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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 computationWed, 24 Nov 2010 19:08:48 +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/Nov/24/t1290625618kyeplroinil0vlr.htm/, Retrieved Fri, 03 May 2024 20:16:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=100521, Retrieved Fri, 03 May 2024 20:16:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact131
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Mean Plot] [] [2010-11-24 15:28:23] [43e84bd88d5f94b739fa54f225367516]
- RMPD    [Central Tendency] [] [2010-11-24 19:08:48] [8eb7c21ac2cd23d1a3046c9313164b8d] [Current]
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Dataseries X:
64.033
65.679
62.776
67.024
67.988
69.529
70.158
69.410
74.049
66.197
67.043
67.459
65.512
64.665
65.382
66.607
58.387
57.564
58.431
65.012
64.176
65.509
65.163
62.158
64.429
61.325
65.339
69.921
70.782
73.287
70.300
71.579
70.700
75.740
75.850
76.381
77.388
75.519
75.573
76.668
79.387
76.876
81.021
82.883
84.016
85.047
85.757
84.792
83.811
84.691
83.496
85.470
85.212
84.802
85.809
85.119
85.228
85.302
85.883
86.315
86.195
88.227
86.411
89.120
88.030
89.372
91.869
92.845
92.787
94.711
94.204
97.217
95.118
93.688
93.140
91.516
90.957
90.372
89.749
85.813
86.026
83.933
83.602
83.384
76.369
60.808
48.071
42.604
41.402
62.121
79.739
79.006
74.472
75.956
75.041
74.873
72.922
70.472
71.423
71.363
73.297
72.081
70.488
65.544
64.450
61.698
61.352
61.072
63.722
61.987
53.802
47.818
50.998
58.438
60.143
61.854
70.987
70.389
72.175
70.243
69.616
69.443
70.833
71.059
72.218
72.647
73.299
73.756
75.557
78.172
75.624
76.959
74.994
76.841
78.043
75.187
73.387
70.798
68.722
68.396
68.466
67.675
65.248
62.974
59.801
57.894
58.592
59.249
59.554
59.753
60.877
60.532
58.452
56.955
56.437
55.588
56.702
57.062
57.826
58.755
60.250
61.142
60.690
58.495
56.020
55.814
56.489
56.587
55.714
55.611
56.093
55.929
54.181
54.810
56.189
57.427
59.432
58.951




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=100521&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=100521&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=100521&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean70.979461.0911558399743865.0497916059967
Geometric Mean70.5762198163618
Harmonic Mean70.1814210400096
Quadratic Mean71.3892441070782
Winsorized Mean ( 1 / 16 )70.981721.0832936990493465.5239849195939
Winsorized Mean ( 2 / 16 )70.973281.0801934705922865.7042297812487
Winsorized Mean ( 3 / 16 )71.140861.0412507788702868.3225035156137
Winsorized Mean ( 4 / 16 )71.15351.0146486719801270.126243659435
Winsorized Mean ( 5 / 16 )71.19480.99844335332352271.3057979333666
Winsorized Mean ( 6 / 16 )71.234280.94533541182427975.3534450407758
Winsorized Mean ( 7 / 16 )70.993620.8789849070655280.7677349512307
Winsorized Mean ( 8 / 16 )70.772660.81380498321283486.96513471888
Winsorized Mean ( 9 / 16 )70.455320.73320750157045196.0919246585616
Winsorized Mean ( 10 / 16 )70.422320.702676822072246100.220069579525
Winsorized Mean ( 11 / 16 )70.409780.688954482836427102.198014170868
Winsorized Mean ( 12 / 16 )70.383140.669745130329441105.089438971179
Winsorized Mean ( 13 / 16 )70.256260.643145085234447109.238586460455
Winsorized Mean ( 14 / 16 )70.261020.632210152020961111.135545317327
Winsorized Mean ( 15 / 16 )70.211820.623243580442883112.655504530198
Winsorized Mean ( 16 / 16 )70.247980.612024849095365114.779620637681
Trimmed Mean ( 1 / 16 )70.95108333333331.0566055116736167.1500219802472
Trimmed Mean ( 2 / 16 )70.91778260869571.0219878895039869.3919990021757
Trimmed Mean ( 3 / 16 )70.886250.97905476112968272.4027427415888
Trimmed Mean ( 4 / 16 )70.78521428571430.94295969207475575.0670626545749
Trimmed Mean ( 5 / 16 )70.6701250.90622616126913377.9828789107449
Trimmed Mean ( 6 / 16 )70.5320526315790.86228850372251781.7963504408219
Trimmed Mean ( 7 / 16 )70.36950.82118984087840885.692121963817
Trimmed Mean ( 8 / 16 )70.23838235294120.78833182818370489.097483879052
Trimmed Mean ( 9 / 16 )70.134031250.76430673901199191.7616287678706
Trimmed Mean ( 10 / 16 )70.07453333333330.75570999383974892.7267521993271
Trimmed Mean ( 11 / 16 )70.01242857142860.74965399325248493.3929909019351
Trimmed Mean ( 12 / 16 )69.94296153846150.74101662284016594.3878441894926
Trimmed Mean ( 13 / 16 )69.86654166666670.72996637548917795.7119999121145
Trimmed Mean ( 14 / 16 )69.79840909090910.71791950693488197.2231683589567
Trimmed Mean ( 15 / 16 )69.71580.696382893770979100.111304604974
Trimmed Mean ( 16 / 16 )69.62394444444440.657162823767922105.946261605681
Median69.725
Midrange71.6605
Midmean - Weighted Average at Xnp69.68544
Midmean - Weighted Average at X(n+1)p69.9429615384615
Midmean - Empirical Distribution Function69.9429615384615
Midmean - Empirical Distribution Function - Averaging69.9429615384615
Midmean - Empirical Distribution Function - Interpolation69.8665416666667
Midmean - Closest Observation69.9429615384615
Midmean - True Basic - Statistics Graphics Toolkit69.9429615384615
Midmean - MS Excel (old versions)69.9429615384615
Number of observations50

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 70.97946 & 1.09115583997438 & 65.0497916059967 \tabularnewline
Geometric Mean & 70.5762198163618 &  &  \tabularnewline
Harmonic Mean & 70.1814210400096 &  &  \tabularnewline
Quadratic Mean & 71.3892441070782 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & 70.98172 & 1.08329369904934 & 65.5239849195939 \tabularnewline
Winsorized Mean ( 2 / 16 ) & 70.97328 & 1.08019347059228 & 65.7042297812487 \tabularnewline
Winsorized Mean ( 3 / 16 ) & 71.14086 & 1.04125077887028 & 68.3225035156137 \tabularnewline
Winsorized Mean ( 4 / 16 ) & 71.1535 & 1.01464867198012 & 70.126243659435 \tabularnewline
Winsorized Mean ( 5 / 16 ) & 71.1948 & 0.998443353323522 & 71.3057979333666 \tabularnewline
Winsorized Mean ( 6 / 16 ) & 71.23428 & 0.945335411824279 & 75.3534450407758 \tabularnewline
Winsorized Mean ( 7 / 16 ) & 70.99362 & 0.87898490706552 & 80.7677349512307 \tabularnewline
Winsorized Mean ( 8 / 16 ) & 70.77266 & 0.813804983212834 & 86.96513471888 \tabularnewline
Winsorized Mean ( 9 / 16 ) & 70.45532 & 0.733207501570451 & 96.0919246585616 \tabularnewline
Winsorized Mean ( 10 / 16 ) & 70.42232 & 0.702676822072246 & 100.220069579525 \tabularnewline
Winsorized Mean ( 11 / 16 ) & 70.40978 & 0.688954482836427 & 102.198014170868 \tabularnewline
Winsorized Mean ( 12 / 16 ) & 70.38314 & 0.669745130329441 & 105.089438971179 \tabularnewline
Winsorized Mean ( 13 / 16 ) & 70.25626 & 0.643145085234447 & 109.238586460455 \tabularnewline
Winsorized Mean ( 14 / 16 ) & 70.26102 & 0.632210152020961 & 111.135545317327 \tabularnewline
Winsorized Mean ( 15 / 16 ) & 70.21182 & 0.623243580442883 & 112.655504530198 \tabularnewline
Winsorized Mean ( 16 / 16 ) & 70.24798 & 0.612024849095365 & 114.779620637681 \tabularnewline
Trimmed Mean ( 1 / 16 ) & 70.9510833333333 & 1.05660551167361 & 67.1500219802472 \tabularnewline
Trimmed Mean ( 2 / 16 ) & 70.9177826086957 & 1.02198788950398 & 69.3919990021757 \tabularnewline
Trimmed Mean ( 3 / 16 ) & 70.88625 & 0.979054761129682 & 72.4027427415888 \tabularnewline
Trimmed Mean ( 4 / 16 ) & 70.7852142857143 & 0.942959692074755 & 75.0670626545749 \tabularnewline
Trimmed Mean ( 5 / 16 ) & 70.670125 & 0.906226161269133 & 77.9828789107449 \tabularnewline
Trimmed Mean ( 6 / 16 ) & 70.532052631579 & 0.862288503722517 & 81.7963504408219 \tabularnewline
Trimmed Mean ( 7 / 16 ) & 70.3695 & 0.821189840878408 & 85.692121963817 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 70.2383823529412 & 0.788331828183704 & 89.097483879052 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 70.13403125 & 0.764306739011991 & 91.7616287678706 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 70.0745333333333 & 0.755709993839748 & 92.7267521993271 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 70.0124285714286 & 0.749653993252484 & 93.3929909019351 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 69.9429615384615 & 0.741016622840165 & 94.3878441894926 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 69.8665416666667 & 0.729966375489177 & 95.7119999121145 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 69.7984090909091 & 0.717919506934881 & 97.2231683589567 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 69.7158 & 0.696382893770979 & 100.111304604974 \tabularnewline
Trimmed Mean ( 16 / 16 ) & 69.6239444444444 & 0.657162823767922 & 105.946261605681 \tabularnewline
Median & 69.725 &  &  \tabularnewline
Midrange & 71.6605 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 69.68544 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 69.9429615384615 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 69.9429615384615 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 69.9429615384615 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 69.8665416666667 &  &  \tabularnewline
Midmean - Closest Observation & 69.9429615384615 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 69.9429615384615 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 69.9429615384615 &  &  \tabularnewline
Number of observations & 50 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=100521&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]70.97946[/C][C]1.09115583997438[/C][C]65.0497916059967[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]70.5762198163618[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]70.1814210400096[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]71.3892441070782[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]70.98172[/C][C]1.08329369904934[/C][C]65.5239849195939[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]70.97328[/C][C]1.08019347059228[/C][C]65.7042297812487[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]71.14086[/C][C]1.04125077887028[/C][C]68.3225035156137[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]71.1535[/C][C]1.01464867198012[/C][C]70.126243659435[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]71.1948[/C][C]0.998443353323522[/C][C]71.3057979333666[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]71.23428[/C][C]0.945335411824279[/C][C]75.3534450407758[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]70.99362[/C][C]0.87898490706552[/C][C]80.7677349512307[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]70.77266[/C][C]0.813804983212834[/C][C]86.96513471888[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]70.45532[/C][C]0.733207501570451[/C][C]96.0919246585616[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]70.42232[/C][C]0.702676822072246[/C][C]100.220069579525[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]70.40978[/C][C]0.688954482836427[/C][C]102.198014170868[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]70.38314[/C][C]0.669745130329441[/C][C]105.089438971179[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]70.25626[/C][C]0.643145085234447[/C][C]109.238586460455[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]70.26102[/C][C]0.632210152020961[/C][C]111.135545317327[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]70.21182[/C][C]0.623243580442883[/C][C]112.655504530198[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]70.24798[/C][C]0.612024849095365[/C][C]114.779620637681[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]70.9510833333333[/C][C]1.05660551167361[/C][C]67.1500219802472[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]70.9177826086957[/C][C]1.02198788950398[/C][C]69.3919990021757[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]70.88625[/C][C]0.979054761129682[/C][C]72.4027427415888[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]70.7852142857143[/C][C]0.942959692074755[/C][C]75.0670626545749[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]70.670125[/C][C]0.906226161269133[/C][C]77.9828789107449[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]70.532052631579[/C][C]0.862288503722517[/C][C]81.7963504408219[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]70.3695[/C][C]0.821189840878408[/C][C]85.692121963817[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]70.2383823529412[/C][C]0.788331828183704[/C][C]89.097483879052[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]70.13403125[/C][C]0.764306739011991[/C][C]91.7616287678706[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]70.0745333333333[/C][C]0.755709993839748[/C][C]92.7267521993271[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]70.0124285714286[/C][C]0.749653993252484[/C][C]93.3929909019351[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]69.9429615384615[/C][C]0.741016622840165[/C][C]94.3878441894926[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]69.8665416666667[/C][C]0.729966375489177[/C][C]95.7119999121145[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]69.7984090909091[/C][C]0.717919506934881[/C][C]97.2231683589567[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]69.7158[/C][C]0.696382893770979[/C][C]100.111304604974[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]69.6239444444444[/C][C]0.657162823767922[/C][C]105.946261605681[/C][/ROW]
[ROW][C]Median[/C][C]69.725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]71.6605[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]69.68544[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]69.9429615384615[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]69.9429615384615[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]69.9429615384615[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]69.8665416666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]69.9429615384615[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]69.9429615384615[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]69.9429615384615[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]50[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=100521&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=100521&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 Mean70.979461.0911558399743865.0497916059967
Geometric Mean70.5762198163618
Harmonic Mean70.1814210400096
Quadratic Mean71.3892441070782
Winsorized Mean ( 1 / 16 )70.981721.0832936990493465.5239849195939
Winsorized Mean ( 2 / 16 )70.973281.0801934705922865.7042297812487
Winsorized Mean ( 3 / 16 )71.140861.0412507788702868.3225035156137
Winsorized Mean ( 4 / 16 )71.15351.0146486719801270.126243659435
Winsorized Mean ( 5 / 16 )71.19480.99844335332352271.3057979333666
Winsorized Mean ( 6 / 16 )71.234280.94533541182427975.3534450407758
Winsorized Mean ( 7 / 16 )70.993620.8789849070655280.7677349512307
Winsorized Mean ( 8 / 16 )70.772660.81380498321283486.96513471888
Winsorized Mean ( 9 / 16 )70.455320.73320750157045196.0919246585616
Winsorized Mean ( 10 / 16 )70.422320.702676822072246100.220069579525
Winsorized Mean ( 11 / 16 )70.409780.688954482836427102.198014170868
Winsorized Mean ( 12 / 16 )70.383140.669745130329441105.089438971179
Winsorized Mean ( 13 / 16 )70.256260.643145085234447109.238586460455
Winsorized Mean ( 14 / 16 )70.261020.632210152020961111.135545317327
Winsorized Mean ( 15 / 16 )70.211820.623243580442883112.655504530198
Winsorized Mean ( 16 / 16 )70.247980.612024849095365114.779620637681
Trimmed Mean ( 1 / 16 )70.95108333333331.0566055116736167.1500219802472
Trimmed Mean ( 2 / 16 )70.91778260869571.0219878895039869.3919990021757
Trimmed Mean ( 3 / 16 )70.886250.97905476112968272.4027427415888
Trimmed Mean ( 4 / 16 )70.78521428571430.94295969207475575.0670626545749
Trimmed Mean ( 5 / 16 )70.6701250.90622616126913377.9828789107449
Trimmed Mean ( 6 / 16 )70.5320526315790.86228850372251781.7963504408219
Trimmed Mean ( 7 / 16 )70.36950.82118984087840885.692121963817
Trimmed Mean ( 8 / 16 )70.23838235294120.78833182818370489.097483879052
Trimmed Mean ( 9 / 16 )70.134031250.76430673901199191.7616287678706
Trimmed Mean ( 10 / 16 )70.07453333333330.75570999383974892.7267521993271
Trimmed Mean ( 11 / 16 )70.01242857142860.74965399325248493.3929909019351
Trimmed Mean ( 12 / 16 )69.94296153846150.74101662284016594.3878441894926
Trimmed Mean ( 13 / 16 )69.86654166666670.72996637548917795.7119999121145
Trimmed Mean ( 14 / 16 )69.79840909090910.71791950693488197.2231683589567
Trimmed Mean ( 15 / 16 )69.71580.696382893770979100.111304604974
Trimmed Mean ( 16 / 16 )69.62394444444440.657162823767922105.946261605681
Median69.725
Midrange71.6605
Midmean - Weighted Average at Xnp69.68544
Midmean - Weighted Average at X(n+1)p69.9429615384615
Midmean - Empirical Distribution Function69.9429615384615
Midmean - Empirical Distribution Function - Averaging69.9429615384615
Midmean - Empirical Distribution Function - Interpolation69.8665416666667
Midmean - Closest Observation69.9429615384615
Midmean - True Basic - Statistics Graphics Toolkit69.9429615384615
Midmean - MS Excel (old versions)69.9429615384615
Number of observations50



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')