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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 Oct 2008 04:58:08 -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/2008/Oct/18/t1224327528pxptd2pzlsujhvi.htm/, Retrieved Sun, 19 May 2024 14:42:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16577, Retrieved Sun, 19 May 2024 14:42:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact175
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [uitvoer van belgi...] [2008-10-13 19:28:16] [1e1d8320a8a1170c475bf6e4ce119de6]
- RMP     [Central Tendency] [Central Tendency ...] [2008-10-18 10:58:08] [fdd69703d301fae09456f660b2f52997] [Current]
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Dataseries X:
53.3
66.9
73.7
71.9
67.9
77.5
82
40.5
76.2
75
64
77.2
63.9
71.4
71.3
50
47.9
55.2
61.8
53.6
60
72.7
63.6
62.1
58.1
68.1
65.5
59.3
65.7
68.3
77.8
49.1
96.9
64.6
67
64.6
84.3
72.6
71.3
52.8
63.9
67.9
74.1
61.7
74.1
83.5
75.6
77.9
69.2
67.8
74.8
69.7
69.9
84.3
81.7
69.3
83.8
96
74.2
70.4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16577&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16577&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16577&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean68.92333333333331.3992721406290149.256560844805
Geometric Mean68.0502983863088
Harmonic Mean67.1280439612671
Quadratic Mean69.7563306565552
Winsorized Mean ( 1 / 20 )69.03166666666671.356614870816850.8852351184265
Winsorized Mean ( 2 / 20 )68.68166666666671.2374556812623755.5023244118143
Winsorized Mean ( 3 / 20 )68.72666666666671.2255930575641956.0762532412333
Winsorized Mean ( 4 / 20 )68.881.1724878181097758.7468790175107
Winsorized Mean ( 5 / 20 )68.89666666666671.1575177187858559.5210471066776
Winsorized Mean ( 6 / 20 )68.77666666666671.1195776207857261.4309051822589
Winsorized Mean ( 7 / 20 )68.92833333333331.0707858977380764.371723123117
Winsorized Mean ( 8 / 20 )68.80833333333330.89368876793656276.9936199290105
Winsorized Mean ( 9 / 20 )68.97333333333330.85553652729102780.6199748732303
Winsorized Mean ( 10 / 20 )69.040.82479649946924783.7054958943533
Winsorized Mean ( 11 / 20 )69.29666666666670.7597054390018391.2151777637855
Winsorized Mean ( 12 / 20 )69.11666666666670.7220074285838995.7284702765853
Winsorized Mean ( 13 / 20 )69.05166666666670.689593721651828100.133838952685
Winsorized Mean ( 14 / 20 )69.26166666666670.609557085041812113.626218718983
Winsorized Mean ( 15 / 20 )69.28666666666670.58989832824376117.455268729013
Winsorized Mean ( 16 / 20 )69.12666666666670.565040204892545122.339377035679
Winsorized Mean ( 17 / 20 )69.12666666666670.556303714687865124.260659854577
Winsorized Mean ( 18 / 20 )69.30666666666670.52865283785819131.100528935887
Winsorized Mean ( 19 / 20 )69.180.509390906912558135.809255841066
Winsorized Mean ( 20 / 20 )69.14666666666670.414772871388577166.709713764976
Trimmed Mean ( 1 / 20 )68.93103448275861.2709947871334754.2339238371085
Trimmed Mean ( 2 / 20 )68.82321428571431.1628614256518359.1843643339841
Trimmed Mean ( 3 / 20 )68.90185185185191.1115381487783861.9878426373198
Trimmed Mean ( 4 / 20 )68.96923076923081.0531556346575765.4881657559147
Trimmed Mean ( 5 / 20 )68.9961.0020385751668768.8556326172474
Trimmed Mean ( 6 / 20 )69.02083333333330.94231662593974273.2459042251336
Trimmed Mean ( 7 / 20 )69.07391304347830.87830774256704878.6443175846253
Trimmed Mean ( 8 / 20 )69.10227272727270.81116344703463685.1890860958903
Trimmed Mean ( 9 / 20 )69.15476190476190.77950818632944288.7158892203541
Trimmed Mean ( 10 / 20 )69.1850.74869587471850992.4073476777361
Trimmed Mean ( 11 / 20 )69.20789473684210.71606620142375296.6501345814622
Trimmed Mean ( 12 / 20 )69.19444444444440.690455847173404100.215596301651
Trimmed Mean ( 13 / 20 )69.20588235294120.665497296754087103.991229852454
Trimmed Mean ( 14 / 20 )69.2281250.639370821889038108.275389851954
Trimmed Mean ( 15 / 20 )69.22333333333330.625634084479766110.645080008540
Trimmed Mean ( 16 / 20 )69.21428571428570.609768676012805113.509087030952
Trimmed Mean ( 17 / 20 )69.22692307692310.592246250559491116.888748576331
Trimmed Mean ( 18 / 20 )69.24166666666670.566130927483334122.306808028440
Trimmed Mean ( 19 / 20 )69.23181818181820.534051992687369129.634977735859
Trimmed Mean ( 20 / 20 )69.240.487604239867582142.000405941514
Median69.25
Midrange68.7
Midmean - Weighted Average at Xnp69.041935483871
Midmean - Weighted Average at X(n+1)p69.2233333333333
Midmean - Empirical Distribution Function69.041935483871
Midmean - Empirical Distribution Function - Averaging69.2233333333333
Midmean - Empirical Distribution Function - Interpolation69.2233333333333
Midmean - Closest Observation69.041935483871
Midmean - True Basic - Statistics Graphics Toolkit69.2233333333333
Midmean - MS Excel (old versions)69.228125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 68.9233333333333 & 1.39927214062901 & 49.256560844805 \tabularnewline
Geometric Mean & 68.0502983863088 &  &  \tabularnewline
Harmonic Mean & 67.1280439612671 &  &  \tabularnewline
Quadratic Mean & 69.7563306565552 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 69.0316666666667 & 1.3566148708168 & 50.8852351184265 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 68.6816666666667 & 1.23745568126237 & 55.5023244118143 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 68.7266666666667 & 1.22559305756419 & 56.0762532412333 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 68.88 & 1.17248781810977 & 58.7468790175107 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 68.8966666666667 & 1.15751771878585 & 59.5210471066776 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 68.7766666666667 & 1.11957762078572 & 61.4309051822589 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 68.9283333333333 & 1.07078589773807 & 64.371723123117 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 68.8083333333333 & 0.893688767936562 & 76.9936199290105 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 68.9733333333333 & 0.855536527291027 & 80.6199748732303 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 69.04 & 0.824796499469247 & 83.7054958943533 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 69.2966666666667 & 0.75970543900183 & 91.2151777637855 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 69.1166666666667 & 0.72200742858389 & 95.7284702765853 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 69.0516666666667 & 0.689593721651828 & 100.133838952685 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 69.2616666666667 & 0.609557085041812 & 113.626218718983 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 69.2866666666667 & 0.58989832824376 & 117.455268729013 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 69.1266666666667 & 0.565040204892545 & 122.339377035679 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 69.1266666666667 & 0.556303714687865 & 124.260659854577 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 69.3066666666667 & 0.52865283785819 & 131.100528935887 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 69.18 & 0.509390906912558 & 135.809255841066 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 69.1466666666667 & 0.414772871388577 & 166.709713764976 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 68.9310344827586 & 1.27099478713347 & 54.2339238371085 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 68.8232142857143 & 1.16286142565183 & 59.1843643339841 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 68.9018518518519 & 1.11153814877838 & 61.9878426373198 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 68.9692307692308 & 1.05315563465757 & 65.4881657559147 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 68.996 & 1.00203857516687 & 68.8556326172474 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 69.0208333333333 & 0.942316625939742 & 73.2459042251336 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 69.0739130434783 & 0.878307742567048 & 78.6443175846253 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 69.1022727272727 & 0.811163447034636 & 85.1890860958903 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 69.1547619047619 & 0.779508186329442 & 88.7158892203541 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 69.185 & 0.748695874718509 & 92.4073476777361 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 69.2078947368421 & 0.716066201423752 & 96.6501345814622 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 69.1944444444444 & 0.690455847173404 & 100.215596301651 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 69.2058823529412 & 0.665497296754087 & 103.991229852454 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 69.228125 & 0.639370821889038 & 108.275389851954 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 69.2233333333333 & 0.625634084479766 & 110.645080008540 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 69.2142857142857 & 0.609768676012805 & 113.509087030952 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 69.2269230769231 & 0.592246250559491 & 116.888748576331 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 69.2416666666667 & 0.566130927483334 & 122.306808028440 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 69.2318181818182 & 0.534051992687369 & 129.634977735859 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 69.24 & 0.487604239867582 & 142.000405941514 \tabularnewline
Median & 69.25 &  &  \tabularnewline
Midrange & 68.7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 69.041935483871 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 69.2233333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 69.041935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 69.2233333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 69.2233333333333 &  &  \tabularnewline
Midmean - Closest Observation & 69.041935483871 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 69.2233333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 69.228125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16577&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]68.9233333333333[/C][C]1.39927214062901[/C][C]49.256560844805[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]68.0502983863088[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]67.1280439612671[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]69.7563306565552[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]69.0316666666667[/C][C]1.3566148708168[/C][C]50.8852351184265[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]68.6816666666667[/C][C]1.23745568126237[/C][C]55.5023244118143[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]68.7266666666667[/C][C]1.22559305756419[/C][C]56.0762532412333[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]68.88[/C][C]1.17248781810977[/C][C]58.7468790175107[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]68.8966666666667[/C][C]1.15751771878585[/C][C]59.5210471066776[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]68.7766666666667[/C][C]1.11957762078572[/C][C]61.4309051822589[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]68.9283333333333[/C][C]1.07078589773807[/C][C]64.371723123117[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]68.8083333333333[/C][C]0.893688767936562[/C][C]76.9936199290105[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]68.9733333333333[/C][C]0.855536527291027[/C][C]80.6199748732303[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]69.04[/C][C]0.824796499469247[/C][C]83.7054958943533[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]69.2966666666667[/C][C]0.75970543900183[/C][C]91.2151777637855[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]69.1166666666667[/C][C]0.72200742858389[/C][C]95.7284702765853[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]69.0516666666667[/C][C]0.689593721651828[/C][C]100.133838952685[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]69.2616666666667[/C][C]0.609557085041812[/C][C]113.626218718983[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]69.2866666666667[/C][C]0.58989832824376[/C][C]117.455268729013[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]69.1266666666667[/C][C]0.565040204892545[/C][C]122.339377035679[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]69.1266666666667[/C][C]0.556303714687865[/C][C]124.260659854577[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]69.3066666666667[/C][C]0.52865283785819[/C][C]131.100528935887[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]69.18[/C][C]0.509390906912558[/C][C]135.809255841066[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]69.1466666666667[/C][C]0.414772871388577[/C][C]166.709713764976[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]68.9310344827586[/C][C]1.27099478713347[/C][C]54.2339238371085[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]68.8232142857143[/C][C]1.16286142565183[/C][C]59.1843643339841[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]68.9018518518519[/C][C]1.11153814877838[/C][C]61.9878426373198[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]68.9692307692308[/C][C]1.05315563465757[/C][C]65.4881657559147[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]68.996[/C][C]1.00203857516687[/C][C]68.8556326172474[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]69.0208333333333[/C][C]0.942316625939742[/C][C]73.2459042251336[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]69.0739130434783[/C][C]0.878307742567048[/C][C]78.6443175846253[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]69.1022727272727[/C][C]0.811163447034636[/C][C]85.1890860958903[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]69.1547619047619[/C][C]0.779508186329442[/C][C]88.7158892203541[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]69.185[/C][C]0.748695874718509[/C][C]92.4073476777361[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]69.2078947368421[/C][C]0.716066201423752[/C][C]96.6501345814622[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]69.1944444444444[/C][C]0.690455847173404[/C][C]100.215596301651[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]69.2058823529412[/C][C]0.665497296754087[/C][C]103.991229852454[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]69.228125[/C][C]0.639370821889038[/C][C]108.275389851954[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]69.2233333333333[/C][C]0.625634084479766[/C][C]110.645080008540[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]69.2142857142857[/C][C]0.609768676012805[/C][C]113.509087030952[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]69.2269230769231[/C][C]0.592246250559491[/C][C]116.888748576331[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]69.2416666666667[/C][C]0.566130927483334[/C][C]122.306808028440[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]69.2318181818182[/C][C]0.534051992687369[/C][C]129.634977735859[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]69.24[/C][C]0.487604239867582[/C][C]142.000405941514[/C][/ROW]
[ROW][C]Median[/C][C]69.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]68.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]69.041935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]69.2233333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]69.041935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]69.2233333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]69.2233333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]69.041935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]69.2233333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]69.228125[/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=16577&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16577&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 Mean68.92333333333331.3992721406290149.256560844805
Geometric Mean68.0502983863088
Harmonic Mean67.1280439612671
Quadratic Mean69.7563306565552
Winsorized Mean ( 1 / 20 )69.03166666666671.356614870816850.8852351184265
Winsorized Mean ( 2 / 20 )68.68166666666671.2374556812623755.5023244118143
Winsorized Mean ( 3 / 20 )68.72666666666671.2255930575641956.0762532412333
Winsorized Mean ( 4 / 20 )68.881.1724878181097758.7468790175107
Winsorized Mean ( 5 / 20 )68.89666666666671.1575177187858559.5210471066776
Winsorized Mean ( 6 / 20 )68.77666666666671.1195776207857261.4309051822589
Winsorized Mean ( 7 / 20 )68.92833333333331.0707858977380764.371723123117
Winsorized Mean ( 8 / 20 )68.80833333333330.89368876793656276.9936199290105
Winsorized Mean ( 9 / 20 )68.97333333333330.85553652729102780.6199748732303
Winsorized Mean ( 10 / 20 )69.040.82479649946924783.7054958943533
Winsorized Mean ( 11 / 20 )69.29666666666670.7597054390018391.2151777637855
Winsorized Mean ( 12 / 20 )69.11666666666670.7220074285838995.7284702765853
Winsorized Mean ( 13 / 20 )69.05166666666670.689593721651828100.133838952685
Winsorized Mean ( 14 / 20 )69.26166666666670.609557085041812113.626218718983
Winsorized Mean ( 15 / 20 )69.28666666666670.58989832824376117.455268729013
Winsorized Mean ( 16 / 20 )69.12666666666670.565040204892545122.339377035679
Winsorized Mean ( 17 / 20 )69.12666666666670.556303714687865124.260659854577
Winsorized Mean ( 18 / 20 )69.30666666666670.52865283785819131.100528935887
Winsorized Mean ( 19 / 20 )69.180.509390906912558135.809255841066
Winsorized Mean ( 20 / 20 )69.14666666666670.414772871388577166.709713764976
Trimmed Mean ( 1 / 20 )68.93103448275861.2709947871334754.2339238371085
Trimmed Mean ( 2 / 20 )68.82321428571431.1628614256518359.1843643339841
Trimmed Mean ( 3 / 20 )68.90185185185191.1115381487783861.9878426373198
Trimmed Mean ( 4 / 20 )68.96923076923081.0531556346575765.4881657559147
Trimmed Mean ( 5 / 20 )68.9961.0020385751668768.8556326172474
Trimmed Mean ( 6 / 20 )69.02083333333330.94231662593974273.2459042251336
Trimmed Mean ( 7 / 20 )69.07391304347830.87830774256704878.6443175846253
Trimmed Mean ( 8 / 20 )69.10227272727270.81116344703463685.1890860958903
Trimmed Mean ( 9 / 20 )69.15476190476190.77950818632944288.7158892203541
Trimmed Mean ( 10 / 20 )69.1850.74869587471850992.4073476777361
Trimmed Mean ( 11 / 20 )69.20789473684210.71606620142375296.6501345814622
Trimmed Mean ( 12 / 20 )69.19444444444440.690455847173404100.215596301651
Trimmed Mean ( 13 / 20 )69.20588235294120.665497296754087103.991229852454
Trimmed Mean ( 14 / 20 )69.2281250.639370821889038108.275389851954
Trimmed Mean ( 15 / 20 )69.22333333333330.625634084479766110.645080008540
Trimmed Mean ( 16 / 20 )69.21428571428570.609768676012805113.509087030952
Trimmed Mean ( 17 / 20 )69.22692307692310.592246250559491116.888748576331
Trimmed Mean ( 18 / 20 )69.24166666666670.566130927483334122.306808028440
Trimmed Mean ( 19 / 20 )69.23181818181820.534051992687369129.634977735859
Trimmed Mean ( 20 / 20 )69.240.487604239867582142.000405941514
Median69.25
Midrange68.7
Midmean - Weighted Average at Xnp69.041935483871
Midmean - Weighted Average at X(n+1)p69.2233333333333
Midmean - Empirical Distribution Function69.041935483871
Midmean - Empirical Distribution Function - Averaging69.2233333333333
Midmean - Empirical Distribution Function - Interpolation69.2233333333333
Midmean - Closest Observation69.041935483871
Midmean - True Basic - Statistics Graphics Toolkit69.2233333333333
Midmean - MS Excel (old versions)69.228125
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')