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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 11:28:52 +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/t1292671627hinabb680pa4zm5.htm/, Retrieved Fri, 19 Apr 2024 12:01:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111852, Retrieved Fri, 19 Apr 2024 12:01:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156
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]
- RM D  [Central Tendency] [US car sales] [2010-11-06 13:18:47] [97ad38b1c3b35a5feca8b85f7bc7b3ff]
-    D    [Central Tendency] [Winsorized en tri...] [2010-11-12 16:09:32] [39c51da0be01189e8a44eb69e891b7a1]
-    D      [Central Tendency] [export van petroleum] [2010-11-12 17:22:47] [39c51da0be01189e8a44eb69e891b7a1]
- R  D          [Central Tendency] [Winsorized Mean Yt] [2010-12-18 11:28:52] [ecfb965f5669057f3ac5b58964283289] [Current]
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Dataseries X:
63.152
60.106
72.616
73.159
68.848
77.056
62.246
60.777
64.513
58.353
56.511
44.554
71.414
65.719
80.997
69.826
65.386
75.589
65.520
59.003
63.961
59.716
57.520
42.886
69.805
64.656
80.353
71.321
76.577
81.580
71.127
63.478
48.152
69.236
57.038
43.621
69.551
72.009
72.140
81.519
73.310
80.406
70.697
59.328
68.281
70.041
51.244
46.538
61.443
62.256
73.117
74.155
65.191
77.889
68.688
59.983
65.470
65.089
54.795
47.123




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=111852&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=111852&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111852&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 Mean65.44391666666671.2581044097428952.017874001444
Geometric Mean64.6727660025979
Harmonic Mean63.8376025492107
Quadratic Mean66.1535562484487
Winsorized Mean ( 1 / 20 )65.455151.2542148345931652.1881484691831
Winsorized Mean ( 2 / 20 )65.468851.2414524129770152.7356903217944
Winsorized Mean ( 3 / 20 )65.53851.2078363296210954.2610769296533
Winsorized Mean ( 4 / 20 )65.57396666666671.1968028671448154.790950512264
Winsorized Mean ( 5 / 20 )65.45438333333331.1338711988281657.7264714025538
Winsorized Mean ( 6 / 20 )65.68028333333331.0419763923965263.034329580414
Winsorized Mean ( 7 / 20 )66.03868333333330.9405530460751170.2126090696427
Winsorized Mean ( 8 / 20 )66.135750.87124991699697375.9090459692174
Winsorized Mean ( 9 / 20 )65.99970.8185213070610980.6328429457416
Winsorized Mean ( 10 / 20 )65.93920.78054514442527684.478393685418
Winsorized Mean ( 11 / 20 )66.06423333333330.7488064119517488.2260518591702
Winsorized Mean ( 12 / 20 )66.18583333333330.72518735166122291.2672196801533
Winsorized Mean ( 13 / 20 )66.14770.69608324527335395.0284329484525
Winsorized Mean ( 14 / 20 )66.12716666666670.66387803707967499.6074022233854
Winsorized Mean ( 15 / 20 )66.16116666666670.648002589521342102.100157833532
Winsorized Mean ( 16 / 20 )66.03530.618858058212616106.705082245714
Winsorized Mean ( 17 / 20 )66.19906666666670.584566430603979113.244728401987
Winsorized Mean ( 18 / 20 )66.34066666666670.544974155125891121.731766621743
Winsorized Mean ( 19 / 20 )66.45878333333330.486727823391152136.541985354975
Winsorized Mean ( 20 / 20 )66.243450.454596972696416145.719074210021
Trimmed Mean ( 1 / 20 )65.55463793103451.2091182504437454.2168955823604
Trimmed Mean ( 2 / 20 )65.66123214285711.1532958271533256.9335556384771
Trimmed Mean ( 3 / 20 )65.76811111111111.0924048863977960.2048855053934
Trimmed Mean ( 4 / 20 )65.85642307692311.0331775129485563.74163418344
Trimmed Mean ( 5 / 20 )65.941160.96244624779034568.5141223745145
Trimmed Mean ( 6 / 20 )66.06285416666670.89559745252908273.7640041071035
Trimmed Mean ( 7 / 20 )66.14602173913040.84234546970210678.526001644578
Trimmed Mean ( 8 / 20 )66.16693181818180.80664842869990482.0269766406472
Trimmed Mean ( 9 / 20 )66.17250.78052517479587384.7794563670618
Trimmed Mean ( 10 / 20 )66.20130.76034889444389487.0670036923227
Trimmed Mean ( 11 / 20 )66.24268421052630.74287503386451889.1706965381843
Trimmed Mean ( 12 / 20 )66.26972222222220.72692599305755791.16433152085
Trimmed Mean ( 13 / 20 )66.28205882352940.71032324486434493.3125296162705
Trimmed Mean ( 14 / 20 )66.30143750.69388571171510695.550947916365
Trimmed Mean ( 15 / 20 )66.32633333333330.67819077154246597.7989322716408
Trimmed Mean ( 16 / 20 )66.34992857142860.658284609264991100.79216138064
Trimmed Mean ( 17 / 20 )66.39530769230770.635995884769538104.39581337286
Trimmed Mean ( 18 / 20 )66.42416666666670.612477718218393108.451564344062
Trimmed Mean ( 19 / 20 )66.43681818181820.588745454799465112.844723709073
Trimmed Mean ( 20 / 20 )66.433350.572222473642993116.097065494578
Median65.495
Midrange62.233
Midmean - Weighted Average at Xnp66.1130967741936
Midmean - Weighted Average at X(n+1)p66.3263333333333
Midmean - Empirical Distribution Function66.1130967741936
Midmean - Empirical Distribution Function - Averaging66.3263333333333
Midmean - Empirical Distribution Function - Interpolation66.3263333333333
Midmean - Closest Observation66.1130967741936
Midmean - True Basic - Statistics Graphics Toolkit66.3263333333333
Midmean - MS Excel (old versions)66.3014375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 65.4439166666667 & 1.25810440974289 & 52.017874001444 \tabularnewline
Geometric Mean & 64.6727660025979 &  &  \tabularnewline
Harmonic Mean & 63.8376025492107 &  &  \tabularnewline
Quadratic Mean & 66.1535562484487 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 65.45515 & 1.25421483459316 & 52.1881484691831 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 65.46885 & 1.24145241297701 & 52.7356903217944 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 65.5385 & 1.20783632962109 & 54.2610769296533 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 65.5739666666667 & 1.19680286714481 & 54.790950512264 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 65.4543833333333 & 1.13387119882816 & 57.7264714025538 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 65.6802833333333 & 1.04197639239652 & 63.034329580414 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 66.0386833333333 & 0.94055304607511 & 70.2126090696427 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 66.13575 & 0.871249916996973 & 75.9090459692174 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 65.9997 & 0.81852130706109 & 80.6328429457416 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 65.9392 & 0.780545144425276 & 84.478393685418 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 66.0642333333333 & 0.74880641195174 & 88.2260518591702 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 66.1858333333333 & 0.725187351661222 & 91.2672196801533 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 66.1477 & 0.696083245273353 & 95.0284329484525 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 66.1271666666667 & 0.663878037079674 & 99.6074022233854 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 66.1611666666667 & 0.648002589521342 & 102.100157833532 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 66.0353 & 0.618858058212616 & 106.705082245714 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 66.1990666666667 & 0.584566430603979 & 113.244728401987 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 66.3406666666667 & 0.544974155125891 & 121.731766621743 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 66.4587833333333 & 0.486727823391152 & 136.541985354975 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 66.24345 & 0.454596972696416 & 145.719074210021 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 65.5546379310345 & 1.20911825044374 & 54.2168955823604 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 65.6612321428571 & 1.15329582715332 & 56.9335556384771 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 65.7681111111111 & 1.09240488639779 & 60.2048855053934 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 65.8564230769231 & 1.03317751294855 & 63.74163418344 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 65.94116 & 0.962446247790345 & 68.5141223745145 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 66.0628541666667 & 0.895597452529082 & 73.7640041071035 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 66.1460217391304 & 0.842345469702106 & 78.526001644578 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 66.1669318181818 & 0.806648428699904 & 82.0269766406472 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 66.1725 & 0.780525174795873 & 84.7794563670618 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 66.2013 & 0.760348894443894 & 87.0670036923227 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 66.2426842105263 & 0.742875033864518 & 89.1706965381843 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 66.2697222222222 & 0.726925993057557 & 91.16433152085 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 66.2820588235294 & 0.710323244864344 & 93.3125296162705 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 66.3014375 & 0.693885711715106 & 95.550947916365 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 66.3263333333333 & 0.678190771542465 & 97.7989322716408 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 66.3499285714286 & 0.658284609264991 & 100.79216138064 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 66.3953076923077 & 0.635995884769538 & 104.39581337286 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 66.4241666666667 & 0.612477718218393 & 108.451564344062 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 66.4368181818182 & 0.588745454799465 & 112.844723709073 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 66.43335 & 0.572222473642993 & 116.097065494578 \tabularnewline
Median & 65.495 &  &  \tabularnewline
Midrange & 62.233 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 66.1130967741936 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 66.3263333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 66.1130967741936 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 66.3263333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 66.3263333333333 &  &  \tabularnewline
Midmean - Closest Observation & 66.1130967741936 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 66.3263333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 66.3014375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111852&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]65.4439166666667[/C][C]1.25810440974289[/C][C]52.017874001444[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]64.6727660025979[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]63.8376025492107[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]66.1535562484487[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]65.45515[/C][C]1.25421483459316[/C][C]52.1881484691831[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]65.46885[/C][C]1.24145241297701[/C][C]52.7356903217944[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]65.5385[/C][C]1.20783632962109[/C][C]54.2610769296533[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]65.5739666666667[/C][C]1.19680286714481[/C][C]54.790950512264[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]65.4543833333333[/C][C]1.13387119882816[/C][C]57.7264714025538[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]65.6802833333333[/C][C]1.04197639239652[/C][C]63.034329580414[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]66.0386833333333[/C][C]0.94055304607511[/C][C]70.2126090696427[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]66.13575[/C][C]0.871249916996973[/C][C]75.9090459692174[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]65.9997[/C][C]0.81852130706109[/C][C]80.6328429457416[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]65.9392[/C][C]0.780545144425276[/C][C]84.478393685418[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]66.0642333333333[/C][C]0.74880641195174[/C][C]88.2260518591702[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]66.1858333333333[/C][C]0.725187351661222[/C][C]91.2672196801533[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]66.1477[/C][C]0.696083245273353[/C][C]95.0284329484525[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]66.1271666666667[/C][C]0.663878037079674[/C][C]99.6074022233854[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]66.1611666666667[/C][C]0.648002589521342[/C][C]102.100157833532[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]66.0353[/C][C]0.618858058212616[/C][C]106.705082245714[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]66.1990666666667[/C][C]0.584566430603979[/C][C]113.244728401987[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]66.3406666666667[/C][C]0.544974155125891[/C][C]121.731766621743[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]66.4587833333333[/C][C]0.486727823391152[/C][C]136.541985354975[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]66.24345[/C][C]0.454596972696416[/C][C]145.719074210021[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]65.5546379310345[/C][C]1.20911825044374[/C][C]54.2168955823604[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]65.6612321428571[/C][C]1.15329582715332[/C][C]56.9335556384771[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]65.7681111111111[/C][C]1.09240488639779[/C][C]60.2048855053934[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]65.8564230769231[/C][C]1.03317751294855[/C][C]63.74163418344[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]65.94116[/C][C]0.962446247790345[/C][C]68.5141223745145[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]66.0628541666667[/C][C]0.895597452529082[/C][C]73.7640041071035[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]66.1460217391304[/C][C]0.842345469702106[/C][C]78.526001644578[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]66.1669318181818[/C][C]0.806648428699904[/C][C]82.0269766406472[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]66.1725[/C][C]0.780525174795873[/C][C]84.7794563670618[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]66.2013[/C][C]0.760348894443894[/C][C]87.0670036923227[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]66.2426842105263[/C][C]0.742875033864518[/C][C]89.1706965381843[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]66.2697222222222[/C][C]0.726925993057557[/C][C]91.16433152085[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]66.2820588235294[/C][C]0.710323244864344[/C][C]93.3125296162705[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]66.3014375[/C][C]0.693885711715106[/C][C]95.550947916365[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]66.3263333333333[/C][C]0.678190771542465[/C][C]97.7989322716408[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]66.3499285714286[/C][C]0.658284609264991[/C][C]100.79216138064[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]66.3953076923077[/C][C]0.635995884769538[/C][C]104.39581337286[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]66.4241666666667[/C][C]0.612477718218393[/C][C]108.451564344062[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]66.4368181818182[/C][C]0.588745454799465[/C][C]112.844723709073[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]66.43335[/C][C]0.572222473642993[/C][C]116.097065494578[/C][/ROW]
[ROW][C]Median[/C][C]65.495[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]62.233[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]66.1130967741936[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]66.3263333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]66.1130967741936[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]66.3263333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]66.3263333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]66.1130967741936[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]66.3263333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]66.3014375[/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=111852&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111852&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 Mean65.44391666666671.2581044097428952.017874001444
Geometric Mean64.6727660025979
Harmonic Mean63.8376025492107
Quadratic Mean66.1535562484487
Winsorized Mean ( 1 / 20 )65.455151.2542148345931652.1881484691831
Winsorized Mean ( 2 / 20 )65.468851.2414524129770152.7356903217944
Winsorized Mean ( 3 / 20 )65.53851.2078363296210954.2610769296533
Winsorized Mean ( 4 / 20 )65.57396666666671.1968028671448154.790950512264
Winsorized Mean ( 5 / 20 )65.45438333333331.1338711988281657.7264714025538
Winsorized Mean ( 6 / 20 )65.68028333333331.0419763923965263.034329580414
Winsorized Mean ( 7 / 20 )66.03868333333330.9405530460751170.2126090696427
Winsorized Mean ( 8 / 20 )66.135750.87124991699697375.9090459692174
Winsorized Mean ( 9 / 20 )65.99970.8185213070610980.6328429457416
Winsorized Mean ( 10 / 20 )65.93920.78054514442527684.478393685418
Winsorized Mean ( 11 / 20 )66.06423333333330.7488064119517488.2260518591702
Winsorized Mean ( 12 / 20 )66.18583333333330.72518735166122291.2672196801533
Winsorized Mean ( 13 / 20 )66.14770.69608324527335395.0284329484525
Winsorized Mean ( 14 / 20 )66.12716666666670.66387803707967499.6074022233854
Winsorized Mean ( 15 / 20 )66.16116666666670.648002589521342102.100157833532
Winsorized Mean ( 16 / 20 )66.03530.618858058212616106.705082245714
Winsorized Mean ( 17 / 20 )66.19906666666670.584566430603979113.244728401987
Winsorized Mean ( 18 / 20 )66.34066666666670.544974155125891121.731766621743
Winsorized Mean ( 19 / 20 )66.45878333333330.486727823391152136.541985354975
Winsorized Mean ( 20 / 20 )66.243450.454596972696416145.719074210021
Trimmed Mean ( 1 / 20 )65.55463793103451.2091182504437454.2168955823604
Trimmed Mean ( 2 / 20 )65.66123214285711.1532958271533256.9335556384771
Trimmed Mean ( 3 / 20 )65.76811111111111.0924048863977960.2048855053934
Trimmed Mean ( 4 / 20 )65.85642307692311.0331775129485563.74163418344
Trimmed Mean ( 5 / 20 )65.941160.96244624779034568.5141223745145
Trimmed Mean ( 6 / 20 )66.06285416666670.89559745252908273.7640041071035
Trimmed Mean ( 7 / 20 )66.14602173913040.84234546970210678.526001644578
Trimmed Mean ( 8 / 20 )66.16693181818180.80664842869990482.0269766406472
Trimmed Mean ( 9 / 20 )66.17250.78052517479587384.7794563670618
Trimmed Mean ( 10 / 20 )66.20130.76034889444389487.0670036923227
Trimmed Mean ( 11 / 20 )66.24268421052630.74287503386451889.1706965381843
Trimmed Mean ( 12 / 20 )66.26972222222220.72692599305755791.16433152085
Trimmed Mean ( 13 / 20 )66.28205882352940.71032324486434493.3125296162705
Trimmed Mean ( 14 / 20 )66.30143750.69388571171510695.550947916365
Trimmed Mean ( 15 / 20 )66.32633333333330.67819077154246597.7989322716408
Trimmed Mean ( 16 / 20 )66.34992857142860.658284609264991100.79216138064
Trimmed Mean ( 17 / 20 )66.39530769230770.635995884769538104.39581337286
Trimmed Mean ( 18 / 20 )66.42416666666670.612477718218393108.451564344062
Trimmed Mean ( 19 / 20 )66.43681818181820.588745454799465112.844723709073
Trimmed Mean ( 20 / 20 )66.433350.572222473642993116.097065494578
Median65.495
Midrange62.233
Midmean - Weighted Average at Xnp66.1130967741936
Midmean - Weighted Average at X(n+1)p66.3263333333333
Midmean - Empirical Distribution Function66.1130967741936
Midmean - Empirical Distribution Function - Averaging66.3263333333333
Midmean - Empirical Distribution Function - Interpolation66.3263333333333
Midmean - Closest Observation66.1130967741936
Midmean - True Basic - Statistics Graphics Toolkit66.3263333333333
Midmean - MS Excel (old versions)66.3014375
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')