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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 computationSun, 15 Dec 2013 06:59:44 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/15/t1387108948if1ezauwxtldc72.htm/, Retrieved Tue, 23 Apr 2024 20:03:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232338, Retrieved Tue, 23 Apr 2024 20:03:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact132
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Winesales - centr...] [2013-12-15 11:59:44] [e87fe8ad852a0fa5d933f43041f410cc] [Current]
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Dataseries X:
1954
2302
3054
2414
2226
2725
2589
3470
2400
3180
4009
3924
2072
2434
2956
2828
2687
2629
3150
4119
3030
3055
3821
4001
2529
2472
3134
2789
2758
2993
3282
3437
2804
3076
3782
3889
2271
2452
3084
2522
2769
3438
2839
3746
2632
2851
3871
3618
2389
2344
2678
2492
2858
2246
2800
3869
3007
3023
3907
4209




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232338&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232338&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232338&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2998.1575.211602907160639.8628653573684
Geometric Mean2944.08532755224
Harmonic Mean2891.93520278421
Quadratic Mean3053.30210591746
Winsorized Mean ( 1 / 20 )2998.6166666666774.376235086043440.3168655041179
Winsorized Mean ( 2 / 20 )3000.0833333333372.467402730943441.3990735182276
Winsorized Mean ( 3 / 20 )3000.6833333333372.194121909126141.56409488726
Winsorized Mean ( 4 / 20 )2997.2166666666770.728278059951442.3764970515207
Winsorized Mean ( 5 / 20 )2998.3833333333369.972351649004242.8509727438324
Winsorized Mean ( 6 / 20 )3000.7833333333368.883845947943743.5629470456841
Winsorized Mean ( 7 / 20 )3003.9333333333367.596943846048244.4388926838879
Winsorized Mean ( 8 / 20 )3005.1333333333367.314144494037944.6434156732022
Winsorized Mean ( 9 / 20 )3000.0333333333365.446083241673745.8397689324672
Winsorized Mean ( 10 / 20 )2996.8666666666763.571510811190647.1416618611984
Winsorized Mean ( 11 / 20 )2993.5666666666761.705466645476248.5137999825196
Winsorized Mean ( 12 / 20 )2971.9666666666755.947831666412853.1203190212433
Winsorized Mean ( 13 / 20 )2944.2333333333349.227509227904559.8087000441696
Winsorized Mean ( 14 / 20 )2943.7666666666746.803504182555462.8962877476997
Winsorized Mean ( 15 / 20 )2945.2666666666746.492292458038363.3495685188017
Winsorized Mean ( 16 / 20 )2919.9333333333336.888485691985779.1556844516312
Winsorized Mean ( 17 / 20 )2902.3666666666730.517791112528995.1040871852327
Winsorized Mean ( 18 / 20 )2894.2666666666729.013856680432899.7546344336425
Winsorized Mean ( 19 / 20 )2903.7666666666726.0687418799126111.38883034874
Winsorized Mean ( 20 / 20 )2890.123.1939830011498124.605592746046
Trimmed Mean ( 1 / 20 )2995.2758620689772.689524451428841.2064308395691
Trimmed Mean ( 2 / 20 )2991.6964285714370.600903748873542.3747610825614
Trimmed Mean ( 3 / 20 )2987.0370370370469.262491843379943.1263293817307
Trimmed Mean ( 4 / 20 )2981.7884615384667.689632717868944.0508884716008
Trimmed Mean ( 5 / 20 )2977.1666.262030005185944.9301055184545
Trimmed Mean ( 6 / 20 )2971.8541666666764.670859173404845.9535284462219
Trimmed Mean ( 7 / 20 )2965.565217391362.932128551581447.1232307828365
Trimmed Mean ( 8 / 20 )2958.0909090909161.014328007276448.4819059014816
Trimmed Mean ( 9 / 20 )2949.6904761904858.530469824732150.3958106781518
Trimmed Mean ( 10 / 20 )2941.355.759869771396352.7494058371856
Trimmed Mean ( 11 / 20 )2932.5263157894752.553836608828155.8004230522127
Trimmed Mean ( 12 / 20 )2923.2777777777848.693365329996460.034416556889
Trimmed Mean ( 13 / 20 )2916.1176470588245.270838057648764.4149251963347
Trimmed Mean ( 14 / 20 )2912.062542.742357775226768.1306004529263
Trimmed Mean ( 15 / 20 )2907.5333333333339.86931909832472.9265861341373
Trimmed Mean ( 16 / 20 )2902.1428571428635.606673854462781.5055870987826
Trimmed Mean ( 17 / 20 )2899.5769230769233.188560266217987.3667582991949
Trimmed Mean ( 18 / 20 )2899.1666666666731.967752471320790.6903501979878
Trimmed Mean ( 19 / 20 )2899.9090909090930.500933850646595.0760755427699
Trimmed Mean ( 20 / 20 )2899.329.278706111762399.024184638926
Median2854.5
Midrange3081.5
Midmean - Weighted Average at Xnp2895.09677419355
Midmean - Weighted Average at X(n+1)p2907.53333333333
Midmean - Empirical Distribution Function2895.09677419355
Midmean - Empirical Distribution Function - Averaging2907.53333333333
Midmean - Empirical Distribution Function - Interpolation2907.53333333333
Midmean - Closest Observation2895.09677419355
Midmean - True Basic - Statistics Graphics Toolkit2907.53333333333
Midmean - MS Excel (old versions)2912.0625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2998.15 & 75.2116029071606 & 39.8628653573684 \tabularnewline
Geometric Mean & 2944.08532755224 &  &  \tabularnewline
Harmonic Mean & 2891.93520278421 &  &  \tabularnewline
Quadratic Mean & 3053.30210591746 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2998.61666666667 & 74.3762350860434 & 40.3168655041179 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 3000.08333333333 & 72.4674027309434 & 41.3990735182276 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 3000.68333333333 & 72.1941219091261 & 41.56409488726 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2997.21666666667 & 70.7282780599514 & 42.3764970515207 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2998.38333333333 & 69.9723516490042 & 42.8509727438324 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 3000.78333333333 & 68.8838459479437 & 43.5629470456841 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 3003.93333333333 & 67.5969438460482 & 44.4388926838879 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 3005.13333333333 & 67.3141444940379 & 44.6434156732022 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 3000.03333333333 & 65.4460832416737 & 45.8397689324672 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2996.86666666667 & 63.5715108111906 & 47.1416618611984 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2993.56666666667 & 61.7054666454762 & 48.5137999825196 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2971.96666666667 & 55.9478316664128 & 53.1203190212433 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2944.23333333333 & 49.2275092279045 & 59.8087000441696 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2943.76666666667 & 46.8035041825554 & 62.8962877476997 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2945.26666666667 & 46.4922924580383 & 63.3495685188017 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2919.93333333333 & 36.8884856919857 & 79.1556844516312 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2902.36666666667 & 30.5177911125289 & 95.1040871852327 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2894.26666666667 & 29.0138566804328 & 99.7546344336425 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2903.76666666667 & 26.0687418799126 & 111.38883034874 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2890.1 & 23.1939830011498 & 124.605592746046 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2995.27586206897 & 72.6895244514288 & 41.2064308395691 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2991.69642857143 & 70.6009037488735 & 42.3747610825614 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2987.03703703704 & 69.2624918433799 & 43.1263293817307 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2981.78846153846 & 67.6896327178689 & 44.0508884716008 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2977.16 & 66.2620300051859 & 44.9301055184545 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2971.85416666667 & 64.6708591734048 & 45.9535284462219 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2965.5652173913 & 62.9321285515814 & 47.1232307828365 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2958.09090909091 & 61.0143280072764 & 48.4819059014816 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2949.69047619048 & 58.5304698247321 & 50.3958106781518 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2941.3 & 55.7598697713963 & 52.7494058371856 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2932.52631578947 & 52.5538366088281 & 55.8004230522127 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2923.27777777778 & 48.6933653299964 & 60.034416556889 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2916.11764705882 & 45.2708380576487 & 64.4149251963347 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2912.0625 & 42.7423577752267 & 68.1306004529263 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2907.53333333333 & 39.869319098324 & 72.9265861341373 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2902.14285714286 & 35.6066738544627 & 81.5055870987826 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2899.57692307692 & 33.1885602662179 & 87.3667582991949 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2899.16666666667 & 31.9677524713207 & 90.6903501979878 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2899.90909090909 & 30.5009338506465 & 95.0760755427699 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2899.3 & 29.2787061117623 & 99.024184638926 \tabularnewline
Median & 2854.5 &  &  \tabularnewline
Midrange & 3081.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2895.09677419355 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2907.53333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2895.09677419355 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2907.53333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2907.53333333333 &  &  \tabularnewline
Midmean - Closest Observation & 2895.09677419355 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2907.53333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2912.0625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232338&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]2998.15[/C][C]75.2116029071606[/C][C]39.8628653573684[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2944.08532755224[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2891.93520278421[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3053.30210591746[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2998.61666666667[/C][C]74.3762350860434[/C][C]40.3168655041179[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]3000.08333333333[/C][C]72.4674027309434[/C][C]41.3990735182276[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]3000.68333333333[/C][C]72.1941219091261[/C][C]41.56409488726[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2997.21666666667[/C][C]70.7282780599514[/C][C]42.3764970515207[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2998.38333333333[/C][C]69.9723516490042[/C][C]42.8509727438324[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]3000.78333333333[/C][C]68.8838459479437[/C][C]43.5629470456841[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]3003.93333333333[/C][C]67.5969438460482[/C][C]44.4388926838879[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]3005.13333333333[/C][C]67.3141444940379[/C][C]44.6434156732022[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]3000.03333333333[/C][C]65.4460832416737[/C][C]45.8397689324672[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2996.86666666667[/C][C]63.5715108111906[/C][C]47.1416618611984[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2993.56666666667[/C][C]61.7054666454762[/C][C]48.5137999825196[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2971.96666666667[/C][C]55.9478316664128[/C][C]53.1203190212433[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2944.23333333333[/C][C]49.2275092279045[/C][C]59.8087000441696[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2943.76666666667[/C][C]46.8035041825554[/C][C]62.8962877476997[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2945.26666666667[/C][C]46.4922924580383[/C][C]63.3495685188017[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2919.93333333333[/C][C]36.8884856919857[/C][C]79.1556844516312[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2902.36666666667[/C][C]30.5177911125289[/C][C]95.1040871852327[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2894.26666666667[/C][C]29.0138566804328[/C][C]99.7546344336425[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2903.76666666667[/C][C]26.0687418799126[/C][C]111.38883034874[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2890.1[/C][C]23.1939830011498[/C][C]124.605592746046[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2995.27586206897[/C][C]72.6895244514288[/C][C]41.2064308395691[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2991.69642857143[/C][C]70.6009037488735[/C][C]42.3747610825614[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2987.03703703704[/C][C]69.2624918433799[/C][C]43.1263293817307[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2981.78846153846[/C][C]67.6896327178689[/C][C]44.0508884716008[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2977.16[/C][C]66.2620300051859[/C][C]44.9301055184545[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2971.85416666667[/C][C]64.6708591734048[/C][C]45.9535284462219[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2965.5652173913[/C][C]62.9321285515814[/C][C]47.1232307828365[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2958.09090909091[/C][C]61.0143280072764[/C][C]48.4819059014816[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2949.69047619048[/C][C]58.5304698247321[/C][C]50.3958106781518[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2941.3[/C][C]55.7598697713963[/C][C]52.7494058371856[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2932.52631578947[/C][C]52.5538366088281[/C][C]55.8004230522127[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2923.27777777778[/C][C]48.6933653299964[/C][C]60.034416556889[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2916.11764705882[/C][C]45.2708380576487[/C][C]64.4149251963347[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2912.0625[/C][C]42.7423577752267[/C][C]68.1306004529263[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2907.53333333333[/C][C]39.869319098324[/C][C]72.9265861341373[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2902.14285714286[/C][C]35.6066738544627[/C][C]81.5055870987826[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2899.57692307692[/C][C]33.1885602662179[/C][C]87.3667582991949[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2899.16666666667[/C][C]31.9677524713207[/C][C]90.6903501979878[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2899.90909090909[/C][C]30.5009338506465[/C][C]95.0760755427699[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2899.3[/C][C]29.2787061117623[/C][C]99.024184638926[/C][/ROW]
[ROW][C]Median[/C][C]2854.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3081.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2895.09677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2907.53333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2895.09677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2907.53333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2907.53333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2895.09677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2907.53333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2912.0625[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232338&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232338&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 Mean2998.1575.211602907160639.8628653573684
Geometric Mean2944.08532755224
Harmonic Mean2891.93520278421
Quadratic Mean3053.30210591746
Winsorized Mean ( 1 / 20 )2998.6166666666774.376235086043440.3168655041179
Winsorized Mean ( 2 / 20 )3000.0833333333372.467402730943441.3990735182276
Winsorized Mean ( 3 / 20 )3000.6833333333372.194121909126141.56409488726
Winsorized Mean ( 4 / 20 )2997.2166666666770.728278059951442.3764970515207
Winsorized Mean ( 5 / 20 )2998.3833333333369.972351649004242.8509727438324
Winsorized Mean ( 6 / 20 )3000.7833333333368.883845947943743.5629470456841
Winsorized Mean ( 7 / 20 )3003.9333333333367.596943846048244.4388926838879
Winsorized Mean ( 8 / 20 )3005.1333333333367.314144494037944.6434156732022
Winsorized Mean ( 9 / 20 )3000.0333333333365.446083241673745.8397689324672
Winsorized Mean ( 10 / 20 )2996.8666666666763.571510811190647.1416618611984
Winsorized Mean ( 11 / 20 )2993.5666666666761.705466645476248.5137999825196
Winsorized Mean ( 12 / 20 )2971.9666666666755.947831666412853.1203190212433
Winsorized Mean ( 13 / 20 )2944.2333333333349.227509227904559.8087000441696
Winsorized Mean ( 14 / 20 )2943.7666666666746.803504182555462.8962877476997
Winsorized Mean ( 15 / 20 )2945.2666666666746.492292458038363.3495685188017
Winsorized Mean ( 16 / 20 )2919.9333333333336.888485691985779.1556844516312
Winsorized Mean ( 17 / 20 )2902.3666666666730.517791112528995.1040871852327
Winsorized Mean ( 18 / 20 )2894.2666666666729.013856680432899.7546344336425
Winsorized Mean ( 19 / 20 )2903.7666666666726.0687418799126111.38883034874
Winsorized Mean ( 20 / 20 )2890.123.1939830011498124.605592746046
Trimmed Mean ( 1 / 20 )2995.2758620689772.689524451428841.2064308395691
Trimmed Mean ( 2 / 20 )2991.6964285714370.600903748873542.3747610825614
Trimmed Mean ( 3 / 20 )2987.0370370370469.262491843379943.1263293817307
Trimmed Mean ( 4 / 20 )2981.7884615384667.689632717868944.0508884716008
Trimmed Mean ( 5 / 20 )2977.1666.262030005185944.9301055184545
Trimmed Mean ( 6 / 20 )2971.8541666666764.670859173404845.9535284462219
Trimmed Mean ( 7 / 20 )2965.565217391362.932128551581447.1232307828365
Trimmed Mean ( 8 / 20 )2958.0909090909161.014328007276448.4819059014816
Trimmed Mean ( 9 / 20 )2949.6904761904858.530469824732150.3958106781518
Trimmed Mean ( 10 / 20 )2941.355.759869771396352.7494058371856
Trimmed Mean ( 11 / 20 )2932.5263157894752.553836608828155.8004230522127
Trimmed Mean ( 12 / 20 )2923.2777777777848.693365329996460.034416556889
Trimmed Mean ( 13 / 20 )2916.1176470588245.270838057648764.4149251963347
Trimmed Mean ( 14 / 20 )2912.062542.742357775226768.1306004529263
Trimmed Mean ( 15 / 20 )2907.5333333333339.86931909832472.9265861341373
Trimmed Mean ( 16 / 20 )2902.1428571428635.606673854462781.5055870987826
Trimmed Mean ( 17 / 20 )2899.5769230769233.188560266217987.3667582991949
Trimmed Mean ( 18 / 20 )2899.1666666666731.967752471320790.6903501979878
Trimmed Mean ( 19 / 20 )2899.9090909090930.500933850646595.0760755427699
Trimmed Mean ( 20 / 20 )2899.329.278706111762399.024184638926
Median2854.5
Midrange3081.5
Midmean - Weighted Average at Xnp2895.09677419355
Midmean - Weighted Average at X(n+1)p2907.53333333333
Midmean - Empirical Distribution Function2895.09677419355
Midmean - Empirical Distribution Function - Averaging2907.53333333333
Midmean - Empirical Distribution Function - Interpolation2907.53333333333
Midmean - Closest Observation2895.09677419355
Midmean - True Basic - Statistics Graphics Toolkit2907.53333333333
Midmean - MS Excel (old versions)2912.0625
Number of observations60



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')