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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 computationThu, 18 Dec 2014 13:28:36 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/18/t14189093311o3ybqluzkt64az.htm/, Retrieved Fri, 17 May 2024 11:29:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270913, Retrieved Fri, 17 May 2024 11:29:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact76
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-12-18 13:28:36] [ce2f801bda31f4b58163e4bbe4fada83] [Current]
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Dataseries X:
12,9
12,2
12,8
7,4
6,7
12,6
14,8
13,3
11,1
8,2
11,4
6,4
10,6
12
6,3
11,9
9,3
10
6,4
13,8
10,8
13,8
11,7
10,9
9,9
11,5
8,3
11,7
9
9,7
10,8
10,3
10,4
9,3
11,8
5,9
11,4
13
10,8
11,3
11,8
12,7
10,9
13,3
10,1
14,3
9,3
12,5
7,6
15,9
9,2
11,1
13
14,5
12,3
11,4
12,6
13
13,2
7,7
4,35
12,7
18,1
17,85
17,1
19,1
16,1
13,35
18,4
14,7
10,6
12,6
16,2
13,6
14,1
14,5
16,15
14,75
14,8
12,45
12,65
17,35
8,6
18,4
16,1
17,75
15,25
17,65
16,35
17,65
13,6
14,35
14,75
18,25
9,9
16
18,25
16,85
18,95
15,6
17,1
16,1
15,4
15,4
13,35
19,1
7,6
19,1
14,75
19,25
13,6
12,75
9,85
15,25
11,9
16,35
12,4
18,15
17,75
12,35
15,6
19,3
17,1
18,4
19,05
18,55
19,1
12,85
9,5
4,5
13,6
11,7
13,35
17,6
14,05
16,1
13,35
11,85
11,95
13,2
7,7
14,6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270913&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270913&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270913&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean13.20457746478870.2924327403592145.1542376840873
Geometric Mean12.6866269654666
Harmonic Mean12.0821799092074
Quadratic Mean13.6535251858266
Winsorized Mean ( 1 / 47 )13.20528169014080.29215584265351245.1994441398248
Winsorized Mean ( 2 / 47 )13.22288732394370.28798424850975945.9153144394826
Winsorized Mean ( 3 / 47 )13.2313380281690.28649714416335346.1831410808927
Winsorized Mean ( 4 / 47 )13.23415492957750.28601679367248446.2705520177664
Winsorized Mean ( 5 / 47 )13.23415492957750.28601679367248446.2705520177664
Winsorized Mean ( 6 / 47 )13.24471830985920.28359823022158746.7024011380836
Winsorized Mean ( 7 / 47 )13.27429577464790.27746576006070847.8412030794125
Winsorized Mean ( 8 / 47 )13.26302816901410.2726044302674248.6530176930848
Winsorized Mean ( 9 / 47 )13.25352112676060.27131106006093548.8499109611819
Winsorized Mean ( 10 / 47 )13.26056338028170.27027690094230749.0628808235162
Winsorized Mean ( 11 / 47 )13.26056338028170.27027690094230749.0628808235162
Winsorized Mean ( 12 / 47 )13.29014084507040.26258325326982950.6130557816402
Winsorized Mean ( 13 / 47 )13.29929577464790.26133287607865550.8902514456126
Winsorized Mean ( 14 / 47 )13.3190140845070.25607089558298252.0129945036682
Winsorized Mean ( 15 / 47 )13.3559859154930.24998825384170953.4264538843088
Winsorized Mean ( 16 / 47 )13.35035211267610.24349108283786254.8289159384367
Winsorized Mean ( 17 / 47 )13.35035211267610.24049117346537355.5128569597932
Winsorized Mean ( 18 / 47 )13.35035211267610.24049117346537355.5128569597932
Winsorized Mean ( 19 / 47 )13.33697183098590.23876601467467355.8579153283519
Winsorized Mean ( 20 / 47 )13.36514084507040.23543687855345456.7674058846987
Winsorized Mean ( 21 / 47 )13.3873239436620.23108573836264257.9322810594797
Winsorized Mean ( 22 / 47 )13.37183098591550.22352272266791959.823139349379
Winsorized Mean ( 23 / 47 )13.33943661971830.21757787938924261.308790476142
Winsorized Mean ( 24 / 47 )13.33943661971830.21757787938924261.308790476142
Winsorized Mean ( 25 / 47 )13.35704225352110.21561889348888661.9474575599267
Winsorized Mean ( 26 / 47 )13.32957746478870.20803409031067464.0740055866929
Winsorized Mean ( 27 / 47 )13.27253521126760.19276091906060368.8549072911132
Winsorized Mean ( 28 / 47 )13.29225352112680.19062162437565869.7310893486655
Winsorized Mean ( 29 / 47 )13.30246478873240.18281703310098472.7638150728791
Winsorized Mean ( 30 / 47 )13.29190140845070.18163388828815473.1796336780704
Winsorized Mean ( 31 / 47 )13.32464788732390.17589600130791775.7529891995574
Winsorized Mean ( 32 / 47 )13.32464788732390.17589600130791775.7529891995574
Winsorized Mean ( 33 / 47 )13.32464788732390.17589600130791775.7529891995574
Winsorized Mean ( 34 / 47 )13.34859154929580.17347876396202776.9465451818511
Winsorized Mean ( 35 / 47 )13.32394366197180.17072234431009178.0445214468875
Winsorized Mean ( 36 / 47 )13.34929577464790.16286748625488981.9641543049062
Winsorized Mean ( 37 / 47 )13.27112676056340.15433932841240285.9866820536002
Winsorized Mean ( 38 / 47 )13.32464788732390.14909052899262189.3728661193727
Winsorized Mean ( 39 / 47 )13.29718309859150.14056478704383894.5982516549082
Winsorized Mean ( 40 / 47 )13.29718309859150.14056478704383894.5982516549082
Winsorized Mean ( 41 / 47 )13.25387323943660.13601256973117697.4459438979235
Winsorized Mean ( 42 / 47 )13.28345070422540.13317815284539699.7419653330518
Winsorized Mean ( 43 / 47 )13.20774647887320.1135050756629116.362606709317
Winsorized Mean ( 44 / 47 )13.20774647887320.1135050756629116.362606709317
Winsorized Mean ( 45 / 47 )13.19190140845070.111934699786384117.853547055793
Winsorized Mean ( 46 / 47 )13.22429577464790.108900820251074121.434308246337
Winsorized Mean ( 47 / 47 )13.22429577464790.108900820251074121.434308246337
Trimmed Mean ( 1 / 47 )13.22428571428570.28643603596878746.168372877939
Trimmed Mean ( 2 / 47 )13.24384057971010.28017957779923947.2691146290467
Trimmed Mean ( 3 / 47 )13.25477941176470.27573326615085848.071020217462
Trimmed Mean ( 4 / 47 )13.26305970149250.2714633062645848.8576518277788
Trimmed Mean ( 5 / 47 )13.27083333333330.26693889445173749.7148733630224
Trimmed Mean ( 6 / 47 )13.27884615384620.26197831449252850.6868142104369
Trimmed Mean ( 7 / 47 )13.27884615384620.25708187864462251.6522059969937
Trimmed Mean ( 8 / 47 )13.28690476190480.25293840053878852.530199975971
Trimmed Mean ( 9 / 47 )13.29032258064520.24925911554219953.3193040974067
Trimmed Mean ( 10 / 47 )13.29508196721310.24541825767810454.1731576656013
Trimmed Mean ( 11 / 47 )13.29916666666670.24134165095080555.105144985428
Trimmed Mean ( 12 / 47 )13.30338983050850.23683329060304756.1719587505377
Trimmed Mean ( 13 / 47 )13.30474137931030.23294363170159557.1157119948828
Trimmed Mean ( 14 / 47 )13.30474137931030.22879938183183858.1502505504539
Trimmed Mean ( 15 / 47 )13.30401785714290.22488927133160859.158081567731
Trimmed Mean ( 16 / 47 )13.29954545454550.22130526380820360.0959291509292
Trimmed Mean ( 17 / 47 )13.29537037037040.21810325030545260.9590657257527
Trimmed Mean ( 18 / 47 )13.29103773584910.21487767594578461.8539719277424
Trimmed Mean ( 19 / 47 )13.28653846153850.21126025564858662.8918033860544
Trimmed Mean ( 20 / 47 )13.28284313725490.2074033739628664.0435248639372
Trimmed Mean ( 21 / 47 )13.2770.20344683866213365.2602915204265
Trimmed Mean ( 22 / 47 )13.2693877551020.1994833858107766.5187614556002
Trimmed Mean ( 23 / 47 )13.26250.19588138641499367.7067905365045
Trimmed Mean ( 24 / 47 )13.25744680851060.1924848611808468.8752701234787
Trimmed Mean ( 25 / 47 )13.25217391304350.18861990449800670.258618507484
Trimmed Mean ( 26 / 47 )13.24555555555560.18443429119355171.8172063873699
Trimmed Mean ( 27 / 47 )13.24034090909090.18055241837244173.3323930437695
Trimmed Mean ( 28 / 47 )13.24034090909090.17786673722120174.4396682367021
Trimmed Mean ( 29 / 47 )13.2351190476190.17500262222833575.6281184767076
Trimmed Mean ( 30 / 47 )13.23109756097560.17256422080211476.6734697347733
Trimmed Mean ( 31 / 47 )13.23109756097560.16985869965386377.894730078223
Trimmed Mean ( 32 / 47 )13.22179487179490.16734690456212579.0083025819369
Trimmed Mean ( 33 / 47 )13.21578947368420.16439471788563780.3905967518856
Trimmed Mean ( 34 / 47 )13.20945945945950.16092129836814482.0864583707238
Trimmed Mean ( 35 / 47 )13.20138888888890.15711780833076184.0222316562461
Trimmed Mean ( 36 / 47 )13.19428571428570.15299813547471886.23821246806
Trimmed Mean ( 37 / 47 )13.18529411764710.14914910408615688.4034416326803
Trimmed Mean ( 38 / 47 )13.1803030303030.14577930915901590.4127143031392
Trimmed Mean ( 39 / 47 )13.1718750.14241258022363292.4909511457209
Trimmed Mean ( 40 / 47 )13.16451612903230.13956468497204594.3255532849814
Trimmed Mean ( 41 / 47 )13.15666666666670.13607941903995896.6837363025736
Trimmed Mean ( 42 / 47 )13.15086206896550.13254735470437199.2163298792099
Trimmed Mean ( 43 / 47 )13.14285714285710.128612908171859102.189254015585
Trimmed Mean ( 44 / 47 )13.13888888888890.126941021060409103.503885340865
Trimmed Mean ( 45 / 47 )13.13461538461540.124773841121607105.2673802982
Trimmed Mean ( 46 / 47 )13.1310.122256755583134107.405107696244
Trimmed Mean ( 47 / 47 )13.1250.119516238251017109.817713409235
Median13
Midrange11.825
Midmean - Weighted Average at Xnp13.1305555555556
Midmean - Weighted Average at X(n+1)p13.1698630136986
Midmean - Empirical Distribution Function13.1698630136986
Midmean - Empirical Distribution Function - Averaging13.1698630136986
Midmean - Empirical Distribution Function - Interpolation13.1942857142857
Midmean - Closest Observation13.1698630136986
Midmean - True Basic - Statistics Graphics Toolkit13.1698630136986
Midmean - MS Excel (old versions)13.1698630136986
Number of observations142

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 13.2045774647887 & 0.29243274035921 & 45.1542376840873 \tabularnewline
Geometric Mean & 12.6866269654666 &  &  \tabularnewline
Harmonic Mean & 12.0821799092074 &  &  \tabularnewline
Quadratic Mean & 13.6535251858266 &  &  \tabularnewline
Winsorized Mean ( 1 / 47 ) & 13.2052816901408 & 0.292155842653512 & 45.1994441398248 \tabularnewline
Winsorized Mean ( 2 / 47 ) & 13.2228873239437 & 0.287984248509759 & 45.9153144394826 \tabularnewline
Winsorized Mean ( 3 / 47 ) & 13.231338028169 & 0.286497144163353 & 46.1831410808927 \tabularnewline
Winsorized Mean ( 4 / 47 ) & 13.2341549295775 & 0.286016793672484 & 46.2705520177664 \tabularnewline
Winsorized Mean ( 5 / 47 ) & 13.2341549295775 & 0.286016793672484 & 46.2705520177664 \tabularnewline
Winsorized Mean ( 6 / 47 ) & 13.2447183098592 & 0.283598230221587 & 46.7024011380836 \tabularnewline
Winsorized Mean ( 7 / 47 ) & 13.2742957746479 & 0.277465760060708 & 47.8412030794125 \tabularnewline
Winsorized Mean ( 8 / 47 ) & 13.2630281690141 & 0.27260443026742 & 48.6530176930848 \tabularnewline
Winsorized Mean ( 9 / 47 ) & 13.2535211267606 & 0.271311060060935 & 48.8499109611819 \tabularnewline
Winsorized Mean ( 10 / 47 ) & 13.2605633802817 & 0.270276900942307 & 49.0628808235162 \tabularnewline
Winsorized Mean ( 11 / 47 ) & 13.2605633802817 & 0.270276900942307 & 49.0628808235162 \tabularnewline
Winsorized Mean ( 12 / 47 ) & 13.2901408450704 & 0.262583253269829 & 50.6130557816402 \tabularnewline
Winsorized Mean ( 13 / 47 ) & 13.2992957746479 & 0.261332876078655 & 50.8902514456126 \tabularnewline
Winsorized Mean ( 14 / 47 ) & 13.319014084507 & 0.256070895582982 & 52.0129945036682 \tabularnewline
Winsorized Mean ( 15 / 47 ) & 13.355985915493 & 0.249988253841709 & 53.4264538843088 \tabularnewline
Winsorized Mean ( 16 / 47 ) & 13.3503521126761 & 0.243491082837862 & 54.8289159384367 \tabularnewline
Winsorized Mean ( 17 / 47 ) & 13.3503521126761 & 0.240491173465373 & 55.5128569597932 \tabularnewline
Winsorized Mean ( 18 / 47 ) & 13.3503521126761 & 0.240491173465373 & 55.5128569597932 \tabularnewline
Winsorized Mean ( 19 / 47 ) & 13.3369718309859 & 0.238766014674673 & 55.8579153283519 \tabularnewline
Winsorized Mean ( 20 / 47 ) & 13.3651408450704 & 0.235436878553454 & 56.7674058846987 \tabularnewline
Winsorized Mean ( 21 / 47 ) & 13.387323943662 & 0.231085738362642 & 57.9322810594797 \tabularnewline
Winsorized Mean ( 22 / 47 ) & 13.3718309859155 & 0.223522722667919 & 59.823139349379 \tabularnewline
Winsorized Mean ( 23 / 47 ) & 13.3394366197183 & 0.217577879389242 & 61.308790476142 \tabularnewline
Winsorized Mean ( 24 / 47 ) & 13.3394366197183 & 0.217577879389242 & 61.308790476142 \tabularnewline
Winsorized Mean ( 25 / 47 ) & 13.3570422535211 & 0.215618893488886 & 61.9474575599267 \tabularnewline
Winsorized Mean ( 26 / 47 ) & 13.3295774647887 & 0.208034090310674 & 64.0740055866929 \tabularnewline
Winsorized Mean ( 27 / 47 ) & 13.2725352112676 & 0.192760919060603 & 68.8549072911132 \tabularnewline
Winsorized Mean ( 28 / 47 ) & 13.2922535211268 & 0.190621624375658 & 69.7310893486655 \tabularnewline
Winsorized Mean ( 29 / 47 ) & 13.3024647887324 & 0.182817033100984 & 72.7638150728791 \tabularnewline
Winsorized Mean ( 30 / 47 ) & 13.2919014084507 & 0.181633888288154 & 73.1796336780704 \tabularnewline
Winsorized Mean ( 31 / 47 ) & 13.3246478873239 & 0.175896001307917 & 75.7529891995574 \tabularnewline
Winsorized Mean ( 32 / 47 ) & 13.3246478873239 & 0.175896001307917 & 75.7529891995574 \tabularnewline
Winsorized Mean ( 33 / 47 ) & 13.3246478873239 & 0.175896001307917 & 75.7529891995574 \tabularnewline
Winsorized Mean ( 34 / 47 ) & 13.3485915492958 & 0.173478763962027 & 76.9465451818511 \tabularnewline
Winsorized Mean ( 35 / 47 ) & 13.3239436619718 & 0.170722344310091 & 78.0445214468875 \tabularnewline
Winsorized Mean ( 36 / 47 ) & 13.3492957746479 & 0.162867486254889 & 81.9641543049062 \tabularnewline
Winsorized Mean ( 37 / 47 ) & 13.2711267605634 & 0.154339328412402 & 85.9866820536002 \tabularnewline
Winsorized Mean ( 38 / 47 ) & 13.3246478873239 & 0.149090528992621 & 89.3728661193727 \tabularnewline
Winsorized Mean ( 39 / 47 ) & 13.2971830985915 & 0.140564787043838 & 94.5982516549082 \tabularnewline
Winsorized Mean ( 40 / 47 ) & 13.2971830985915 & 0.140564787043838 & 94.5982516549082 \tabularnewline
Winsorized Mean ( 41 / 47 ) & 13.2538732394366 & 0.136012569731176 & 97.4459438979235 \tabularnewline
Winsorized Mean ( 42 / 47 ) & 13.2834507042254 & 0.133178152845396 & 99.7419653330518 \tabularnewline
Winsorized Mean ( 43 / 47 ) & 13.2077464788732 & 0.1135050756629 & 116.362606709317 \tabularnewline
Winsorized Mean ( 44 / 47 ) & 13.2077464788732 & 0.1135050756629 & 116.362606709317 \tabularnewline
Winsorized Mean ( 45 / 47 ) & 13.1919014084507 & 0.111934699786384 & 117.853547055793 \tabularnewline
Winsorized Mean ( 46 / 47 ) & 13.2242957746479 & 0.108900820251074 & 121.434308246337 \tabularnewline
Winsorized Mean ( 47 / 47 ) & 13.2242957746479 & 0.108900820251074 & 121.434308246337 \tabularnewline
Trimmed Mean ( 1 / 47 ) & 13.2242857142857 & 0.286436035968787 & 46.168372877939 \tabularnewline
Trimmed Mean ( 2 / 47 ) & 13.2438405797101 & 0.280179577799239 & 47.2691146290467 \tabularnewline
Trimmed Mean ( 3 / 47 ) & 13.2547794117647 & 0.275733266150858 & 48.071020217462 \tabularnewline
Trimmed Mean ( 4 / 47 ) & 13.2630597014925 & 0.27146330626458 & 48.8576518277788 \tabularnewline
Trimmed Mean ( 5 / 47 ) & 13.2708333333333 & 0.266938894451737 & 49.7148733630224 \tabularnewline
Trimmed Mean ( 6 / 47 ) & 13.2788461538462 & 0.261978314492528 & 50.6868142104369 \tabularnewline
Trimmed Mean ( 7 / 47 ) & 13.2788461538462 & 0.257081878644622 & 51.6522059969937 \tabularnewline
Trimmed Mean ( 8 / 47 ) & 13.2869047619048 & 0.252938400538788 & 52.530199975971 \tabularnewline
Trimmed Mean ( 9 / 47 ) & 13.2903225806452 & 0.249259115542199 & 53.3193040974067 \tabularnewline
Trimmed Mean ( 10 / 47 ) & 13.2950819672131 & 0.245418257678104 & 54.1731576656013 \tabularnewline
Trimmed Mean ( 11 / 47 ) & 13.2991666666667 & 0.241341650950805 & 55.105144985428 \tabularnewline
Trimmed Mean ( 12 / 47 ) & 13.3033898305085 & 0.236833290603047 & 56.1719587505377 \tabularnewline
Trimmed Mean ( 13 / 47 ) & 13.3047413793103 & 0.232943631701595 & 57.1157119948828 \tabularnewline
Trimmed Mean ( 14 / 47 ) & 13.3047413793103 & 0.228799381831838 & 58.1502505504539 \tabularnewline
Trimmed Mean ( 15 / 47 ) & 13.3040178571429 & 0.224889271331608 & 59.158081567731 \tabularnewline
Trimmed Mean ( 16 / 47 ) & 13.2995454545455 & 0.221305263808203 & 60.0959291509292 \tabularnewline
Trimmed Mean ( 17 / 47 ) & 13.2953703703704 & 0.218103250305452 & 60.9590657257527 \tabularnewline
Trimmed Mean ( 18 / 47 ) & 13.2910377358491 & 0.214877675945784 & 61.8539719277424 \tabularnewline
Trimmed Mean ( 19 / 47 ) & 13.2865384615385 & 0.211260255648586 & 62.8918033860544 \tabularnewline
Trimmed Mean ( 20 / 47 ) & 13.2828431372549 & 0.20740337396286 & 64.0435248639372 \tabularnewline
Trimmed Mean ( 21 / 47 ) & 13.277 & 0.203446838662133 & 65.2602915204265 \tabularnewline
Trimmed Mean ( 22 / 47 ) & 13.269387755102 & 0.19948338581077 & 66.5187614556002 \tabularnewline
Trimmed Mean ( 23 / 47 ) & 13.2625 & 0.195881386414993 & 67.7067905365045 \tabularnewline
Trimmed Mean ( 24 / 47 ) & 13.2574468085106 & 0.19248486118084 & 68.8752701234787 \tabularnewline
Trimmed Mean ( 25 / 47 ) & 13.2521739130435 & 0.188619904498006 & 70.258618507484 \tabularnewline
Trimmed Mean ( 26 / 47 ) & 13.2455555555556 & 0.184434291193551 & 71.8172063873699 \tabularnewline
Trimmed Mean ( 27 / 47 ) & 13.2403409090909 & 0.180552418372441 & 73.3323930437695 \tabularnewline
Trimmed Mean ( 28 / 47 ) & 13.2403409090909 & 0.177866737221201 & 74.4396682367021 \tabularnewline
Trimmed Mean ( 29 / 47 ) & 13.235119047619 & 0.175002622228335 & 75.6281184767076 \tabularnewline
Trimmed Mean ( 30 / 47 ) & 13.2310975609756 & 0.172564220802114 & 76.6734697347733 \tabularnewline
Trimmed Mean ( 31 / 47 ) & 13.2310975609756 & 0.169858699653863 & 77.894730078223 \tabularnewline
Trimmed Mean ( 32 / 47 ) & 13.2217948717949 & 0.167346904562125 & 79.0083025819369 \tabularnewline
Trimmed Mean ( 33 / 47 ) & 13.2157894736842 & 0.164394717885637 & 80.3905967518856 \tabularnewline
Trimmed Mean ( 34 / 47 ) & 13.2094594594595 & 0.160921298368144 & 82.0864583707238 \tabularnewline
Trimmed Mean ( 35 / 47 ) & 13.2013888888889 & 0.157117808330761 & 84.0222316562461 \tabularnewline
Trimmed Mean ( 36 / 47 ) & 13.1942857142857 & 0.152998135474718 & 86.23821246806 \tabularnewline
Trimmed Mean ( 37 / 47 ) & 13.1852941176471 & 0.149149104086156 & 88.4034416326803 \tabularnewline
Trimmed Mean ( 38 / 47 ) & 13.180303030303 & 0.145779309159015 & 90.4127143031392 \tabularnewline
Trimmed Mean ( 39 / 47 ) & 13.171875 & 0.142412580223632 & 92.4909511457209 \tabularnewline
Trimmed Mean ( 40 / 47 ) & 13.1645161290323 & 0.139564684972045 & 94.3255532849814 \tabularnewline
Trimmed Mean ( 41 / 47 ) & 13.1566666666667 & 0.136079419039958 & 96.6837363025736 \tabularnewline
Trimmed Mean ( 42 / 47 ) & 13.1508620689655 & 0.132547354704371 & 99.2163298792099 \tabularnewline
Trimmed Mean ( 43 / 47 ) & 13.1428571428571 & 0.128612908171859 & 102.189254015585 \tabularnewline
Trimmed Mean ( 44 / 47 ) & 13.1388888888889 & 0.126941021060409 & 103.503885340865 \tabularnewline
Trimmed Mean ( 45 / 47 ) & 13.1346153846154 & 0.124773841121607 & 105.2673802982 \tabularnewline
Trimmed Mean ( 46 / 47 ) & 13.131 & 0.122256755583134 & 107.405107696244 \tabularnewline
Trimmed Mean ( 47 / 47 ) & 13.125 & 0.119516238251017 & 109.817713409235 \tabularnewline
Median & 13 &  &  \tabularnewline
Midrange & 11.825 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 13.1305555555556 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 13.1698630136986 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 13.1698630136986 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 13.1698630136986 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 13.1942857142857 &  &  \tabularnewline
Midmean - Closest Observation & 13.1698630136986 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 13.1698630136986 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 13.1698630136986 &  &  \tabularnewline
Number of observations & 142 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270913&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]13.2045774647887[/C][C]0.29243274035921[/C][C]45.1542376840873[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]12.6866269654666[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]12.0821799092074[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]13.6535251858266[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 47 )[/C][C]13.2052816901408[/C][C]0.292155842653512[/C][C]45.1994441398248[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 47 )[/C][C]13.2228873239437[/C][C]0.287984248509759[/C][C]45.9153144394826[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 47 )[/C][C]13.231338028169[/C][C]0.286497144163353[/C][C]46.1831410808927[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 47 )[/C][C]13.2341549295775[/C][C]0.286016793672484[/C][C]46.2705520177664[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 47 )[/C][C]13.2341549295775[/C][C]0.286016793672484[/C][C]46.2705520177664[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 47 )[/C][C]13.2447183098592[/C][C]0.283598230221587[/C][C]46.7024011380836[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 47 )[/C][C]13.2742957746479[/C][C]0.277465760060708[/C][C]47.8412030794125[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 47 )[/C][C]13.2630281690141[/C][C]0.27260443026742[/C][C]48.6530176930848[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 47 )[/C][C]13.2535211267606[/C][C]0.271311060060935[/C][C]48.8499109611819[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 47 )[/C][C]13.2605633802817[/C][C]0.270276900942307[/C][C]49.0628808235162[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 47 )[/C][C]13.2605633802817[/C][C]0.270276900942307[/C][C]49.0628808235162[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 47 )[/C][C]13.2901408450704[/C][C]0.262583253269829[/C][C]50.6130557816402[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 47 )[/C][C]13.2992957746479[/C][C]0.261332876078655[/C][C]50.8902514456126[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 47 )[/C][C]13.319014084507[/C][C]0.256070895582982[/C][C]52.0129945036682[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 47 )[/C][C]13.355985915493[/C][C]0.249988253841709[/C][C]53.4264538843088[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 47 )[/C][C]13.3503521126761[/C][C]0.243491082837862[/C][C]54.8289159384367[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 47 )[/C][C]13.3503521126761[/C][C]0.240491173465373[/C][C]55.5128569597932[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 47 )[/C][C]13.3503521126761[/C][C]0.240491173465373[/C][C]55.5128569597932[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 47 )[/C][C]13.3369718309859[/C][C]0.238766014674673[/C][C]55.8579153283519[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 47 )[/C][C]13.3651408450704[/C][C]0.235436878553454[/C][C]56.7674058846987[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 47 )[/C][C]13.387323943662[/C][C]0.231085738362642[/C][C]57.9322810594797[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 47 )[/C][C]13.3718309859155[/C][C]0.223522722667919[/C][C]59.823139349379[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 47 )[/C][C]13.3394366197183[/C][C]0.217577879389242[/C][C]61.308790476142[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 47 )[/C][C]13.3394366197183[/C][C]0.217577879389242[/C][C]61.308790476142[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 47 )[/C][C]13.3570422535211[/C][C]0.215618893488886[/C][C]61.9474575599267[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 47 )[/C][C]13.3295774647887[/C][C]0.208034090310674[/C][C]64.0740055866929[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 47 )[/C][C]13.2725352112676[/C][C]0.192760919060603[/C][C]68.8549072911132[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 47 )[/C][C]13.2922535211268[/C][C]0.190621624375658[/C][C]69.7310893486655[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 47 )[/C][C]13.3024647887324[/C][C]0.182817033100984[/C][C]72.7638150728791[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 47 )[/C][C]13.2919014084507[/C][C]0.181633888288154[/C][C]73.1796336780704[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 47 )[/C][C]13.3246478873239[/C][C]0.175896001307917[/C][C]75.7529891995574[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 47 )[/C][C]13.3246478873239[/C][C]0.175896001307917[/C][C]75.7529891995574[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 47 )[/C][C]13.3246478873239[/C][C]0.175896001307917[/C][C]75.7529891995574[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 47 )[/C][C]13.3485915492958[/C][C]0.173478763962027[/C][C]76.9465451818511[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 47 )[/C][C]13.3239436619718[/C][C]0.170722344310091[/C][C]78.0445214468875[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 47 )[/C][C]13.3492957746479[/C][C]0.162867486254889[/C][C]81.9641543049062[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 47 )[/C][C]13.2711267605634[/C][C]0.154339328412402[/C][C]85.9866820536002[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 47 )[/C][C]13.3246478873239[/C][C]0.149090528992621[/C][C]89.3728661193727[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 47 )[/C][C]13.2971830985915[/C][C]0.140564787043838[/C][C]94.5982516549082[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 47 )[/C][C]13.2971830985915[/C][C]0.140564787043838[/C][C]94.5982516549082[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 47 )[/C][C]13.2538732394366[/C][C]0.136012569731176[/C][C]97.4459438979235[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 47 )[/C][C]13.2834507042254[/C][C]0.133178152845396[/C][C]99.7419653330518[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 47 )[/C][C]13.2077464788732[/C][C]0.1135050756629[/C][C]116.362606709317[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 47 )[/C][C]13.2077464788732[/C][C]0.1135050756629[/C][C]116.362606709317[/C][/ROW]
[ROW][C]Winsorized Mean ( 45 / 47 )[/C][C]13.1919014084507[/C][C]0.111934699786384[/C][C]117.853547055793[/C][/ROW]
[ROW][C]Winsorized Mean ( 46 / 47 )[/C][C]13.2242957746479[/C][C]0.108900820251074[/C][C]121.434308246337[/C][/ROW]
[ROW][C]Winsorized Mean ( 47 / 47 )[/C][C]13.2242957746479[/C][C]0.108900820251074[/C][C]121.434308246337[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 47 )[/C][C]13.2242857142857[/C][C]0.286436035968787[/C][C]46.168372877939[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 47 )[/C][C]13.2438405797101[/C][C]0.280179577799239[/C][C]47.2691146290467[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 47 )[/C][C]13.2547794117647[/C][C]0.275733266150858[/C][C]48.071020217462[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 47 )[/C][C]13.2630597014925[/C][C]0.27146330626458[/C][C]48.8576518277788[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 47 )[/C][C]13.2708333333333[/C][C]0.266938894451737[/C][C]49.7148733630224[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 47 )[/C][C]13.2788461538462[/C][C]0.261978314492528[/C][C]50.6868142104369[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 47 )[/C][C]13.2788461538462[/C][C]0.257081878644622[/C][C]51.6522059969937[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 47 )[/C][C]13.2869047619048[/C][C]0.252938400538788[/C][C]52.530199975971[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 47 )[/C][C]13.2903225806452[/C][C]0.249259115542199[/C][C]53.3193040974067[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 47 )[/C][C]13.2950819672131[/C][C]0.245418257678104[/C][C]54.1731576656013[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 47 )[/C][C]13.2991666666667[/C][C]0.241341650950805[/C][C]55.105144985428[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 47 )[/C][C]13.3033898305085[/C][C]0.236833290603047[/C][C]56.1719587505377[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 47 )[/C][C]13.3047413793103[/C][C]0.232943631701595[/C][C]57.1157119948828[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 47 )[/C][C]13.3047413793103[/C][C]0.228799381831838[/C][C]58.1502505504539[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 47 )[/C][C]13.3040178571429[/C][C]0.224889271331608[/C][C]59.158081567731[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 47 )[/C][C]13.2995454545455[/C][C]0.221305263808203[/C][C]60.0959291509292[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 47 )[/C][C]13.2953703703704[/C][C]0.218103250305452[/C][C]60.9590657257527[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 47 )[/C][C]13.2910377358491[/C][C]0.214877675945784[/C][C]61.8539719277424[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 47 )[/C][C]13.2865384615385[/C][C]0.211260255648586[/C][C]62.8918033860544[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 47 )[/C][C]13.2828431372549[/C][C]0.20740337396286[/C][C]64.0435248639372[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 47 )[/C][C]13.277[/C][C]0.203446838662133[/C][C]65.2602915204265[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 47 )[/C][C]13.269387755102[/C][C]0.19948338581077[/C][C]66.5187614556002[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 47 )[/C][C]13.2625[/C][C]0.195881386414993[/C][C]67.7067905365045[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 47 )[/C][C]13.2574468085106[/C][C]0.19248486118084[/C][C]68.8752701234787[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 47 )[/C][C]13.2521739130435[/C][C]0.188619904498006[/C][C]70.258618507484[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 47 )[/C][C]13.2455555555556[/C][C]0.184434291193551[/C][C]71.8172063873699[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 47 )[/C][C]13.2403409090909[/C][C]0.180552418372441[/C][C]73.3323930437695[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 47 )[/C][C]13.2403409090909[/C][C]0.177866737221201[/C][C]74.4396682367021[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 47 )[/C][C]13.235119047619[/C][C]0.175002622228335[/C][C]75.6281184767076[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 47 )[/C][C]13.2310975609756[/C][C]0.172564220802114[/C][C]76.6734697347733[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 47 )[/C][C]13.2310975609756[/C][C]0.169858699653863[/C][C]77.894730078223[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 47 )[/C][C]13.2217948717949[/C][C]0.167346904562125[/C][C]79.0083025819369[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 47 )[/C][C]13.2157894736842[/C][C]0.164394717885637[/C][C]80.3905967518856[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 47 )[/C][C]13.2094594594595[/C][C]0.160921298368144[/C][C]82.0864583707238[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 47 )[/C][C]13.2013888888889[/C][C]0.157117808330761[/C][C]84.0222316562461[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 47 )[/C][C]13.1942857142857[/C][C]0.152998135474718[/C][C]86.23821246806[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 47 )[/C][C]13.1852941176471[/C][C]0.149149104086156[/C][C]88.4034416326803[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 47 )[/C][C]13.180303030303[/C][C]0.145779309159015[/C][C]90.4127143031392[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 47 )[/C][C]13.171875[/C][C]0.142412580223632[/C][C]92.4909511457209[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 47 )[/C][C]13.1645161290323[/C][C]0.139564684972045[/C][C]94.3255532849814[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 47 )[/C][C]13.1566666666667[/C][C]0.136079419039958[/C][C]96.6837363025736[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 47 )[/C][C]13.1508620689655[/C][C]0.132547354704371[/C][C]99.2163298792099[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 47 )[/C][C]13.1428571428571[/C][C]0.128612908171859[/C][C]102.189254015585[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 47 )[/C][C]13.1388888888889[/C][C]0.126941021060409[/C][C]103.503885340865[/C][/ROW]
[ROW][C]Trimmed Mean ( 45 / 47 )[/C][C]13.1346153846154[/C][C]0.124773841121607[/C][C]105.2673802982[/C][/ROW]
[ROW][C]Trimmed Mean ( 46 / 47 )[/C][C]13.131[/C][C]0.122256755583134[/C][C]107.405107696244[/C][/ROW]
[ROW][C]Trimmed Mean ( 47 / 47 )[/C][C]13.125[/C][C]0.119516238251017[/C][C]109.817713409235[/C][/ROW]
[ROW][C]Median[/C][C]13[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]11.825[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]13.1305555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]13.1698630136986[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]13.1698630136986[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]13.1698630136986[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]13.1942857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]13.1698630136986[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]13.1698630136986[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]13.1698630136986[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]142[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270913&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270913&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 Mean13.20457746478870.2924327403592145.1542376840873
Geometric Mean12.6866269654666
Harmonic Mean12.0821799092074
Quadratic Mean13.6535251858266
Winsorized Mean ( 1 / 47 )13.20528169014080.29215584265351245.1994441398248
Winsorized Mean ( 2 / 47 )13.22288732394370.28798424850975945.9153144394826
Winsorized Mean ( 3 / 47 )13.2313380281690.28649714416335346.1831410808927
Winsorized Mean ( 4 / 47 )13.23415492957750.28601679367248446.2705520177664
Winsorized Mean ( 5 / 47 )13.23415492957750.28601679367248446.2705520177664
Winsorized Mean ( 6 / 47 )13.24471830985920.28359823022158746.7024011380836
Winsorized Mean ( 7 / 47 )13.27429577464790.27746576006070847.8412030794125
Winsorized Mean ( 8 / 47 )13.26302816901410.2726044302674248.6530176930848
Winsorized Mean ( 9 / 47 )13.25352112676060.27131106006093548.8499109611819
Winsorized Mean ( 10 / 47 )13.26056338028170.27027690094230749.0628808235162
Winsorized Mean ( 11 / 47 )13.26056338028170.27027690094230749.0628808235162
Winsorized Mean ( 12 / 47 )13.29014084507040.26258325326982950.6130557816402
Winsorized Mean ( 13 / 47 )13.29929577464790.26133287607865550.8902514456126
Winsorized Mean ( 14 / 47 )13.3190140845070.25607089558298252.0129945036682
Winsorized Mean ( 15 / 47 )13.3559859154930.24998825384170953.4264538843088
Winsorized Mean ( 16 / 47 )13.35035211267610.24349108283786254.8289159384367
Winsorized Mean ( 17 / 47 )13.35035211267610.24049117346537355.5128569597932
Winsorized Mean ( 18 / 47 )13.35035211267610.24049117346537355.5128569597932
Winsorized Mean ( 19 / 47 )13.33697183098590.23876601467467355.8579153283519
Winsorized Mean ( 20 / 47 )13.36514084507040.23543687855345456.7674058846987
Winsorized Mean ( 21 / 47 )13.3873239436620.23108573836264257.9322810594797
Winsorized Mean ( 22 / 47 )13.37183098591550.22352272266791959.823139349379
Winsorized Mean ( 23 / 47 )13.33943661971830.21757787938924261.308790476142
Winsorized Mean ( 24 / 47 )13.33943661971830.21757787938924261.308790476142
Winsorized Mean ( 25 / 47 )13.35704225352110.21561889348888661.9474575599267
Winsorized Mean ( 26 / 47 )13.32957746478870.20803409031067464.0740055866929
Winsorized Mean ( 27 / 47 )13.27253521126760.19276091906060368.8549072911132
Winsorized Mean ( 28 / 47 )13.29225352112680.19062162437565869.7310893486655
Winsorized Mean ( 29 / 47 )13.30246478873240.18281703310098472.7638150728791
Winsorized Mean ( 30 / 47 )13.29190140845070.18163388828815473.1796336780704
Winsorized Mean ( 31 / 47 )13.32464788732390.17589600130791775.7529891995574
Winsorized Mean ( 32 / 47 )13.32464788732390.17589600130791775.7529891995574
Winsorized Mean ( 33 / 47 )13.32464788732390.17589600130791775.7529891995574
Winsorized Mean ( 34 / 47 )13.34859154929580.17347876396202776.9465451818511
Winsorized Mean ( 35 / 47 )13.32394366197180.17072234431009178.0445214468875
Winsorized Mean ( 36 / 47 )13.34929577464790.16286748625488981.9641543049062
Winsorized Mean ( 37 / 47 )13.27112676056340.15433932841240285.9866820536002
Winsorized Mean ( 38 / 47 )13.32464788732390.14909052899262189.3728661193727
Winsorized Mean ( 39 / 47 )13.29718309859150.14056478704383894.5982516549082
Winsorized Mean ( 40 / 47 )13.29718309859150.14056478704383894.5982516549082
Winsorized Mean ( 41 / 47 )13.25387323943660.13601256973117697.4459438979235
Winsorized Mean ( 42 / 47 )13.28345070422540.13317815284539699.7419653330518
Winsorized Mean ( 43 / 47 )13.20774647887320.1135050756629116.362606709317
Winsorized Mean ( 44 / 47 )13.20774647887320.1135050756629116.362606709317
Winsorized Mean ( 45 / 47 )13.19190140845070.111934699786384117.853547055793
Winsorized Mean ( 46 / 47 )13.22429577464790.108900820251074121.434308246337
Winsorized Mean ( 47 / 47 )13.22429577464790.108900820251074121.434308246337
Trimmed Mean ( 1 / 47 )13.22428571428570.28643603596878746.168372877939
Trimmed Mean ( 2 / 47 )13.24384057971010.28017957779923947.2691146290467
Trimmed Mean ( 3 / 47 )13.25477941176470.27573326615085848.071020217462
Trimmed Mean ( 4 / 47 )13.26305970149250.2714633062645848.8576518277788
Trimmed Mean ( 5 / 47 )13.27083333333330.26693889445173749.7148733630224
Trimmed Mean ( 6 / 47 )13.27884615384620.26197831449252850.6868142104369
Trimmed Mean ( 7 / 47 )13.27884615384620.25708187864462251.6522059969937
Trimmed Mean ( 8 / 47 )13.28690476190480.25293840053878852.530199975971
Trimmed Mean ( 9 / 47 )13.29032258064520.24925911554219953.3193040974067
Trimmed Mean ( 10 / 47 )13.29508196721310.24541825767810454.1731576656013
Trimmed Mean ( 11 / 47 )13.29916666666670.24134165095080555.105144985428
Trimmed Mean ( 12 / 47 )13.30338983050850.23683329060304756.1719587505377
Trimmed Mean ( 13 / 47 )13.30474137931030.23294363170159557.1157119948828
Trimmed Mean ( 14 / 47 )13.30474137931030.22879938183183858.1502505504539
Trimmed Mean ( 15 / 47 )13.30401785714290.22488927133160859.158081567731
Trimmed Mean ( 16 / 47 )13.29954545454550.22130526380820360.0959291509292
Trimmed Mean ( 17 / 47 )13.29537037037040.21810325030545260.9590657257527
Trimmed Mean ( 18 / 47 )13.29103773584910.21487767594578461.8539719277424
Trimmed Mean ( 19 / 47 )13.28653846153850.21126025564858662.8918033860544
Trimmed Mean ( 20 / 47 )13.28284313725490.2074033739628664.0435248639372
Trimmed Mean ( 21 / 47 )13.2770.20344683866213365.2602915204265
Trimmed Mean ( 22 / 47 )13.2693877551020.1994833858107766.5187614556002
Trimmed Mean ( 23 / 47 )13.26250.19588138641499367.7067905365045
Trimmed Mean ( 24 / 47 )13.25744680851060.1924848611808468.8752701234787
Trimmed Mean ( 25 / 47 )13.25217391304350.18861990449800670.258618507484
Trimmed Mean ( 26 / 47 )13.24555555555560.18443429119355171.8172063873699
Trimmed Mean ( 27 / 47 )13.24034090909090.18055241837244173.3323930437695
Trimmed Mean ( 28 / 47 )13.24034090909090.17786673722120174.4396682367021
Trimmed Mean ( 29 / 47 )13.2351190476190.17500262222833575.6281184767076
Trimmed Mean ( 30 / 47 )13.23109756097560.17256422080211476.6734697347733
Trimmed Mean ( 31 / 47 )13.23109756097560.16985869965386377.894730078223
Trimmed Mean ( 32 / 47 )13.22179487179490.16734690456212579.0083025819369
Trimmed Mean ( 33 / 47 )13.21578947368420.16439471788563780.3905967518856
Trimmed Mean ( 34 / 47 )13.20945945945950.16092129836814482.0864583707238
Trimmed Mean ( 35 / 47 )13.20138888888890.15711780833076184.0222316562461
Trimmed Mean ( 36 / 47 )13.19428571428570.15299813547471886.23821246806
Trimmed Mean ( 37 / 47 )13.18529411764710.14914910408615688.4034416326803
Trimmed Mean ( 38 / 47 )13.1803030303030.14577930915901590.4127143031392
Trimmed Mean ( 39 / 47 )13.1718750.14241258022363292.4909511457209
Trimmed Mean ( 40 / 47 )13.16451612903230.13956468497204594.3255532849814
Trimmed Mean ( 41 / 47 )13.15666666666670.13607941903995896.6837363025736
Trimmed Mean ( 42 / 47 )13.15086206896550.13254735470437199.2163298792099
Trimmed Mean ( 43 / 47 )13.14285714285710.128612908171859102.189254015585
Trimmed Mean ( 44 / 47 )13.13888888888890.126941021060409103.503885340865
Trimmed Mean ( 45 / 47 )13.13461538461540.124773841121607105.2673802982
Trimmed Mean ( 46 / 47 )13.1310.122256755583134107.405107696244
Trimmed Mean ( 47 / 47 )13.1250.119516238251017109.817713409235
Median13
Midrange11.825
Midmean - Weighted Average at Xnp13.1305555555556
Midmean - Weighted Average at X(n+1)p13.1698630136986
Midmean - Empirical Distribution Function13.1698630136986
Midmean - Empirical Distribution Function - Averaging13.1698630136986
Midmean - Empirical Distribution Function - Interpolation13.1942857142857
Midmean - Closest Observation13.1698630136986
Midmean - True Basic - Statistics Graphics Toolkit13.1698630136986
Midmean - MS Excel (old versions)13.1698630136986
Number of observations142



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')