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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 24 Oct 2009 07:03:23 -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/2009/Oct/24/t1256389452wataavje8mcsdqn.htm/, Retrieved Fri, 03 May 2024 11:26:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=50124, Retrieved Fri, 03 May 2024 11:26:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact99
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [central tendency ...] [2009-10-24 13:03:23] [7044607f369a4bf4b500443314d450f3] [Current]
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Dataseries X:
10,1200
10,1200
10,0500
10,1400
10,1700
10,2000
10,2000
10,3500
10,4300
10,5200
10,5700
10,5700
10,5700
10,6500
10,5700
10,6100
10,6300
10,7100
10,7200
10,7700
10,7900
10,8200
10,9000
10,8300
10,9200
10,9100
10,8800
10,8700
11,0000
10,9900
11,0300
11,0400
10,9900
10,9000
11,0000
10,9900
10,9200
10,9800
11,1500
11,1900
11,3300
11,3800
11,4000
11,4500
11,5600
11,6100
11,8200
11,7700
11,8500
11,8200
11,9200
11,8600
11,8700
11,9400
11,8600
11,9200
11,8300
11,9100
11,9300
11,9900
11,9600
12,1200
11,8500
12,0100
12,1000
12,2100
12,3100
12,3100
12,3900
12,3500
12,4100
12,5100




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50124&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=50124&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50124&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 time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean11.24055555555560.0812665990962663138.317041448237
Geometric Mean11.2197284505257
Harmonic Mean11.1989575410599
Quadratic Mean11.2613938598500
Winsorized Mean ( 1 / 24 )11.24013888888890.0807768650000199139.150471968504
Winsorized Mean ( 2 / 24 )11.23958333333330.0806644059115553139.337582745691
Winsorized Mean ( 3 / 24 )11.238750.0801724319079082140.182226390608
Winsorized Mean ( 4 / 24 )11.23819444444440.0794255900205534141.493370606832
Winsorized Mean ( 5 / 24 )11.24027777777780.0790351569476095142.218706356574
Winsorized Mean ( 6 / 24 )11.23194444444440.0774997195433587144.928839880001
Winsorized Mean ( 7 / 24 )11.23777777777780.0733664623797643153.173226747776
Winsorized Mean ( 8 / 24 )11.24444444444440.0715201824522306157.22057828858
Winsorized Mean ( 9 / 24 )11.24444444444440.0679296126343161165.530819452429
Winsorized Mean ( 10 / 24 )11.24861111111110.0664698696127523169.228722376688
Winsorized Mean ( 11 / 24 )11.24402777777780.0657583841867618170.990025330357
Winsorized Mean ( 12 / 24 )11.24069444444440.0652512078413948172.26799037601
Winsorized Mean ( 13 / 24 )11.23888888888890.0649796993565268172.960001357101
Winsorized Mean ( 14 / 24 )11.24472222222220.0635777875005668176.865579383711
Winsorized Mean ( 15 / 24 )11.24888888888890.062996558130499178.563547322483
Winsorized Mean ( 16 / 24 )11.25111111111110.0620529569495265181.314665153873
Winsorized Mean ( 17 / 24 )11.25583333333330.0587569294684752191.566057572365
Winsorized Mean ( 18 / 24 )11.25583333333330.058063679224369193.853257039374
Winsorized Mean ( 19 / 24 )11.26902777777780.0563832874751306199.864681227541
Winsorized Mean ( 20 / 24 )11.27180555555560.0552863956093305203.880275270708
Winsorized Mean ( 21 / 24 )11.28055555555560.054225911583354208.028878190743
Winsorized Mean ( 22 / 24 )11.27750.0529603854372785212.942181347151
Winsorized Mean ( 23 / 24 )11.28708333333330.0509938155982123221.342200047667
Winsorized Mean ( 24 / 24 )11.29041666666670.050611455857407223.080258716057
Trimmed Mean ( 1 / 24 )11.23942857142860.0797667110198668140.903748289550
Trimmed Mean ( 2 / 24 )11.23867647058820.0785466382574865143.082845044830
Trimmed Mean ( 3 / 24 )11.23818181818180.077145431966098145.675272427284
Trimmed Mean ( 4 / 24 )11.237968750.0756739493583038148.505117617029
Trimmed Mean ( 5 / 24 )11.23790322580650.0741595379937792151.536855943589
Trimmed Mean ( 6 / 24 )11.23733333333330.0724334359017632155.140139266261
Trimmed Mean ( 7 / 24 )11.23844827586210.0707550676357291158.835948454200
Trimmed Mean ( 8 / 24 )11.23857142857140.0697497514641704161.127046228180
Trimmed Mean ( 9 / 24 )11.23759259259260.0689047465273849163.088802425627
Trimmed Mean ( 10 / 24 )11.23653846153850.0685905752617288163.820443532685
Trimmed Mean ( 11 / 24 )11.23480.068406492113434164.235873714589
Trimmed Mean ( 12 / 24 )11.23354166666670.0682113746359662164.687220080498
Trimmed Mean ( 13 / 24 )11.23260869565220.0679488545812171165.309757830078
Trimmed Mean ( 14 / 24 )11.23181818181820.0675447332215446166.287105539053
Trimmed Mean ( 15 / 24 )11.23023809523810.0671793481616464167.168012232211
Trimmed Mean ( 16 / 24 )11.2280.0666758327032116168.396847025192
Trimmed Mean ( 17 / 24 )11.22526315789470.0660603810634287169.924287102078
Trimmed Mean ( 18 / 24 )11.22166666666670.0657924828050347170.561532081412
Trimmed Mean ( 19 / 24 )11.21764705882350.0653689090045393171.605236031162
Trimmed Mean ( 20 / 24 )11.21156250.0649148160417471172.711919768667
Trimmed Mean ( 21 / 24 )11.20433333333330.064267192490814174.339859873836
Trimmed Mean ( 22 / 24 )11.1950.0632696003467884176.941215665009
Trimmed Mean ( 23 / 24 )11.18461538461540.0618564859337403180.815563894079
Trimmed Mean ( 24 / 24 )11.171250.0598921509580079186.522771703966
Median11.015
Midrange11.28
Midmean - Weighted Average at Xnp11.2078378378378
Midmean - Weighted Average at X(n+1)p11.2216666666667
Midmean - Empirical Distribution Function11.2078378378378
Midmean - Empirical Distribution Function - Averaging11.2216666666667
Midmean - Empirical Distribution Function - Interpolation11.2216666666667
Midmean - Closest Observation11.2078378378378
Midmean - True Basic - Statistics Graphics Toolkit11.2216666666667
Midmean - MS Excel (old versions)11.2252631578947
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 11.2405555555556 & 0.0812665990962663 & 138.317041448237 \tabularnewline
Geometric Mean & 11.2197284505257 &  &  \tabularnewline
Harmonic Mean & 11.1989575410599 &  &  \tabularnewline
Quadratic Mean & 11.2613938598500 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 11.2401388888889 & 0.0807768650000199 & 139.150471968504 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 11.2395833333333 & 0.0806644059115553 & 139.337582745691 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 11.23875 & 0.0801724319079082 & 140.182226390608 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 11.2381944444444 & 0.0794255900205534 & 141.493370606832 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 11.2402777777778 & 0.0790351569476095 & 142.218706356574 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 11.2319444444444 & 0.0774997195433587 & 144.928839880001 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 11.2377777777778 & 0.0733664623797643 & 153.173226747776 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 11.2444444444444 & 0.0715201824522306 & 157.22057828858 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 11.2444444444444 & 0.0679296126343161 & 165.530819452429 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 11.2486111111111 & 0.0664698696127523 & 169.228722376688 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 11.2440277777778 & 0.0657583841867618 & 170.990025330357 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 11.2406944444444 & 0.0652512078413948 & 172.26799037601 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 11.2388888888889 & 0.0649796993565268 & 172.960001357101 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 11.2447222222222 & 0.0635777875005668 & 176.865579383711 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 11.2488888888889 & 0.062996558130499 & 178.563547322483 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 11.2511111111111 & 0.0620529569495265 & 181.314665153873 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 11.2558333333333 & 0.0587569294684752 & 191.566057572365 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 11.2558333333333 & 0.058063679224369 & 193.853257039374 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 11.2690277777778 & 0.0563832874751306 & 199.864681227541 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 11.2718055555556 & 0.0552863956093305 & 203.880275270708 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 11.2805555555556 & 0.054225911583354 & 208.028878190743 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 11.2775 & 0.0529603854372785 & 212.942181347151 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 11.2870833333333 & 0.0509938155982123 & 221.342200047667 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 11.2904166666667 & 0.050611455857407 & 223.080258716057 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 11.2394285714286 & 0.0797667110198668 & 140.903748289550 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 11.2386764705882 & 0.0785466382574865 & 143.082845044830 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 11.2381818181818 & 0.077145431966098 & 145.675272427284 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 11.23796875 & 0.0756739493583038 & 148.505117617029 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 11.2379032258065 & 0.0741595379937792 & 151.536855943589 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 11.2373333333333 & 0.0724334359017632 & 155.140139266261 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 11.2384482758621 & 0.0707550676357291 & 158.835948454200 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 11.2385714285714 & 0.0697497514641704 & 161.127046228180 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 11.2375925925926 & 0.0689047465273849 & 163.088802425627 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 11.2365384615385 & 0.0685905752617288 & 163.820443532685 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 11.2348 & 0.068406492113434 & 164.235873714589 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 11.2335416666667 & 0.0682113746359662 & 164.687220080498 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 11.2326086956522 & 0.0679488545812171 & 165.309757830078 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 11.2318181818182 & 0.0675447332215446 & 166.287105539053 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 11.2302380952381 & 0.0671793481616464 & 167.168012232211 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 11.228 & 0.0666758327032116 & 168.396847025192 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 11.2252631578947 & 0.0660603810634287 & 169.924287102078 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 11.2216666666667 & 0.0657924828050347 & 170.561532081412 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 11.2176470588235 & 0.0653689090045393 & 171.605236031162 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 11.2115625 & 0.0649148160417471 & 172.711919768667 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 11.2043333333333 & 0.064267192490814 & 174.339859873836 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 11.195 & 0.0632696003467884 & 176.941215665009 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 11.1846153846154 & 0.0618564859337403 & 180.815563894079 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 11.17125 & 0.0598921509580079 & 186.522771703966 \tabularnewline
Median & 11.015 &  &  \tabularnewline
Midrange & 11.28 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 11.2078378378378 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 11.2216666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 11.2078378378378 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 11.2216666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 11.2216666666667 &  &  \tabularnewline
Midmean - Closest Observation & 11.2078378378378 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 11.2216666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 11.2252631578947 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50124&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]11.2405555555556[/C][C]0.0812665990962663[/C][C]138.317041448237[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]11.2197284505257[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]11.1989575410599[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]11.2613938598500[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]11.2401388888889[/C][C]0.0807768650000199[/C][C]139.150471968504[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]11.2395833333333[/C][C]0.0806644059115553[/C][C]139.337582745691[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]11.23875[/C][C]0.0801724319079082[/C][C]140.182226390608[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]11.2381944444444[/C][C]0.0794255900205534[/C][C]141.493370606832[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]11.2402777777778[/C][C]0.0790351569476095[/C][C]142.218706356574[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]11.2319444444444[/C][C]0.0774997195433587[/C][C]144.928839880001[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]11.2377777777778[/C][C]0.0733664623797643[/C][C]153.173226747776[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]11.2444444444444[/C][C]0.0715201824522306[/C][C]157.22057828858[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]11.2444444444444[/C][C]0.0679296126343161[/C][C]165.530819452429[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]11.2486111111111[/C][C]0.0664698696127523[/C][C]169.228722376688[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]11.2440277777778[/C][C]0.0657583841867618[/C][C]170.990025330357[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]11.2406944444444[/C][C]0.0652512078413948[/C][C]172.26799037601[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]11.2388888888889[/C][C]0.0649796993565268[/C][C]172.960001357101[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]11.2447222222222[/C][C]0.0635777875005668[/C][C]176.865579383711[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]11.2488888888889[/C][C]0.062996558130499[/C][C]178.563547322483[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]11.2511111111111[/C][C]0.0620529569495265[/C][C]181.314665153873[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]11.2558333333333[/C][C]0.0587569294684752[/C][C]191.566057572365[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]11.2558333333333[/C][C]0.058063679224369[/C][C]193.853257039374[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]11.2690277777778[/C][C]0.0563832874751306[/C][C]199.864681227541[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]11.2718055555556[/C][C]0.0552863956093305[/C][C]203.880275270708[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]11.2805555555556[/C][C]0.054225911583354[/C][C]208.028878190743[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]11.2775[/C][C]0.0529603854372785[/C][C]212.942181347151[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]11.2870833333333[/C][C]0.0509938155982123[/C][C]221.342200047667[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]11.2904166666667[/C][C]0.050611455857407[/C][C]223.080258716057[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]11.2394285714286[/C][C]0.0797667110198668[/C][C]140.903748289550[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]11.2386764705882[/C][C]0.0785466382574865[/C][C]143.082845044830[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]11.2381818181818[/C][C]0.077145431966098[/C][C]145.675272427284[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]11.23796875[/C][C]0.0756739493583038[/C][C]148.505117617029[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]11.2379032258065[/C][C]0.0741595379937792[/C][C]151.536855943589[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]11.2373333333333[/C][C]0.0724334359017632[/C][C]155.140139266261[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]11.2384482758621[/C][C]0.0707550676357291[/C][C]158.835948454200[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]11.2385714285714[/C][C]0.0697497514641704[/C][C]161.127046228180[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]11.2375925925926[/C][C]0.0689047465273849[/C][C]163.088802425627[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]11.2365384615385[/C][C]0.0685905752617288[/C][C]163.820443532685[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]11.2348[/C][C]0.068406492113434[/C][C]164.235873714589[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]11.2335416666667[/C][C]0.0682113746359662[/C][C]164.687220080498[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]11.2326086956522[/C][C]0.0679488545812171[/C][C]165.309757830078[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]11.2318181818182[/C][C]0.0675447332215446[/C][C]166.287105539053[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]11.2302380952381[/C][C]0.0671793481616464[/C][C]167.168012232211[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]11.228[/C][C]0.0666758327032116[/C][C]168.396847025192[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]11.2252631578947[/C][C]0.0660603810634287[/C][C]169.924287102078[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]11.2216666666667[/C][C]0.0657924828050347[/C][C]170.561532081412[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]11.2176470588235[/C][C]0.0653689090045393[/C][C]171.605236031162[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]11.2115625[/C][C]0.0649148160417471[/C][C]172.711919768667[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]11.2043333333333[/C][C]0.064267192490814[/C][C]174.339859873836[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]11.195[/C][C]0.0632696003467884[/C][C]176.941215665009[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]11.1846153846154[/C][C]0.0618564859337403[/C][C]180.815563894079[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]11.17125[/C][C]0.0598921509580079[/C][C]186.522771703966[/C][/ROW]
[ROW][C]Median[/C][C]11.015[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]11.28[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]11.2078378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]11.2216666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]11.2078378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]11.2216666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]11.2216666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]11.2078378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]11.2216666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]11.2252631578947[/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=50124&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50124&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 Mean11.24055555555560.0812665990962663138.317041448237
Geometric Mean11.2197284505257
Harmonic Mean11.1989575410599
Quadratic Mean11.2613938598500
Winsorized Mean ( 1 / 24 )11.24013888888890.0807768650000199139.150471968504
Winsorized Mean ( 2 / 24 )11.23958333333330.0806644059115553139.337582745691
Winsorized Mean ( 3 / 24 )11.238750.0801724319079082140.182226390608
Winsorized Mean ( 4 / 24 )11.23819444444440.0794255900205534141.493370606832
Winsorized Mean ( 5 / 24 )11.24027777777780.0790351569476095142.218706356574
Winsorized Mean ( 6 / 24 )11.23194444444440.0774997195433587144.928839880001
Winsorized Mean ( 7 / 24 )11.23777777777780.0733664623797643153.173226747776
Winsorized Mean ( 8 / 24 )11.24444444444440.0715201824522306157.22057828858
Winsorized Mean ( 9 / 24 )11.24444444444440.0679296126343161165.530819452429
Winsorized Mean ( 10 / 24 )11.24861111111110.0664698696127523169.228722376688
Winsorized Mean ( 11 / 24 )11.24402777777780.0657583841867618170.990025330357
Winsorized Mean ( 12 / 24 )11.24069444444440.0652512078413948172.26799037601
Winsorized Mean ( 13 / 24 )11.23888888888890.0649796993565268172.960001357101
Winsorized Mean ( 14 / 24 )11.24472222222220.0635777875005668176.865579383711
Winsorized Mean ( 15 / 24 )11.24888888888890.062996558130499178.563547322483
Winsorized Mean ( 16 / 24 )11.25111111111110.0620529569495265181.314665153873
Winsorized Mean ( 17 / 24 )11.25583333333330.0587569294684752191.566057572365
Winsorized Mean ( 18 / 24 )11.25583333333330.058063679224369193.853257039374
Winsorized Mean ( 19 / 24 )11.26902777777780.0563832874751306199.864681227541
Winsorized Mean ( 20 / 24 )11.27180555555560.0552863956093305203.880275270708
Winsorized Mean ( 21 / 24 )11.28055555555560.054225911583354208.028878190743
Winsorized Mean ( 22 / 24 )11.27750.0529603854372785212.942181347151
Winsorized Mean ( 23 / 24 )11.28708333333330.0509938155982123221.342200047667
Winsorized Mean ( 24 / 24 )11.29041666666670.050611455857407223.080258716057
Trimmed Mean ( 1 / 24 )11.23942857142860.0797667110198668140.903748289550
Trimmed Mean ( 2 / 24 )11.23867647058820.0785466382574865143.082845044830
Trimmed Mean ( 3 / 24 )11.23818181818180.077145431966098145.675272427284
Trimmed Mean ( 4 / 24 )11.237968750.0756739493583038148.505117617029
Trimmed Mean ( 5 / 24 )11.23790322580650.0741595379937792151.536855943589
Trimmed Mean ( 6 / 24 )11.23733333333330.0724334359017632155.140139266261
Trimmed Mean ( 7 / 24 )11.23844827586210.0707550676357291158.835948454200
Trimmed Mean ( 8 / 24 )11.23857142857140.0697497514641704161.127046228180
Trimmed Mean ( 9 / 24 )11.23759259259260.0689047465273849163.088802425627
Trimmed Mean ( 10 / 24 )11.23653846153850.0685905752617288163.820443532685
Trimmed Mean ( 11 / 24 )11.23480.068406492113434164.235873714589
Trimmed Mean ( 12 / 24 )11.23354166666670.0682113746359662164.687220080498
Trimmed Mean ( 13 / 24 )11.23260869565220.0679488545812171165.309757830078
Trimmed Mean ( 14 / 24 )11.23181818181820.0675447332215446166.287105539053
Trimmed Mean ( 15 / 24 )11.23023809523810.0671793481616464167.168012232211
Trimmed Mean ( 16 / 24 )11.2280.0666758327032116168.396847025192
Trimmed Mean ( 17 / 24 )11.22526315789470.0660603810634287169.924287102078
Trimmed Mean ( 18 / 24 )11.22166666666670.0657924828050347170.561532081412
Trimmed Mean ( 19 / 24 )11.21764705882350.0653689090045393171.605236031162
Trimmed Mean ( 20 / 24 )11.21156250.0649148160417471172.711919768667
Trimmed Mean ( 21 / 24 )11.20433333333330.064267192490814174.339859873836
Trimmed Mean ( 22 / 24 )11.1950.0632696003467884176.941215665009
Trimmed Mean ( 23 / 24 )11.18461538461540.0618564859337403180.815563894079
Trimmed Mean ( 24 / 24 )11.171250.0598921509580079186.522771703966
Median11.015
Midrange11.28
Midmean - Weighted Average at Xnp11.2078378378378
Midmean - Weighted Average at X(n+1)p11.2216666666667
Midmean - Empirical Distribution Function11.2078378378378
Midmean - Empirical Distribution Function - Averaging11.2216666666667
Midmean - Empirical Distribution Function - Interpolation11.2216666666667
Midmean - Closest Observation11.2078378378378
Midmean - True Basic - Statistics Graphics Toolkit11.2216666666667
Midmean - MS Excel (old versions)11.2252631578947
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')