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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 computationSat, 18 Dec 2010 17:27:55 +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/2010/Dec/18/t1292693283zmh7po3of336eaz.htm/, Retrieved Tue, 30 Apr 2024 07:29:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112121, Retrieved Tue, 30 Apr 2024 07:29:39 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
-  MPD    [Central Tendency] [Winsorized & trim...] [2010-12-18 17:27:55] [dfb0309aec67f282200eef05efe0d5bd] [Current]
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Dataseries X:
13
16
19
15
14
13
19
15
14
15
16
16
16
17
15
15
20
18
16
16
19
16
17
17
16
15
14
15
12
14
16
14
7
10
14
16
16
16
14
20
14
14
11
15
16
14
16
14
12
16
9
14
16
16
15
16
12
16
16
14
16
17
18
18
12
16
10
14
18
18
16
16
16
13
16
16
20
16
15
15
16
14
15
12
17
16
15
13
16
16
16
16
14
16
16
20
15
16
13
17
16
12
16
16
17
13
12
18
14
14
13
16
13
16
13
16
15
16
15
17
15
12
16
10
16
14
15
13
15
11
12
8
16
15
17
16
10
18
13
15
16
16
14
10
17
13
15
16
12
13




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112121&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 Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112121&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112121&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 Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean14.960.18558330558259380.6106990768205
Geometric Mean14.7676609687896
Harmonic Mean14.5463336247130
Quadratic Mean15.130543061415
Winsorized Mean ( 1 / 50 )14.96666666666670.1837751438711181.4401031140723
Winsorized Mean ( 2 / 50 )14.980.18059558438863182.9477644800214
Winsorized Mean ( 3 / 50 )150.17646795629041485.0012677390248
Winsorized Mean ( 4 / 50 )14.97333333333330.17182965048119487.1405679485574
Winsorized Mean ( 5 / 50 )14.97333333333330.17182965048119487.1405679485574
Winsorized Mean ( 6 / 50 )14.97333333333330.17182965048119487.1405679485574
Winsorized Mean ( 7 / 50 )14.92666666666670.16523230658063490.3374586699385
Winsorized Mean ( 8 / 50 )14.980.15528569326386396.4673543656456
Winsorized Mean ( 9 / 50 )14.980.15528569326386396.4673543656456
Winsorized Mean ( 10 / 50 )15.04666666666670.144809267957899103.906793251943
Winsorized Mean ( 11 / 50 )15.04666666666670.144809267957899103.906793251943
Winsorized Mean ( 12 / 50 )15.04666666666670.144809267957899103.906793251943
Winsorized Mean ( 13 / 50 )15.04666666666670.144809267957899103.906793251943
Winsorized Mean ( 14 / 50 )14.95333333333330.133557976306353111.961364995780
Winsorized Mean ( 15 / 50 )14.95333333333330.133557976306353111.961364995780
Winsorized Mean ( 16 / 50 )14.95333333333330.133557976306353111.961364995780
Winsorized Mean ( 17 / 50 )14.95333333333330.133557976306353111.961364995780
Winsorized Mean ( 18 / 50 )14.95333333333330.133557976306353111.961364995780
Winsorized Mean ( 19 / 50 )14.95333333333330.133557976306353111.961364995780
Winsorized Mean ( 20 / 50 )15.08666666666670.115445510614118130.682142479273
Winsorized Mean ( 21 / 50 )15.08666666666670.115445510614118130.682142479273
Winsorized Mean ( 22 / 50 )15.08666666666670.115445510614118130.682142479273
Winsorized Mean ( 23 / 50 )15.08666666666670.115445510614118130.682142479273
Winsorized Mean ( 24 / 50 )14.92666666666670.100600731032461148.375330014752
Winsorized Mean ( 25 / 50 )14.92666666666670.100600731032461148.375330014752
Winsorized Mean ( 26 / 50 )14.92666666666670.100600731032461148.375330014752
Winsorized Mean ( 27 / 50 )14.92666666666670.100600731032461148.375330014752
Winsorized Mean ( 28 / 50 )14.92666666666670.100600731032461148.375330014752
Winsorized Mean ( 29 / 50 )14.92666666666670.100600731032461148.375330014752
Winsorized Mean ( 30 / 50 )14.92666666666670.100600731032461148.375330014752
Winsorized Mean ( 31 / 50 )14.92666666666670.100600731032461148.375330014752
Winsorized Mean ( 32 / 50 )14.92666666666670.100600731032461148.375330014752
Winsorized Mean ( 33 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 34 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 35 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 36 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 37 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 38 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 39 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 40 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 41 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 42 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 43 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 44 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 45 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 46 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 47 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 48 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 49 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 50 / 50 )15.14666666666670.0747174643440306202.719227688523
Trimmed Mean ( 1 / 50 )14.97972972972970.17691499299059184.671906413983
Trimmed Mean ( 2 / 50 )14.99315068493150.16932904782595488.5444693478834
Trimmed Mean ( 3 / 50 )150.16283473681973292.1179368294486
Trimmed Mean ( 4 / 50 )150.15739361478480595.3024684038717
Trimmed Mean ( 5 / 50 )15.00714285714290.15290823362635798.1447663165997
Trimmed Mean ( 6 / 50 )15.01449275362320.147973906757126101.467164601303
Trimmed Mean ( 7 / 50 )15.02205882352940.142521225635005105.402256797880
Trimmed Mean ( 8 / 50 )15.03731343283580.137880258991412109.060670054097
Trimmed Mean ( 9 / 50 )15.04545454545450.134695635497317111.699644089465
Trimmed Mean ( 10 / 50 )15.05384615384620.131189475222852114.748886130340
Trimmed Mean ( 11 / 50 )15.05468750.129024101311507116.681204108161
Trimmed Mean ( 12 / 50 )15.05555555555560.126644386790206118.880559471585
Trimmed Mean ( 13 / 50 )15.05645161290320.124023814449464121.399681825124
Trimmed Mean ( 14 / 50 )15.05737704918030.121130910633449124.306644525649
Trimmed Mean ( 15 / 50 )15.06666666666670.119366519648819126.221881235990
Trimmed Mean ( 16 / 50 )15.07627118644070.117408876246647128.408274300907
Trimmed Mean ( 17 / 50 )15.08620689655170.115233265487223130.918852579288
Trimmed Mean ( 18 / 50 )15.09649122807020.112810353191718133.821859438859
Trimmed Mean ( 19 / 50 )15.10714285714290.110104915785969137.206797256077
Trimmed Mean ( 20 / 50 )15.11818181818180.107074072855514141.193674761792
Trimmed Mean ( 21 / 50 )15.12037037037040.105833317055945142.869663268492
Trimmed Mean ( 22 / 50 )15.12264150943400.104441207825005144.795735556529
Trimmed Mean ( 23 / 50 )15.1250.102878202601791147.018509436291
Trimmed Mean ( 24 / 50 )15.12745098039220.101121231792389149.597178676088
Trimmed Mean ( 25 / 50 )15.140.100523880272553150.610978793801
Trimmed Mean ( 26 / 50 )15.15306122448980.099812617218106151.815087579339
Trimmed Mean ( 27 / 50 )15.16666666666670.0989713172460936153.243051509101
Trimmed Mean ( 28 / 50 )15.18085106382980.0979809509468221154.936759820478
Trimmed Mean ( 29 / 50 )15.19565217391300.0968188846503415156.949258698772
Trimmed Mean ( 30 / 50 )15.21111111111110.0954579532310812159.348808519795
Trimmed Mean ( 31 / 50 )15.22727272727270.0938652081762732162.224886335700
Trimmed Mean ( 32 / 50 )15.24418604651160.092000188115593165.697335611512
Trimmed Mean ( 33 / 50 )15.26190476190480.0898124641702169.930809747994
Trimmed Mean ( 34 / 50 )15.26829268292680.0902483783487627169.180798173712
Trimmed Mean ( 35 / 50 )15.2750.0906638666110196168.479467851677
Trimmed Mean ( 36 / 50 )15.28205128205130.0910541292018138167.834796906134
Trimmed Mean ( 37 / 50 )15.28947368421050.09141344189553167.256295870402
Trimmed Mean ( 38 / 50 )15.29729729729730.091734953207778166.755383443094
Trimmed Mean ( 39 / 50 )15.30555555555560.0920104285970553166.345878276296
Trimmed Mean ( 40 / 50 )15.31428571428570.0922299249992391166.044651065390
Trimmed Mean ( 41 / 50 )15.32352941176470.0923813727394815165.87250175398
Trimmed Mean ( 42 / 50 )15.33333333333330.0924500327042048165.855358671344
Trimmed Mean ( 43 / 50 )15.343750.092417783066811166.025947505229
Trimmed Mean ( 44 / 50 )15.35483870967740.0922621692570532166.426161809583
Trimmed Mean ( 45 / 50 )15.36666666666670.0919551188323559167.110508493625
Trimmed Mean ( 46 / 50 )15.37931034482760.091461171655996168.151250048188
Trimmed Mean ( 47 / 50 )15.39285714285710.0907349909901436169.646318083938
Trimmed Mean ( 48 / 50 )15.40740740740740.0897177752083877171.731937975731
Trimmed Mean ( 49 / 50 )15.42307692307690.088331926820046174.603651004891
Trimmed Mean ( 50 / 50 )15.440.0864728340024089178.553185842965
Median15.5
Midrange13.5
Midmean - Weighted Average at Xnp15.3333333333333
Midmean - Weighted Average at X(n+1)p15.3333333333333
Midmean - Empirical Distribution Function15.3333333333333
Midmean - Empirical Distribution Function - Averaging15.3333333333333
Midmean - Empirical Distribution Function - Interpolation15.3333333333333
Midmean - Closest Observation15.3333333333333
Midmean - True Basic - Statistics Graphics Toolkit15.3333333333333
Midmean - MS Excel (old versions)15.3333333333333
Number of observations150

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 14.96 & 0.185583305582593 & 80.6106990768205 \tabularnewline
Geometric Mean & 14.7676609687896 &  &  \tabularnewline
Harmonic Mean & 14.5463336247130 &  &  \tabularnewline
Quadratic Mean & 15.130543061415 &  &  \tabularnewline
Winsorized Mean ( 1 / 50 ) & 14.9666666666667 & 0.18377514387111 & 81.4401031140723 \tabularnewline
Winsorized Mean ( 2 / 50 ) & 14.98 & 0.180595584388631 & 82.9477644800214 \tabularnewline
Winsorized Mean ( 3 / 50 ) & 15 & 0.176467956290414 & 85.0012677390248 \tabularnewline
Winsorized Mean ( 4 / 50 ) & 14.9733333333333 & 0.171829650481194 & 87.1405679485574 \tabularnewline
Winsorized Mean ( 5 / 50 ) & 14.9733333333333 & 0.171829650481194 & 87.1405679485574 \tabularnewline
Winsorized Mean ( 6 / 50 ) & 14.9733333333333 & 0.171829650481194 & 87.1405679485574 \tabularnewline
Winsorized Mean ( 7 / 50 ) & 14.9266666666667 & 0.165232306580634 & 90.3374586699385 \tabularnewline
Winsorized Mean ( 8 / 50 ) & 14.98 & 0.155285693263863 & 96.4673543656456 \tabularnewline
Winsorized Mean ( 9 / 50 ) & 14.98 & 0.155285693263863 & 96.4673543656456 \tabularnewline
Winsorized Mean ( 10 / 50 ) & 15.0466666666667 & 0.144809267957899 & 103.906793251943 \tabularnewline
Winsorized Mean ( 11 / 50 ) & 15.0466666666667 & 0.144809267957899 & 103.906793251943 \tabularnewline
Winsorized Mean ( 12 / 50 ) & 15.0466666666667 & 0.144809267957899 & 103.906793251943 \tabularnewline
Winsorized Mean ( 13 / 50 ) & 15.0466666666667 & 0.144809267957899 & 103.906793251943 \tabularnewline
Winsorized Mean ( 14 / 50 ) & 14.9533333333333 & 0.133557976306353 & 111.961364995780 \tabularnewline
Winsorized Mean ( 15 / 50 ) & 14.9533333333333 & 0.133557976306353 & 111.961364995780 \tabularnewline
Winsorized Mean ( 16 / 50 ) & 14.9533333333333 & 0.133557976306353 & 111.961364995780 \tabularnewline
Winsorized Mean ( 17 / 50 ) & 14.9533333333333 & 0.133557976306353 & 111.961364995780 \tabularnewline
Winsorized Mean ( 18 / 50 ) & 14.9533333333333 & 0.133557976306353 & 111.961364995780 \tabularnewline
Winsorized Mean ( 19 / 50 ) & 14.9533333333333 & 0.133557976306353 & 111.961364995780 \tabularnewline
Winsorized Mean ( 20 / 50 ) & 15.0866666666667 & 0.115445510614118 & 130.682142479273 \tabularnewline
Winsorized Mean ( 21 / 50 ) & 15.0866666666667 & 0.115445510614118 & 130.682142479273 \tabularnewline
Winsorized Mean ( 22 / 50 ) & 15.0866666666667 & 0.115445510614118 & 130.682142479273 \tabularnewline
Winsorized Mean ( 23 / 50 ) & 15.0866666666667 & 0.115445510614118 & 130.682142479273 \tabularnewline
Winsorized Mean ( 24 / 50 ) & 14.9266666666667 & 0.100600731032461 & 148.375330014752 \tabularnewline
Winsorized Mean ( 25 / 50 ) & 14.9266666666667 & 0.100600731032461 & 148.375330014752 \tabularnewline
Winsorized Mean ( 26 / 50 ) & 14.9266666666667 & 0.100600731032461 & 148.375330014752 \tabularnewline
Winsorized Mean ( 27 / 50 ) & 14.9266666666667 & 0.100600731032461 & 148.375330014752 \tabularnewline
Winsorized Mean ( 28 / 50 ) & 14.9266666666667 & 0.100600731032461 & 148.375330014752 \tabularnewline
Winsorized Mean ( 29 / 50 ) & 14.9266666666667 & 0.100600731032461 & 148.375330014752 \tabularnewline
Winsorized Mean ( 30 / 50 ) & 14.9266666666667 & 0.100600731032461 & 148.375330014752 \tabularnewline
Winsorized Mean ( 31 / 50 ) & 14.9266666666667 & 0.100600731032461 & 148.375330014752 \tabularnewline
Winsorized Mean ( 32 / 50 ) & 14.9266666666667 & 0.100600731032461 & 148.375330014752 \tabularnewline
Winsorized Mean ( 33 / 50 ) & 15.1466666666667 & 0.0747174643440306 & 202.719227688523 \tabularnewline
Winsorized Mean ( 34 / 50 ) & 15.1466666666667 & 0.0747174643440306 & 202.719227688523 \tabularnewline
Winsorized Mean ( 35 / 50 ) & 15.1466666666667 & 0.0747174643440306 & 202.719227688523 \tabularnewline
Winsorized Mean ( 36 / 50 ) & 15.1466666666667 & 0.0747174643440306 & 202.719227688523 \tabularnewline
Winsorized Mean ( 37 / 50 ) & 15.1466666666667 & 0.0747174643440306 & 202.719227688523 \tabularnewline
Winsorized Mean ( 38 / 50 ) & 15.1466666666667 & 0.0747174643440306 & 202.719227688523 \tabularnewline
Winsorized Mean ( 39 / 50 ) & 15.1466666666667 & 0.0747174643440306 & 202.719227688523 \tabularnewline
Winsorized Mean ( 40 / 50 ) & 15.1466666666667 & 0.0747174643440306 & 202.719227688523 \tabularnewline
Winsorized Mean ( 41 / 50 ) & 15.1466666666667 & 0.0747174643440306 & 202.719227688523 \tabularnewline
Winsorized Mean ( 42 / 50 ) & 15.1466666666667 & 0.0747174643440306 & 202.719227688523 \tabularnewline
Winsorized Mean ( 43 / 50 ) & 15.1466666666667 & 0.0747174643440306 & 202.719227688523 \tabularnewline
Winsorized Mean ( 44 / 50 ) & 15.1466666666667 & 0.0747174643440306 & 202.719227688523 \tabularnewline
Winsorized Mean ( 45 / 50 ) & 15.1466666666667 & 0.0747174643440306 & 202.719227688523 \tabularnewline
Winsorized Mean ( 46 / 50 ) & 15.1466666666667 & 0.0747174643440306 & 202.719227688523 \tabularnewline
Winsorized Mean ( 47 / 50 ) & 15.1466666666667 & 0.0747174643440306 & 202.719227688523 \tabularnewline
Winsorized Mean ( 48 / 50 ) & 15.1466666666667 & 0.0747174643440306 & 202.719227688523 \tabularnewline
Winsorized Mean ( 49 / 50 ) & 15.1466666666667 & 0.0747174643440306 & 202.719227688523 \tabularnewline
Winsorized Mean ( 50 / 50 ) & 15.1466666666667 & 0.0747174643440306 & 202.719227688523 \tabularnewline
Trimmed Mean ( 1 / 50 ) & 14.9797297297297 & 0.176914992990591 & 84.671906413983 \tabularnewline
Trimmed Mean ( 2 / 50 ) & 14.9931506849315 & 0.169329047825954 & 88.5444693478834 \tabularnewline
Trimmed Mean ( 3 / 50 ) & 15 & 0.162834736819732 & 92.1179368294486 \tabularnewline
Trimmed Mean ( 4 / 50 ) & 15 & 0.157393614784805 & 95.3024684038717 \tabularnewline
Trimmed Mean ( 5 / 50 ) & 15.0071428571429 & 0.152908233626357 & 98.1447663165997 \tabularnewline
Trimmed Mean ( 6 / 50 ) & 15.0144927536232 & 0.147973906757126 & 101.467164601303 \tabularnewline
Trimmed Mean ( 7 / 50 ) & 15.0220588235294 & 0.142521225635005 & 105.402256797880 \tabularnewline
Trimmed Mean ( 8 / 50 ) & 15.0373134328358 & 0.137880258991412 & 109.060670054097 \tabularnewline
Trimmed Mean ( 9 / 50 ) & 15.0454545454545 & 0.134695635497317 & 111.699644089465 \tabularnewline
Trimmed Mean ( 10 / 50 ) & 15.0538461538462 & 0.131189475222852 & 114.748886130340 \tabularnewline
Trimmed Mean ( 11 / 50 ) & 15.0546875 & 0.129024101311507 & 116.681204108161 \tabularnewline
Trimmed Mean ( 12 / 50 ) & 15.0555555555556 & 0.126644386790206 & 118.880559471585 \tabularnewline
Trimmed Mean ( 13 / 50 ) & 15.0564516129032 & 0.124023814449464 & 121.399681825124 \tabularnewline
Trimmed Mean ( 14 / 50 ) & 15.0573770491803 & 0.121130910633449 & 124.306644525649 \tabularnewline
Trimmed Mean ( 15 / 50 ) & 15.0666666666667 & 0.119366519648819 & 126.221881235990 \tabularnewline
Trimmed Mean ( 16 / 50 ) & 15.0762711864407 & 0.117408876246647 & 128.408274300907 \tabularnewline
Trimmed Mean ( 17 / 50 ) & 15.0862068965517 & 0.115233265487223 & 130.918852579288 \tabularnewline
Trimmed Mean ( 18 / 50 ) & 15.0964912280702 & 0.112810353191718 & 133.821859438859 \tabularnewline
Trimmed Mean ( 19 / 50 ) & 15.1071428571429 & 0.110104915785969 & 137.206797256077 \tabularnewline
Trimmed Mean ( 20 / 50 ) & 15.1181818181818 & 0.107074072855514 & 141.193674761792 \tabularnewline
Trimmed Mean ( 21 / 50 ) & 15.1203703703704 & 0.105833317055945 & 142.869663268492 \tabularnewline
Trimmed Mean ( 22 / 50 ) & 15.1226415094340 & 0.104441207825005 & 144.795735556529 \tabularnewline
Trimmed Mean ( 23 / 50 ) & 15.125 & 0.102878202601791 & 147.018509436291 \tabularnewline
Trimmed Mean ( 24 / 50 ) & 15.1274509803922 & 0.101121231792389 & 149.597178676088 \tabularnewline
Trimmed Mean ( 25 / 50 ) & 15.14 & 0.100523880272553 & 150.610978793801 \tabularnewline
Trimmed Mean ( 26 / 50 ) & 15.1530612244898 & 0.099812617218106 & 151.815087579339 \tabularnewline
Trimmed Mean ( 27 / 50 ) & 15.1666666666667 & 0.0989713172460936 & 153.243051509101 \tabularnewline
Trimmed Mean ( 28 / 50 ) & 15.1808510638298 & 0.0979809509468221 & 154.936759820478 \tabularnewline
Trimmed Mean ( 29 / 50 ) & 15.1956521739130 & 0.0968188846503415 & 156.949258698772 \tabularnewline
Trimmed Mean ( 30 / 50 ) & 15.2111111111111 & 0.0954579532310812 & 159.348808519795 \tabularnewline
Trimmed Mean ( 31 / 50 ) & 15.2272727272727 & 0.0938652081762732 & 162.224886335700 \tabularnewline
Trimmed Mean ( 32 / 50 ) & 15.2441860465116 & 0.092000188115593 & 165.697335611512 \tabularnewline
Trimmed Mean ( 33 / 50 ) & 15.2619047619048 & 0.0898124641702 & 169.930809747994 \tabularnewline
Trimmed Mean ( 34 / 50 ) & 15.2682926829268 & 0.0902483783487627 & 169.180798173712 \tabularnewline
Trimmed Mean ( 35 / 50 ) & 15.275 & 0.0906638666110196 & 168.479467851677 \tabularnewline
Trimmed Mean ( 36 / 50 ) & 15.2820512820513 & 0.0910541292018138 & 167.834796906134 \tabularnewline
Trimmed Mean ( 37 / 50 ) & 15.2894736842105 & 0.09141344189553 & 167.256295870402 \tabularnewline
Trimmed Mean ( 38 / 50 ) & 15.2972972972973 & 0.091734953207778 & 166.755383443094 \tabularnewline
Trimmed Mean ( 39 / 50 ) & 15.3055555555556 & 0.0920104285970553 & 166.345878276296 \tabularnewline
Trimmed Mean ( 40 / 50 ) & 15.3142857142857 & 0.0922299249992391 & 166.044651065390 \tabularnewline
Trimmed Mean ( 41 / 50 ) & 15.3235294117647 & 0.0923813727394815 & 165.87250175398 \tabularnewline
Trimmed Mean ( 42 / 50 ) & 15.3333333333333 & 0.0924500327042048 & 165.855358671344 \tabularnewline
Trimmed Mean ( 43 / 50 ) & 15.34375 & 0.092417783066811 & 166.025947505229 \tabularnewline
Trimmed Mean ( 44 / 50 ) & 15.3548387096774 & 0.0922621692570532 & 166.426161809583 \tabularnewline
Trimmed Mean ( 45 / 50 ) & 15.3666666666667 & 0.0919551188323559 & 167.110508493625 \tabularnewline
Trimmed Mean ( 46 / 50 ) & 15.3793103448276 & 0.091461171655996 & 168.151250048188 \tabularnewline
Trimmed Mean ( 47 / 50 ) & 15.3928571428571 & 0.0907349909901436 & 169.646318083938 \tabularnewline
Trimmed Mean ( 48 / 50 ) & 15.4074074074074 & 0.0897177752083877 & 171.731937975731 \tabularnewline
Trimmed Mean ( 49 / 50 ) & 15.4230769230769 & 0.088331926820046 & 174.603651004891 \tabularnewline
Trimmed Mean ( 50 / 50 ) & 15.44 & 0.0864728340024089 & 178.553185842965 \tabularnewline
Median & 15.5 &  &  \tabularnewline
Midrange & 13.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 15.3333333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 15.3333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 15.3333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 15.3333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 15.3333333333333 &  &  \tabularnewline
Midmean - Closest Observation & 15.3333333333333 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 15.3333333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 15.3333333333333 &  &  \tabularnewline
Number of observations & 150 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112121&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]14.96[/C][C]0.185583305582593[/C][C]80.6106990768205[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]14.7676609687896[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]14.5463336247130[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]15.130543061415[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 50 )[/C][C]14.9666666666667[/C][C]0.18377514387111[/C][C]81.4401031140723[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 50 )[/C][C]14.98[/C][C]0.180595584388631[/C][C]82.9477644800214[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 50 )[/C][C]15[/C][C]0.176467956290414[/C][C]85.0012677390248[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 50 )[/C][C]14.9733333333333[/C][C]0.171829650481194[/C][C]87.1405679485574[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 50 )[/C][C]14.9733333333333[/C][C]0.171829650481194[/C][C]87.1405679485574[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 50 )[/C][C]14.9733333333333[/C][C]0.171829650481194[/C][C]87.1405679485574[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 50 )[/C][C]14.9266666666667[/C][C]0.165232306580634[/C][C]90.3374586699385[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 50 )[/C][C]14.98[/C][C]0.155285693263863[/C][C]96.4673543656456[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 50 )[/C][C]14.98[/C][C]0.155285693263863[/C][C]96.4673543656456[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 50 )[/C][C]15.0466666666667[/C][C]0.144809267957899[/C][C]103.906793251943[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 50 )[/C][C]15.0466666666667[/C][C]0.144809267957899[/C][C]103.906793251943[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 50 )[/C][C]15.0466666666667[/C][C]0.144809267957899[/C][C]103.906793251943[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 50 )[/C][C]15.0466666666667[/C][C]0.144809267957899[/C][C]103.906793251943[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 50 )[/C][C]14.9533333333333[/C][C]0.133557976306353[/C][C]111.961364995780[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 50 )[/C][C]14.9533333333333[/C][C]0.133557976306353[/C][C]111.961364995780[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 50 )[/C][C]14.9533333333333[/C][C]0.133557976306353[/C][C]111.961364995780[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 50 )[/C][C]14.9533333333333[/C][C]0.133557976306353[/C][C]111.961364995780[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 50 )[/C][C]14.9533333333333[/C][C]0.133557976306353[/C][C]111.961364995780[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 50 )[/C][C]14.9533333333333[/C][C]0.133557976306353[/C][C]111.961364995780[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 50 )[/C][C]15.0866666666667[/C][C]0.115445510614118[/C][C]130.682142479273[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 50 )[/C][C]15.0866666666667[/C][C]0.115445510614118[/C][C]130.682142479273[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 50 )[/C][C]15.0866666666667[/C][C]0.115445510614118[/C][C]130.682142479273[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 50 )[/C][C]15.0866666666667[/C][C]0.115445510614118[/C][C]130.682142479273[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 50 )[/C][C]14.9266666666667[/C][C]0.100600731032461[/C][C]148.375330014752[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 50 )[/C][C]14.9266666666667[/C][C]0.100600731032461[/C][C]148.375330014752[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 50 )[/C][C]14.9266666666667[/C][C]0.100600731032461[/C][C]148.375330014752[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 50 )[/C][C]14.9266666666667[/C][C]0.100600731032461[/C][C]148.375330014752[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 50 )[/C][C]14.9266666666667[/C][C]0.100600731032461[/C][C]148.375330014752[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 50 )[/C][C]14.9266666666667[/C][C]0.100600731032461[/C][C]148.375330014752[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 50 )[/C][C]14.9266666666667[/C][C]0.100600731032461[/C][C]148.375330014752[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 50 )[/C][C]14.9266666666667[/C][C]0.100600731032461[/C][C]148.375330014752[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 50 )[/C][C]14.9266666666667[/C][C]0.100600731032461[/C][C]148.375330014752[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 50 )[/C][C]15.1466666666667[/C][C]0.0747174643440306[/C][C]202.719227688523[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 50 )[/C][C]15.1466666666667[/C][C]0.0747174643440306[/C][C]202.719227688523[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 50 )[/C][C]15.1466666666667[/C][C]0.0747174643440306[/C][C]202.719227688523[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 50 )[/C][C]15.1466666666667[/C][C]0.0747174643440306[/C][C]202.719227688523[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 50 )[/C][C]15.1466666666667[/C][C]0.0747174643440306[/C][C]202.719227688523[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 50 )[/C][C]15.1466666666667[/C][C]0.0747174643440306[/C][C]202.719227688523[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 50 )[/C][C]15.1466666666667[/C][C]0.0747174643440306[/C][C]202.719227688523[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 50 )[/C][C]15.1466666666667[/C][C]0.0747174643440306[/C][C]202.719227688523[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 50 )[/C][C]15.1466666666667[/C][C]0.0747174643440306[/C][C]202.719227688523[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 50 )[/C][C]15.1466666666667[/C][C]0.0747174643440306[/C][C]202.719227688523[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 50 )[/C][C]15.1466666666667[/C][C]0.0747174643440306[/C][C]202.719227688523[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 50 )[/C][C]15.1466666666667[/C][C]0.0747174643440306[/C][C]202.719227688523[/C][/ROW]
[ROW][C]Winsorized Mean ( 45 / 50 )[/C][C]15.1466666666667[/C][C]0.0747174643440306[/C][C]202.719227688523[/C][/ROW]
[ROW][C]Winsorized Mean ( 46 / 50 )[/C][C]15.1466666666667[/C][C]0.0747174643440306[/C][C]202.719227688523[/C][/ROW]
[ROW][C]Winsorized Mean ( 47 / 50 )[/C][C]15.1466666666667[/C][C]0.0747174643440306[/C][C]202.719227688523[/C][/ROW]
[ROW][C]Winsorized Mean ( 48 / 50 )[/C][C]15.1466666666667[/C][C]0.0747174643440306[/C][C]202.719227688523[/C][/ROW]
[ROW][C]Winsorized Mean ( 49 / 50 )[/C][C]15.1466666666667[/C][C]0.0747174643440306[/C][C]202.719227688523[/C][/ROW]
[ROW][C]Winsorized Mean ( 50 / 50 )[/C][C]15.1466666666667[/C][C]0.0747174643440306[/C][C]202.719227688523[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 50 )[/C][C]14.9797297297297[/C][C]0.176914992990591[/C][C]84.671906413983[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 50 )[/C][C]14.9931506849315[/C][C]0.169329047825954[/C][C]88.5444693478834[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 50 )[/C][C]15[/C][C]0.162834736819732[/C][C]92.1179368294486[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 50 )[/C][C]15[/C][C]0.157393614784805[/C][C]95.3024684038717[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 50 )[/C][C]15.0071428571429[/C][C]0.152908233626357[/C][C]98.1447663165997[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 50 )[/C][C]15.0144927536232[/C][C]0.147973906757126[/C][C]101.467164601303[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 50 )[/C][C]15.0220588235294[/C][C]0.142521225635005[/C][C]105.402256797880[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 50 )[/C][C]15.0373134328358[/C][C]0.137880258991412[/C][C]109.060670054097[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 50 )[/C][C]15.0454545454545[/C][C]0.134695635497317[/C][C]111.699644089465[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 50 )[/C][C]15.0538461538462[/C][C]0.131189475222852[/C][C]114.748886130340[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 50 )[/C][C]15.0546875[/C][C]0.129024101311507[/C][C]116.681204108161[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 50 )[/C][C]15.0555555555556[/C][C]0.126644386790206[/C][C]118.880559471585[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 50 )[/C][C]15.0564516129032[/C][C]0.124023814449464[/C][C]121.399681825124[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 50 )[/C][C]15.0573770491803[/C][C]0.121130910633449[/C][C]124.306644525649[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 50 )[/C][C]15.0666666666667[/C][C]0.119366519648819[/C][C]126.221881235990[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 50 )[/C][C]15.0762711864407[/C][C]0.117408876246647[/C][C]128.408274300907[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 50 )[/C][C]15.0862068965517[/C][C]0.115233265487223[/C][C]130.918852579288[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 50 )[/C][C]15.0964912280702[/C][C]0.112810353191718[/C][C]133.821859438859[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 50 )[/C][C]15.1071428571429[/C][C]0.110104915785969[/C][C]137.206797256077[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 50 )[/C][C]15.1181818181818[/C][C]0.107074072855514[/C][C]141.193674761792[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 50 )[/C][C]15.1203703703704[/C][C]0.105833317055945[/C][C]142.869663268492[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 50 )[/C][C]15.1226415094340[/C][C]0.104441207825005[/C][C]144.795735556529[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 50 )[/C][C]15.125[/C][C]0.102878202601791[/C][C]147.018509436291[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 50 )[/C][C]15.1274509803922[/C][C]0.101121231792389[/C][C]149.597178676088[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 50 )[/C][C]15.14[/C][C]0.100523880272553[/C][C]150.610978793801[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 50 )[/C][C]15.1530612244898[/C][C]0.099812617218106[/C][C]151.815087579339[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 50 )[/C][C]15.1666666666667[/C][C]0.0989713172460936[/C][C]153.243051509101[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 50 )[/C][C]15.1808510638298[/C][C]0.0979809509468221[/C][C]154.936759820478[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 50 )[/C][C]15.1956521739130[/C][C]0.0968188846503415[/C][C]156.949258698772[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 50 )[/C][C]15.2111111111111[/C][C]0.0954579532310812[/C][C]159.348808519795[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 50 )[/C][C]15.2272727272727[/C][C]0.0938652081762732[/C][C]162.224886335700[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 50 )[/C][C]15.2441860465116[/C][C]0.092000188115593[/C][C]165.697335611512[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 50 )[/C][C]15.2619047619048[/C][C]0.0898124641702[/C][C]169.930809747994[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 50 )[/C][C]15.2682926829268[/C][C]0.0902483783487627[/C][C]169.180798173712[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 50 )[/C][C]15.275[/C][C]0.0906638666110196[/C][C]168.479467851677[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 50 )[/C][C]15.2820512820513[/C][C]0.0910541292018138[/C][C]167.834796906134[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 50 )[/C][C]15.2894736842105[/C][C]0.09141344189553[/C][C]167.256295870402[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 50 )[/C][C]15.2972972972973[/C][C]0.091734953207778[/C][C]166.755383443094[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 50 )[/C][C]15.3055555555556[/C][C]0.0920104285970553[/C][C]166.345878276296[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 50 )[/C][C]15.3142857142857[/C][C]0.0922299249992391[/C][C]166.044651065390[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 50 )[/C][C]15.3235294117647[/C][C]0.0923813727394815[/C][C]165.87250175398[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 50 )[/C][C]15.3333333333333[/C][C]0.0924500327042048[/C][C]165.855358671344[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 50 )[/C][C]15.34375[/C][C]0.092417783066811[/C][C]166.025947505229[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 50 )[/C][C]15.3548387096774[/C][C]0.0922621692570532[/C][C]166.426161809583[/C][/ROW]
[ROW][C]Trimmed Mean ( 45 / 50 )[/C][C]15.3666666666667[/C][C]0.0919551188323559[/C][C]167.110508493625[/C][/ROW]
[ROW][C]Trimmed Mean ( 46 / 50 )[/C][C]15.3793103448276[/C][C]0.091461171655996[/C][C]168.151250048188[/C][/ROW]
[ROW][C]Trimmed Mean ( 47 / 50 )[/C][C]15.3928571428571[/C][C]0.0907349909901436[/C][C]169.646318083938[/C][/ROW]
[ROW][C]Trimmed Mean ( 48 / 50 )[/C][C]15.4074074074074[/C][C]0.0897177752083877[/C][C]171.731937975731[/C][/ROW]
[ROW][C]Trimmed Mean ( 49 / 50 )[/C][C]15.4230769230769[/C][C]0.088331926820046[/C][C]174.603651004891[/C][/ROW]
[ROW][C]Trimmed Mean ( 50 / 50 )[/C][C]15.44[/C][C]0.0864728340024089[/C][C]178.553185842965[/C][/ROW]
[ROW][C]Median[/C][C]15.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]13.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]15.3333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]15.3333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]15.3333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]15.3333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]15.3333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]15.3333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]15.3333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]15.3333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]150[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112121&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112121&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 Mean14.960.18558330558259380.6106990768205
Geometric Mean14.7676609687896
Harmonic Mean14.5463336247130
Quadratic Mean15.130543061415
Winsorized Mean ( 1 / 50 )14.96666666666670.1837751438711181.4401031140723
Winsorized Mean ( 2 / 50 )14.980.18059558438863182.9477644800214
Winsorized Mean ( 3 / 50 )150.17646795629041485.0012677390248
Winsorized Mean ( 4 / 50 )14.97333333333330.17182965048119487.1405679485574
Winsorized Mean ( 5 / 50 )14.97333333333330.17182965048119487.1405679485574
Winsorized Mean ( 6 / 50 )14.97333333333330.17182965048119487.1405679485574
Winsorized Mean ( 7 / 50 )14.92666666666670.16523230658063490.3374586699385
Winsorized Mean ( 8 / 50 )14.980.15528569326386396.4673543656456
Winsorized Mean ( 9 / 50 )14.980.15528569326386396.4673543656456
Winsorized Mean ( 10 / 50 )15.04666666666670.144809267957899103.906793251943
Winsorized Mean ( 11 / 50 )15.04666666666670.144809267957899103.906793251943
Winsorized Mean ( 12 / 50 )15.04666666666670.144809267957899103.906793251943
Winsorized Mean ( 13 / 50 )15.04666666666670.144809267957899103.906793251943
Winsorized Mean ( 14 / 50 )14.95333333333330.133557976306353111.961364995780
Winsorized Mean ( 15 / 50 )14.95333333333330.133557976306353111.961364995780
Winsorized Mean ( 16 / 50 )14.95333333333330.133557976306353111.961364995780
Winsorized Mean ( 17 / 50 )14.95333333333330.133557976306353111.961364995780
Winsorized Mean ( 18 / 50 )14.95333333333330.133557976306353111.961364995780
Winsorized Mean ( 19 / 50 )14.95333333333330.133557976306353111.961364995780
Winsorized Mean ( 20 / 50 )15.08666666666670.115445510614118130.682142479273
Winsorized Mean ( 21 / 50 )15.08666666666670.115445510614118130.682142479273
Winsorized Mean ( 22 / 50 )15.08666666666670.115445510614118130.682142479273
Winsorized Mean ( 23 / 50 )15.08666666666670.115445510614118130.682142479273
Winsorized Mean ( 24 / 50 )14.92666666666670.100600731032461148.375330014752
Winsorized Mean ( 25 / 50 )14.92666666666670.100600731032461148.375330014752
Winsorized Mean ( 26 / 50 )14.92666666666670.100600731032461148.375330014752
Winsorized Mean ( 27 / 50 )14.92666666666670.100600731032461148.375330014752
Winsorized Mean ( 28 / 50 )14.92666666666670.100600731032461148.375330014752
Winsorized Mean ( 29 / 50 )14.92666666666670.100600731032461148.375330014752
Winsorized Mean ( 30 / 50 )14.92666666666670.100600731032461148.375330014752
Winsorized Mean ( 31 / 50 )14.92666666666670.100600731032461148.375330014752
Winsorized Mean ( 32 / 50 )14.92666666666670.100600731032461148.375330014752
Winsorized Mean ( 33 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 34 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 35 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 36 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 37 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 38 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 39 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 40 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 41 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 42 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 43 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 44 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 45 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 46 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 47 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 48 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 49 / 50 )15.14666666666670.0747174643440306202.719227688523
Winsorized Mean ( 50 / 50 )15.14666666666670.0747174643440306202.719227688523
Trimmed Mean ( 1 / 50 )14.97972972972970.17691499299059184.671906413983
Trimmed Mean ( 2 / 50 )14.99315068493150.16932904782595488.5444693478834
Trimmed Mean ( 3 / 50 )150.16283473681973292.1179368294486
Trimmed Mean ( 4 / 50 )150.15739361478480595.3024684038717
Trimmed Mean ( 5 / 50 )15.00714285714290.15290823362635798.1447663165997
Trimmed Mean ( 6 / 50 )15.01449275362320.147973906757126101.467164601303
Trimmed Mean ( 7 / 50 )15.02205882352940.142521225635005105.402256797880
Trimmed Mean ( 8 / 50 )15.03731343283580.137880258991412109.060670054097
Trimmed Mean ( 9 / 50 )15.04545454545450.134695635497317111.699644089465
Trimmed Mean ( 10 / 50 )15.05384615384620.131189475222852114.748886130340
Trimmed Mean ( 11 / 50 )15.05468750.129024101311507116.681204108161
Trimmed Mean ( 12 / 50 )15.05555555555560.126644386790206118.880559471585
Trimmed Mean ( 13 / 50 )15.05645161290320.124023814449464121.399681825124
Trimmed Mean ( 14 / 50 )15.05737704918030.121130910633449124.306644525649
Trimmed Mean ( 15 / 50 )15.06666666666670.119366519648819126.221881235990
Trimmed Mean ( 16 / 50 )15.07627118644070.117408876246647128.408274300907
Trimmed Mean ( 17 / 50 )15.08620689655170.115233265487223130.918852579288
Trimmed Mean ( 18 / 50 )15.09649122807020.112810353191718133.821859438859
Trimmed Mean ( 19 / 50 )15.10714285714290.110104915785969137.206797256077
Trimmed Mean ( 20 / 50 )15.11818181818180.107074072855514141.193674761792
Trimmed Mean ( 21 / 50 )15.12037037037040.105833317055945142.869663268492
Trimmed Mean ( 22 / 50 )15.12264150943400.104441207825005144.795735556529
Trimmed Mean ( 23 / 50 )15.1250.102878202601791147.018509436291
Trimmed Mean ( 24 / 50 )15.12745098039220.101121231792389149.597178676088
Trimmed Mean ( 25 / 50 )15.140.100523880272553150.610978793801
Trimmed Mean ( 26 / 50 )15.15306122448980.099812617218106151.815087579339
Trimmed Mean ( 27 / 50 )15.16666666666670.0989713172460936153.243051509101
Trimmed Mean ( 28 / 50 )15.18085106382980.0979809509468221154.936759820478
Trimmed Mean ( 29 / 50 )15.19565217391300.0968188846503415156.949258698772
Trimmed Mean ( 30 / 50 )15.21111111111110.0954579532310812159.348808519795
Trimmed Mean ( 31 / 50 )15.22727272727270.0938652081762732162.224886335700
Trimmed Mean ( 32 / 50 )15.24418604651160.092000188115593165.697335611512
Trimmed Mean ( 33 / 50 )15.26190476190480.0898124641702169.930809747994
Trimmed Mean ( 34 / 50 )15.26829268292680.0902483783487627169.180798173712
Trimmed Mean ( 35 / 50 )15.2750.0906638666110196168.479467851677
Trimmed Mean ( 36 / 50 )15.28205128205130.0910541292018138167.834796906134
Trimmed Mean ( 37 / 50 )15.28947368421050.09141344189553167.256295870402
Trimmed Mean ( 38 / 50 )15.29729729729730.091734953207778166.755383443094
Trimmed Mean ( 39 / 50 )15.30555555555560.0920104285970553166.345878276296
Trimmed Mean ( 40 / 50 )15.31428571428570.0922299249992391166.044651065390
Trimmed Mean ( 41 / 50 )15.32352941176470.0923813727394815165.87250175398
Trimmed Mean ( 42 / 50 )15.33333333333330.0924500327042048165.855358671344
Trimmed Mean ( 43 / 50 )15.343750.092417783066811166.025947505229
Trimmed Mean ( 44 / 50 )15.35483870967740.0922621692570532166.426161809583
Trimmed Mean ( 45 / 50 )15.36666666666670.0919551188323559167.110508493625
Trimmed Mean ( 46 / 50 )15.37931034482760.091461171655996168.151250048188
Trimmed Mean ( 47 / 50 )15.39285714285710.0907349909901436169.646318083938
Trimmed Mean ( 48 / 50 )15.40740740740740.0897177752083877171.731937975731
Trimmed Mean ( 49 / 50 )15.42307692307690.088331926820046174.603651004891
Trimmed Mean ( 50 / 50 )15.440.0864728340024089178.553185842965
Median15.5
Midrange13.5
Midmean - Weighted Average at Xnp15.3333333333333
Midmean - Weighted Average at X(n+1)p15.3333333333333
Midmean - Empirical Distribution Function15.3333333333333
Midmean - Empirical Distribution Function - Averaging15.3333333333333
Midmean - Empirical Distribution Function - Interpolation15.3333333333333
Midmean - Closest Observation15.3333333333333
Midmean - True Basic - Statistics Graphics Toolkit15.3333333333333
Midmean - MS Excel (old versions)15.3333333333333
Number of observations150



Parameters (Session):
par1 = 20 ;
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')