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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, 17 Oct 2009 03:27:04 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/17/t12557716576motyxsopo6xz88.htm/, Retrieved Mon, 06 May 2024 07:41:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47085, Retrieved Mon, 06 May 2024 07:41:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact164
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
-   PD      [Univariate Data Series] [WS 3Yt] [2009-10-17 09:25:12] [6e4e01d7eb22a9f33d58ebb35753a195]
- RMPD          [Central Tendency] [WS 3 CT] [2009-10-17 09:27:04] [2e4ef2c1b76db9b31c0a03b96e94ad77] [Current]
Feedback Forum

Post a new message
Dataseries X:
103.63
103.64
103.66
103.77
103.88
103.91
103.91
103.92
104.05
104.23
104.30
104.31
104.31
104.34
104.55
104.65
104.73
104.75
104.75
104.76
104.94
105.29
105.38
105.43
105.43
105.42
105.52
105.69
105.72
105.74
105.74
105.74
105.95
106.17
106.34
106.37
106.37
106.36
106.44
106.29
106.23
106.23
106.23
106.23
106.34
106.44
106.44
106.48
106.50
106.57
106.40
106.37
106.25
106.21
106.21
106.24
106.19
106.08
106.13
106.09




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47085&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47085&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47085&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean105.4373333333330.124891561250403844.231045538261
Geometric Mean105.432953942329
Harmonic Mean105.428559374746
Quadratic Mean105.441697333961
Winsorized Mean ( 1 / 20 )105.4363333333330.124676749645119845.67759131874
Winsorized Mean ( 2 / 20 )105.4363333333330.124419094640297847.428874467831
Winsorized Mean ( 3 / 20 )105.4398333333330.122839634484871858.353525517202
Winsorized Mean ( 4 / 20 )105.4471666666670.121190910621737870.09138000283
Winsorized Mean ( 5 / 20 )105.4496666666670.120646555429900874.037939093397
Winsorized Mean ( 6 / 20 )105.4456666666670.120098915603723877.990164495687
Winsorized Mean ( 7 / 20 )105.4433333333330.119380383995288883.25510276039
Winsorized Mean ( 8 / 20 )105.4606666666670.115713914380111911.39140207665
Winsorized Mean ( 9 / 20 )105.4876666666670.110311415031502956.27153940997
Winsorized Mean ( 10 / 20 )105.4976666666670.107860122503015978.097041042373
Winsorized Mean ( 11 / 20 )105.4958333333330.107021908012925985.740539409865
Winsorized Mean ( 12 / 20 )105.4958333333330.107021908012925985.740539409865
Winsorized Mean ( 13 / 20 )105.49150.1043770395450111010.67725679754
Winsorized Mean ( 14 / 20 )105.5311666666670.09425146424454671119.67668102061
Winsorized Mean ( 15 / 20 )105.5536666666670.08958314216245491178.27600281368
Winsorized Mean ( 16 / 20 )105.5723333333330.08563335543518371232.84125440164
Winsorized Mean ( 17 / 20 )105.5780.08469146396064141246.61914037836
Winsorized Mean ( 18 / 20 )105.5780.08469146396064141246.61914037836
Winsorized Mean ( 19 / 20 )105.5811666666670.08416727079270781254.42069907076
Winsorized Mean ( 20 / 20 )105.63450.0735148338157711436.91408273766
Trimmed Mean ( 1 / 20 )105.4489655172410.123787938425549851.851697818384
Trimmed Mean ( 2 / 20 )105.46250.122569950873544860.427039811793
Trimmed Mean ( 3 / 20 )105.4770370370370.121106484331533870.94458747799
Trimmed Mean ( 4 / 20 )105.4913461538460.119898784880618879.836657718281
Trimmed Mean ( 5 / 20 )105.50460.118870950434254887.555787301905
Trimmed Mean ( 6 / 20 )105.5183333333330.117585917483956897.372198909199
Trimmed Mean ( 7 / 20 )105.5341304347830.115922919620866910.381922573546
Trimmed Mean ( 8 / 20 )105.5518181818180.113792619842319927.580526119182
Trimmed Mean ( 9 / 20 )105.5680952380950.111902167167882943.396342625933
Trimmed Mean ( 10 / 20 )105.58150.11071536038708953.630098216443
Trimmed Mean ( 11 / 20 )105.5947368421050.109529406433611964.076591669556
Trimmed Mean ( 12 / 20 )105.6097222222220.107840627641059979.312941072055
Trimmed Mean ( 13 / 20 )105.6264705882350.1052167632287691003.89393616467
Trimmed Mean ( 14 / 20 )105.64593750.1019654228385151036.09571322344
Trimmed Mean ( 15 / 20 )105.6623333333330.1002281114732881054.21853989031
Trimmed Mean ( 16 / 20 )105.6778571428570.09876533722280641069.98933142360
Trimmed Mean ( 17 / 20 )105.6930769230770.09739020521082131085.25366277114
Trimmed Mean ( 18 / 20 )105.710.09498855766331271112.87088256134
Trimmed Mean ( 19 / 20 )105.730.0904510103944961168.92005450095
Trimmed Mean ( 20 / 20 )105.75350.08236400274008281283.97718034331
Median105.74
Midrange105.1
Midmean - Weighted Average at Xnp105.626451612903
Midmean - Weighted Average at X(n+1)p105.662333333333
Midmean - Empirical Distribution Function105.626451612903
Midmean - Empirical Distribution Function - Averaging105.662333333333
Midmean - Empirical Distribution Function - Interpolation105.662333333333
Midmean - Closest Observation105.626451612903
Midmean - True Basic - Statistics Graphics Toolkit105.662333333333
Midmean - MS Excel (old versions)105.6459375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 105.437333333333 & 0.124891561250403 & 844.231045538261 \tabularnewline
Geometric Mean & 105.432953942329 &  &  \tabularnewline
Harmonic Mean & 105.428559374746 &  &  \tabularnewline
Quadratic Mean & 105.441697333961 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 105.436333333333 & 0.124676749645119 & 845.67759131874 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 105.436333333333 & 0.124419094640297 & 847.428874467831 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 105.439833333333 & 0.122839634484871 & 858.353525517202 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 105.447166666667 & 0.121190910621737 & 870.09138000283 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 105.449666666667 & 0.120646555429900 & 874.037939093397 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 105.445666666667 & 0.120098915603723 & 877.990164495687 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 105.443333333333 & 0.119380383995288 & 883.25510276039 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 105.460666666667 & 0.115713914380111 & 911.39140207665 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 105.487666666667 & 0.110311415031502 & 956.27153940997 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 105.497666666667 & 0.107860122503015 & 978.097041042373 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 105.495833333333 & 0.107021908012925 & 985.740539409865 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 105.495833333333 & 0.107021908012925 & 985.740539409865 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 105.4915 & 0.104377039545011 & 1010.67725679754 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 105.531166666667 & 0.0942514642445467 & 1119.67668102061 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 105.553666666667 & 0.0895831421624549 & 1178.27600281368 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 105.572333333333 & 0.0856333554351837 & 1232.84125440164 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 105.578 & 0.0846914639606414 & 1246.61914037836 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 105.578 & 0.0846914639606414 & 1246.61914037836 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 105.581166666667 & 0.0841672707927078 & 1254.42069907076 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 105.6345 & 0.073514833815771 & 1436.91408273766 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 105.448965517241 & 0.123787938425549 & 851.851697818384 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 105.4625 & 0.122569950873544 & 860.427039811793 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 105.477037037037 & 0.121106484331533 & 870.94458747799 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 105.491346153846 & 0.119898784880618 & 879.836657718281 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 105.5046 & 0.118870950434254 & 887.555787301905 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 105.518333333333 & 0.117585917483956 & 897.372198909199 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 105.534130434783 & 0.115922919620866 & 910.381922573546 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 105.551818181818 & 0.113792619842319 & 927.580526119182 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 105.568095238095 & 0.111902167167882 & 943.396342625933 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 105.5815 & 0.11071536038708 & 953.630098216443 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 105.594736842105 & 0.109529406433611 & 964.076591669556 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 105.609722222222 & 0.107840627641059 & 979.312941072055 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 105.626470588235 & 0.105216763228769 & 1003.89393616467 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 105.6459375 & 0.101965422838515 & 1036.09571322344 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 105.662333333333 & 0.100228111473288 & 1054.21853989031 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 105.677857142857 & 0.0987653372228064 & 1069.98933142360 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 105.693076923077 & 0.0973902052108213 & 1085.25366277114 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 105.71 & 0.0949885576633127 & 1112.87088256134 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 105.73 & 0.090451010394496 & 1168.92005450095 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 105.7535 & 0.0823640027400828 & 1283.97718034331 \tabularnewline
Median & 105.74 &  &  \tabularnewline
Midrange & 105.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 105.626451612903 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 105.662333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 105.626451612903 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 105.662333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 105.662333333333 &  &  \tabularnewline
Midmean - Closest Observation & 105.626451612903 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 105.662333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 105.6459375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47085&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]105.437333333333[/C][C]0.124891561250403[/C][C]844.231045538261[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]105.432953942329[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]105.428559374746[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]105.441697333961[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]105.436333333333[/C][C]0.124676749645119[/C][C]845.67759131874[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]105.436333333333[/C][C]0.124419094640297[/C][C]847.428874467831[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]105.439833333333[/C][C]0.122839634484871[/C][C]858.353525517202[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]105.447166666667[/C][C]0.121190910621737[/C][C]870.09138000283[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]105.449666666667[/C][C]0.120646555429900[/C][C]874.037939093397[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]105.445666666667[/C][C]0.120098915603723[/C][C]877.990164495687[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]105.443333333333[/C][C]0.119380383995288[/C][C]883.25510276039[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]105.460666666667[/C][C]0.115713914380111[/C][C]911.39140207665[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]105.487666666667[/C][C]0.110311415031502[/C][C]956.27153940997[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]105.497666666667[/C][C]0.107860122503015[/C][C]978.097041042373[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]105.495833333333[/C][C]0.107021908012925[/C][C]985.740539409865[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]105.495833333333[/C][C]0.107021908012925[/C][C]985.740539409865[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]105.4915[/C][C]0.104377039545011[/C][C]1010.67725679754[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]105.531166666667[/C][C]0.0942514642445467[/C][C]1119.67668102061[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]105.553666666667[/C][C]0.0895831421624549[/C][C]1178.27600281368[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]105.572333333333[/C][C]0.0856333554351837[/C][C]1232.84125440164[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]105.578[/C][C]0.0846914639606414[/C][C]1246.61914037836[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]105.578[/C][C]0.0846914639606414[/C][C]1246.61914037836[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]105.581166666667[/C][C]0.0841672707927078[/C][C]1254.42069907076[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]105.6345[/C][C]0.073514833815771[/C][C]1436.91408273766[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]105.448965517241[/C][C]0.123787938425549[/C][C]851.851697818384[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]105.4625[/C][C]0.122569950873544[/C][C]860.427039811793[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]105.477037037037[/C][C]0.121106484331533[/C][C]870.94458747799[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]105.491346153846[/C][C]0.119898784880618[/C][C]879.836657718281[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]105.5046[/C][C]0.118870950434254[/C][C]887.555787301905[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]105.518333333333[/C][C]0.117585917483956[/C][C]897.372198909199[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]105.534130434783[/C][C]0.115922919620866[/C][C]910.381922573546[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]105.551818181818[/C][C]0.113792619842319[/C][C]927.580526119182[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]105.568095238095[/C][C]0.111902167167882[/C][C]943.396342625933[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]105.5815[/C][C]0.11071536038708[/C][C]953.630098216443[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]105.594736842105[/C][C]0.109529406433611[/C][C]964.076591669556[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]105.609722222222[/C][C]0.107840627641059[/C][C]979.312941072055[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]105.626470588235[/C][C]0.105216763228769[/C][C]1003.89393616467[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]105.6459375[/C][C]0.101965422838515[/C][C]1036.09571322344[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]105.662333333333[/C][C]0.100228111473288[/C][C]1054.21853989031[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]105.677857142857[/C][C]0.0987653372228064[/C][C]1069.98933142360[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]105.693076923077[/C][C]0.0973902052108213[/C][C]1085.25366277114[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]105.71[/C][C]0.0949885576633127[/C][C]1112.87088256134[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]105.73[/C][C]0.090451010394496[/C][C]1168.92005450095[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]105.7535[/C][C]0.0823640027400828[/C][C]1283.97718034331[/C][/ROW]
[ROW][C]Median[/C][C]105.74[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]105.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]105.626451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]105.662333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]105.626451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]105.662333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]105.662333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]105.626451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]105.662333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]105.6459375[/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=47085&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47085&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 Mean105.4373333333330.124891561250403844.231045538261
Geometric Mean105.432953942329
Harmonic Mean105.428559374746
Quadratic Mean105.441697333961
Winsorized Mean ( 1 / 20 )105.4363333333330.124676749645119845.67759131874
Winsorized Mean ( 2 / 20 )105.4363333333330.124419094640297847.428874467831
Winsorized Mean ( 3 / 20 )105.4398333333330.122839634484871858.353525517202
Winsorized Mean ( 4 / 20 )105.4471666666670.121190910621737870.09138000283
Winsorized Mean ( 5 / 20 )105.4496666666670.120646555429900874.037939093397
Winsorized Mean ( 6 / 20 )105.4456666666670.120098915603723877.990164495687
Winsorized Mean ( 7 / 20 )105.4433333333330.119380383995288883.25510276039
Winsorized Mean ( 8 / 20 )105.4606666666670.115713914380111911.39140207665
Winsorized Mean ( 9 / 20 )105.4876666666670.110311415031502956.27153940997
Winsorized Mean ( 10 / 20 )105.4976666666670.107860122503015978.097041042373
Winsorized Mean ( 11 / 20 )105.4958333333330.107021908012925985.740539409865
Winsorized Mean ( 12 / 20 )105.4958333333330.107021908012925985.740539409865
Winsorized Mean ( 13 / 20 )105.49150.1043770395450111010.67725679754
Winsorized Mean ( 14 / 20 )105.5311666666670.09425146424454671119.67668102061
Winsorized Mean ( 15 / 20 )105.5536666666670.08958314216245491178.27600281368
Winsorized Mean ( 16 / 20 )105.5723333333330.08563335543518371232.84125440164
Winsorized Mean ( 17 / 20 )105.5780.08469146396064141246.61914037836
Winsorized Mean ( 18 / 20 )105.5780.08469146396064141246.61914037836
Winsorized Mean ( 19 / 20 )105.5811666666670.08416727079270781254.42069907076
Winsorized Mean ( 20 / 20 )105.63450.0735148338157711436.91408273766
Trimmed Mean ( 1 / 20 )105.4489655172410.123787938425549851.851697818384
Trimmed Mean ( 2 / 20 )105.46250.122569950873544860.427039811793
Trimmed Mean ( 3 / 20 )105.4770370370370.121106484331533870.94458747799
Trimmed Mean ( 4 / 20 )105.4913461538460.119898784880618879.836657718281
Trimmed Mean ( 5 / 20 )105.50460.118870950434254887.555787301905
Trimmed Mean ( 6 / 20 )105.5183333333330.117585917483956897.372198909199
Trimmed Mean ( 7 / 20 )105.5341304347830.115922919620866910.381922573546
Trimmed Mean ( 8 / 20 )105.5518181818180.113792619842319927.580526119182
Trimmed Mean ( 9 / 20 )105.5680952380950.111902167167882943.396342625933
Trimmed Mean ( 10 / 20 )105.58150.11071536038708953.630098216443
Trimmed Mean ( 11 / 20 )105.5947368421050.109529406433611964.076591669556
Trimmed Mean ( 12 / 20 )105.6097222222220.107840627641059979.312941072055
Trimmed Mean ( 13 / 20 )105.6264705882350.1052167632287691003.89393616467
Trimmed Mean ( 14 / 20 )105.64593750.1019654228385151036.09571322344
Trimmed Mean ( 15 / 20 )105.6623333333330.1002281114732881054.21853989031
Trimmed Mean ( 16 / 20 )105.6778571428570.09876533722280641069.98933142360
Trimmed Mean ( 17 / 20 )105.6930769230770.09739020521082131085.25366277114
Trimmed Mean ( 18 / 20 )105.710.09498855766331271112.87088256134
Trimmed Mean ( 19 / 20 )105.730.0904510103944961168.92005450095
Trimmed Mean ( 20 / 20 )105.75350.08236400274008281283.97718034331
Median105.74
Midrange105.1
Midmean - Weighted Average at Xnp105.626451612903
Midmean - Weighted Average at X(n+1)p105.662333333333
Midmean - Empirical Distribution Function105.626451612903
Midmean - Empirical Distribution Function - Averaging105.662333333333
Midmean - Empirical Distribution Function - Interpolation105.662333333333
Midmean - Closest Observation105.626451612903
Midmean - True Basic - Statistics Graphics Toolkit105.662333333333
Midmean - MS Excel (old versions)105.6459375
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')