791232[/C][C]146.763444649001[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]6.75810344827586[/C][C]0.0455041377406004[/C][C]148.516240145037[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]6.75714285714286[/C][C]0.0448863747915723[/C][C]150.538841430597[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]6.75611111111111[/C][C]0.0441864234650756[/C][C]152.900157589153[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]6.75480769230769[/C][C]0.0435236195515715[/C][C]155.19866596352[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]6.7534[/C][C]0.0428615331084664[/C][C]157.563192686311[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]6.7525[/C][C]0.0421596720013618[/C][C]160.164908298667[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]6.75152173913043[/C][C]0.0413445139054472[/C][C]163.299095850318[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]6.75[/C][C]0.0405016116924114[/C][C]166.660034451536[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]6.74761904761905[/C][C]0.0396790397217665[/C][C]170.054998682782[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]6.74525[/C][C]0.038772822063518[/C][C]173.968507862282[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]6.74526315789474[/C][C]0.0384510493008137[/C][C]175.4246836055[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]6.74555555555556[/C][C]0.0380005105321687[/C][C]177.512234996033[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]6.74588235294118[/C][C]0.0376235164803292[/C][C]179.299623852761[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]6.7459375[/C][C]0.0370778914621943[/C][C]181.939620457608[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]6.746[/C][C]0.0363969178940183[/C][C]185.345364122402[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]6.74607142857143[/C][C]0.0355245622074394[/C][C]189.898791410262[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]6.74769230769231[/C][C]0.0348769604017309[/C][C]193.471341251327[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]6.74916666666667[/C][C]0.034441278879003[/C][C]195.961557942649[/C][/ROW]
[ROW][C]Median[/C][C]6.79[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]6.805[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]6.72631578947369[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]6.74555555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]6.72631578947369[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]6.74555555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]6.74555555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]6.72631578947369[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]6.74555555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]6.73589743589744[/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=182135&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=182135&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 Mean6.7650.0496001224189514136.390792402867
Geometric Mean6.75212102795677
Harmonic Mean6.73929240194605
Quadratic Mean6.77789769930339
Winsorized Mean ( 1 / 24 )6.764861111111110.0494638678198634136.763690533608
Winsorized Mean ( 2 / 24 )6.765138888888890.0493093906242866137.197779231058
Winsorized Mean ( 3 / 24 )6.763888888888890.0490658254305197137.853359839365
Winsorized Mean ( 4 / 24 )6.763333333333330.0487584509748931138.710996721695
Winsorized Mean ( 5 / 24 )6.763333333333330.0482624540998834140.136540080122
Winsorized Mean ( 6 / 24 )6.763333333333330.0473937325412765142.705226422987
Winsorized Mean ( 7 / 24 )6.763333333333330.047063204596766143.707454502537
Winsorized Mean ( 8 / 24 )6.763333333333330.0466892969944303144.858324470813
Winsorized Mean ( 9 / 24 )6.764583333333330.045664086790154148.137930895662
Winsorized Mean ( 10 / 24 )6.764583333333330.0447641784307389151.115994316746
Winsorized Mean ( 11 / 24 )6.760.0440039299710281153.622642442408
Winsorized Mean ( 12 / 24 )6.760.0434779997610721155.480933740023
Winsorized Mean ( 13 / 24 )6.763611111111110.0423739526188671159.617186811589
Winsorized Mean ( 14 / 24 )6.769444444444440.0409377026277172165.359656500635
Winsorized Mean ( 15 / 24 )6.767361111111110.0399755368541121169.287560434976
Winsorized Mean ( 16 / 24 )6.745138888888890.0359544535906605187.602319470126
Winsorized Mean ( 17 / 24 )6.742777777777780.0356189526741285189.303089270093
Winsorized Mean ( 18 / 24 )6.742777777777780.0342069911027853197.116950670027
Winsorized Mean ( 19 / 24 )6.745416666666670.0338365406444808199.353023039219
Winsorized Mean ( 20 / 24 )6.745416666666670.0330646078201049204.007157845832
Winsorized Mean ( 21 / 24 )6.745416666666670.0322596672436795209.097527749245
Winsorized Mean ( 22 / 24 )6.733194444444450.0297865557610079226.048103663551
Winsorized Mean ( 23 / 24 )6.736388888888890.0276401716816836243.717331660169
Winsorized Mean ( 24 / 24 )6.733055555555560.0272117406603976247.432005162185
Trimmed Mean ( 1 / 24 )6.763857142857140.0490216045907504137.977065404615
Trimmed Mean ( 2 / 24 )6.762794117647060.0484767286603399139.505991937527
Trimmed Mean ( 3 / 24 )6.761515151515150.0479044515327611141.145862966223
Trimmed Mean ( 4 / 24 )6.7606250.047308445733277142.905244406382
Trimmed Mean ( 5 / 24 )6.759838709677420.0466812338712479144.80848403283
Trimmed Mean ( 6 / 24 )6.7590.0460537023791232146.763444649001
Trimmed Mean ( 7 / 24 )6.758103448275860.0455041377406004148.516240145037
Trimmed Mean ( 8 / 24 )6.757142857142860.0448863747915723150.538841430597
Trimmed Mean ( 9 / 24 )6.756111111111110.0441864234650756152.900157589153
Trimmed Mean ( 10 / 24 )6.754807692307690.0435236195515715155.19866596352
Trimmed Mean ( 11 / 24 )6.75340.0428615331084664157.563192686311
Trimmed Mean ( 12 / 24 )6.75250.0421596720013618160.164908298667
Trimmed Mean ( 13 / 24 )6.751521739130430.0413445139054472163.299095850318
Trimmed Mean ( 14 / 24 )6.750.0405016116924114166.660034451536
Trimmed Mean ( 15 / 24 )6.747619047619050.0396790397217665170.054998682782
Trimmed Mean ( 16 / 24 )6.745250.038772822063518173.968507862282
Trimmed Mean ( 17 / 24 )6.745263157894740.0384510493008137175.4246836055
Trimmed Mean ( 18 / 24 )6.745555555555560.0380005105321687177.512234996033
Trimmed Mean ( 19 / 24 )6.745882352941180.0376235164803292179.299623852761
Trimmed Mean ( 20 / 24 )6.74593750.0370778914621943181.939620457608
Trimmed Mean ( 21 / 24 )6.7460.0363969178940183185.345364122402
Trimmed Mean ( 22 / 24 )6.746071428571430.0355245622074394189.898791410262
Trimmed Mean ( 23 / 24 )6.747692307692310.0348769604017309193.471341251327
Trimmed Mean ( 24 / 24 )6.749166666666670.034441278879003195.961557942649
Median6.79
Midrange6.805
Midmean - Weighted Average at Xnp6.72631578947369
Midmean - Weighted Average at X(n+1)p6.74555555555556
Midmean - Empirical Distribution Function6.72631578947369
Midmean - Empirical Distribution Function - Averaging6.74555555555556
Midmean - Empirical Distribution Function - Interpolation6.74555555555556
Midmean - Closest Observation6.72631578947369
Midmean - True Basic - Statistics Graphics Toolkit6.74555555555556
Midmean - MS Excel (old versions)6.73589743589744
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')