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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 18 Oct 2009 08:13:25 -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/18/t1255875364y51ny9nhehwvrik.htm/, Retrieved Mon, 29 Apr 2024 09:20:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47314, Retrieved Mon, 29 Apr 2024 09:20:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsworkshop 3 deel 2
Estimated Impact144
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]
- RMPD      [Percentiles] [Percentielen] [2009-10-18 13:47:08] [03557919bc1ce1475f4920f6a43c36b0]
- RM D          [Central Tendency] [central tendency] [2009-10-18 14:13:25] [e7a989b306049c061a54f626f1127c12] [Current]
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Post a new message
Dataseries X:
65.35
55.81
55.40
61.89
40.07
47.30
58.00
54.75
47.61
41.43
46.33
48.74
42.22
44.11
39.34
38.37
52.45
48.17
41.43
42.57
45.18
58.09
50.50
50.11
54.92
59.58
58.48
73.63
93.71
85.20
83.33
103.41
100.50
100.17
94.22
132.54
142.15
136.69
153.83
151.00
97.86
74.45
78.94
74.09
80.28
70.66
78.29
61.78
57.45
53.24
52.72
49.80
45.00
61.38
70.70
98.29
103.32
332.50
284.14
306.29




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47314&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47314&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47314&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean82.16266666666677.7139458743835510.6511852694627
Geometric Mean70.5700053649813
Harmonic Mean63.9035577349635
Quadratic Mean101.299044862230
Winsorized Mean ( 1 / 20 )81.7427.4809967982913310.9266187653856
Winsorized Mean ( 2 / 20 )81.0287.1119014748216711.3932961932704
Winsorized Mean ( 3 / 20 )74.58054.3945337413282316.9711974898748
Winsorized Mean ( 4 / 20 )74.39183333333334.337457145731217.1510243983731
Winsorized Mean ( 5 / 20 )73.72016666666674.1144418276604117.9174162023786
Winsorized Mean ( 6 / 20 )73.20916666666673.9586660160523618.4933930697372
Winsorized Mean ( 7 / 20 )72.90466666666673.8052241926473719.1590989060609
Winsorized Mean ( 8 / 20 )69.13933333333332.8620596260737724.1571952951169
Winsorized Mean ( 9 / 20 )69.15283333333332.8554699029688324.2176719360394
Winsorized Mean ( 10 / 20 )68.87452.7346812725488525.1855675801684
Winsorized Mean ( 11 / 20 )68.99183333333332.6982860273523425.568762034109
Winsorized Mean ( 12 / 20 )68.67783333333332.6169455509196926.2435087001323
Winsorized Mean ( 13 / 20 )68.7062.582643689977126.6029728632869
Winsorized Mean ( 14 / 20 )67.98966666666672.404803114750928.272446193047
Winsorized Mean ( 15 / 20 )68.12716666666672.3457049232799529.0433660221021
Winsorized Mean ( 16 / 20 )65.94051.9312403207663434.1441193470081
Winsorized Mean ( 17 / 20 )65.52116666666671.8273000998457935.8568177565339
Winsorized Mean ( 18 / 20 )65.19116666666671.5979869944894540.7958055300036
Winsorized Mean ( 19 / 20 )64.85233333333331.5191039837256042.6911745529644
Winsorized Mean ( 20 / 20 )64.8091.4617814512776644.3356289295872
Trimmed Mean ( 1 / 20 )78.6015517241386.6300899441848411.8552768342273
Trimmed Mean ( 2 / 20 )75.23678571428575.4447622579795313.8181948356006
Trimmed Mean ( 3 / 20 )72.01944444444444.0034802244452117.9892094894573
Trimmed Mean ( 4 / 20 )71.03442307692313.7949211357226618.7182870305936
Trimmed Mean ( 5 / 20 )70.02723.5497020632666019.7276274887019
Trimmed Mean ( 6 / 20 )69.10395833333333.3192359218008320.8192367042839
Trimmed Mean ( 7 / 20 )68.21152173913043.072908706674322.1977052526736
Trimmed Mean ( 8 / 20 )67.29727272727272.7959797921784524.0692986821765
Trimmed Mean ( 9 / 20 )66.96833333333332.7460111270622524.3874952557012
Trimmed Mean ( 10 / 20 )66.604252.6774696696192024.8758186715417
Trimmed Mean ( 11 / 20 )66.24578947368422.6155442068699425.3277269409878
Trimmed Mean ( 12 / 20 )65.82972222222222.5358570601556925.9595555508877
Trimmed Mean ( 13 / 20 )65.41088235294122.4456529650801926.7457743542925
Trimmed Mean ( 14 / 20 )64.9356252.3230754234167827.9524394022871
Trimmed Mean ( 15 / 20 )64.49933333333332.2044684470637429.2584515869319
Trimmed Mean ( 16 / 20 )63.98107142857142.0415876135836131.3388810761176
Trimmed Mean ( 17 / 20 )63.69846153846151.9636474454292532.4388482702082
Trimmed Mean ( 18 / 20 )63.43041666666671.8771226129493833.7913017663792
Trimmed Mean ( 19 / 20 )63.16363636363641.8251356523687334.6076393180202
Trimmed Mean ( 20 / 20 )62.8971.7618713287148335.6989747065577
Median60.48
Midrange185.435
Midmean - Weighted Average at Xnp63.9909677419355
Midmean - Weighted Average at X(n+1)p64.4993333333333
Midmean - Empirical Distribution Function63.9909677419355
Midmean - Empirical Distribution Function - Averaging64.4993333333333
Midmean - Empirical Distribution Function - Interpolation64.4993333333333
Midmean - Closest Observation63.9909677419355
Midmean - True Basic - Statistics Graphics Toolkit64.4993333333333
Midmean - MS Excel (old versions)64.935625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 82.1626666666667 & 7.71394587438355 & 10.6511852694627 \tabularnewline
Geometric Mean & 70.5700053649813 &  &  \tabularnewline
Harmonic Mean & 63.9035577349635 &  &  \tabularnewline
Quadratic Mean & 101.299044862230 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 81.742 & 7.48099679829133 & 10.9266187653856 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 81.028 & 7.11190147482167 & 11.3932961932704 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 74.5805 & 4.39453374132823 & 16.9711974898748 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 74.3918333333333 & 4.3374571457312 & 17.1510243983731 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 73.7201666666667 & 4.11444182766041 & 17.9174162023786 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 73.2091666666667 & 3.95866601605236 & 18.4933930697372 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 72.9046666666667 & 3.80522419264737 & 19.1590989060609 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 69.1393333333333 & 2.86205962607377 & 24.1571952951169 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 69.1528333333333 & 2.85546990296883 & 24.2176719360394 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 68.8745 & 2.73468127254885 & 25.1855675801684 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 68.9918333333333 & 2.69828602735234 & 25.568762034109 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 68.6778333333333 & 2.61694555091969 & 26.2435087001323 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 68.706 & 2.5826436899771 & 26.6029728632869 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 67.9896666666667 & 2.4048031147509 & 28.272446193047 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 68.1271666666667 & 2.34570492327995 & 29.0433660221021 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 65.9405 & 1.93124032076634 & 34.1441193470081 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 65.5211666666667 & 1.82730009984579 & 35.8568177565339 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 65.1911666666667 & 1.59798699448945 & 40.7958055300036 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 64.8523333333333 & 1.51910398372560 & 42.6911745529644 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 64.809 & 1.46178145127766 & 44.3356289295872 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 78.601551724138 & 6.63008994418484 & 11.8552768342273 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 75.2367857142857 & 5.44476225797953 & 13.8181948356006 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 72.0194444444444 & 4.00348022444521 & 17.9892094894573 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 71.0344230769231 & 3.79492113572266 & 18.7182870305936 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 70.0272 & 3.54970206326660 & 19.7276274887019 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 69.1039583333333 & 3.31923592180083 & 20.8192367042839 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 68.2115217391304 & 3.0729087066743 & 22.1977052526736 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 67.2972727272727 & 2.79597979217845 & 24.0692986821765 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 66.9683333333333 & 2.74601112706225 & 24.3874952557012 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 66.60425 & 2.67746966961920 & 24.8758186715417 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 66.2457894736842 & 2.61554420686994 & 25.3277269409878 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 65.8297222222222 & 2.53585706015569 & 25.9595555508877 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 65.4108823529412 & 2.44565296508019 & 26.7457743542925 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 64.935625 & 2.32307542341678 & 27.9524394022871 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 64.4993333333333 & 2.20446844706374 & 29.2584515869319 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 63.9810714285714 & 2.04158761358361 & 31.3388810761176 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 63.6984615384615 & 1.96364744542925 & 32.4388482702082 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 63.4304166666667 & 1.87712261294938 & 33.7913017663792 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 63.1636363636364 & 1.82513565236873 & 34.6076393180202 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 62.897 & 1.76187132871483 & 35.6989747065577 \tabularnewline
Median & 60.48 &  &  \tabularnewline
Midrange & 185.435 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 63.9909677419355 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 64.4993333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 63.9909677419355 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 64.4993333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 64.4993333333333 &  &  \tabularnewline
Midmean - Closest Observation & 63.9909677419355 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 64.4993333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 64.935625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47314&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]82.1626666666667[/C][C]7.71394587438355[/C][C]10.6511852694627[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]70.5700053649813[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]63.9035577349635[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]101.299044862230[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]81.742[/C][C]7.48099679829133[/C][C]10.9266187653856[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]81.028[/C][C]7.11190147482167[/C][C]11.3932961932704[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]74.5805[/C][C]4.39453374132823[/C][C]16.9711974898748[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]74.3918333333333[/C][C]4.3374571457312[/C][C]17.1510243983731[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]73.7201666666667[/C][C]4.11444182766041[/C][C]17.9174162023786[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]73.2091666666667[/C][C]3.95866601605236[/C][C]18.4933930697372[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]72.9046666666667[/C][C]3.80522419264737[/C][C]19.1590989060609[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]69.1393333333333[/C][C]2.86205962607377[/C][C]24.1571952951169[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]69.1528333333333[/C][C]2.85546990296883[/C][C]24.2176719360394[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]68.8745[/C][C]2.73468127254885[/C][C]25.1855675801684[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]68.9918333333333[/C][C]2.69828602735234[/C][C]25.568762034109[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]68.6778333333333[/C][C]2.61694555091969[/C][C]26.2435087001323[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]68.706[/C][C]2.5826436899771[/C][C]26.6029728632869[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]67.9896666666667[/C][C]2.4048031147509[/C][C]28.272446193047[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]68.1271666666667[/C][C]2.34570492327995[/C][C]29.0433660221021[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]65.9405[/C][C]1.93124032076634[/C][C]34.1441193470081[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]65.5211666666667[/C][C]1.82730009984579[/C][C]35.8568177565339[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]65.1911666666667[/C][C]1.59798699448945[/C][C]40.7958055300036[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]64.8523333333333[/C][C]1.51910398372560[/C][C]42.6911745529644[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]64.809[/C][C]1.46178145127766[/C][C]44.3356289295872[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]78.601551724138[/C][C]6.63008994418484[/C][C]11.8552768342273[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]75.2367857142857[/C][C]5.44476225797953[/C][C]13.8181948356006[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]72.0194444444444[/C][C]4.00348022444521[/C][C]17.9892094894573[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]71.0344230769231[/C][C]3.79492113572266[/C][C]18.7182870305936[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]70.0272[/C][C]3.54970206326660[/C][C]19.7276274887019[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]69.1039583333333[/C][C]3.31923592180083[/C][C]20.8192367042839[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]68.2115217391304[/C][C]3.0729087066743[/C][C]22.1977052526736[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]67.2972727272727[/C][C]2.79597979217845[/C][C]24.0692986821765[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]66.9683333333333[/C][C]2.74601112706225[/C][C]24.3874952557012[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]66.60425[/C][C]2.67746966961920[/C][C]24.8758186715417[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]66.2457894736842[/C][C]2.61554420686994[/C][C]25.3277269409878[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]65.8297222222222[/C][C]2.53585706015569[/C][C]25.9595555508877[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]65.4108823529412[/C][C]2.44565296508019[/C][C]26.7457743542925[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]64.935625[/C][C]2.32307542341678[/C][C]27.9524394022871[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]64.4993333333333[/C][C]2.20446844706374[/C][C]29.2584515869319[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]63.9810714285714[/C][C]2.04158761358361[/C][C]31.3388810761176[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]63.6984615384615[/C][C]1.96364744542925[/C][C]32.4388482702082[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]63.4304166666667[/C][C]1.87712261294938[/C][C]33.7913017663792[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]63.1636363636364[/C][C]1.82513565236873[/C][C]34.6076393180202[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]62.897[/C][C]1.76187132871483[/C][C]35.6989747065577[/C][/ROW]
[ROW][C]Median[/C][C]60.48[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]185.435[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]63.9909677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]64.4993333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]63.9909677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]64.4993333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]64.4993333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]63.9909677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]64.4993333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]64.935625[/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=47314&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47314&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 Mean82.16266666666677.7139458743835510.6511852694627
Geometric Mean70.5700053649813
Harmonic Mean63.9035577349635
Quadratic Mean101.299044862230
Winsorized Mean ( 1 / 20 )81.7427.4809967982913310.9266187653856
Winsorized Mean ( 2 / 20 )81.0287.1119014748216711.3932961932704
Winsorized Mean ( 3 / 20 )74.58054.3945337413282316.9711974898748
Winsorized Mean ( 4 / 20 )74.39183333333334.337457145731217.1510243983731
Winsorized Mean ( 5 / 20 )73.72016666666674.1144418276604117.9174162023786
Winsorized Mean ( 6 / 20 )73.20916666666673.9586660160523618.4933930697372
Winsorized Mean ( 7 / 20 )72.90466666666673.8052241926473719.1590989060609
Winsorized Mean ( 8 / 20 )69.13933333333332.8620596260737724.1571952951169
Winsorized Mean ( 9 / 20 )69.15283333333332.8554699029688324.2176719360394
Winsorized Mean ( 10 / 20 )68.87452.7346812725488525.1855675801684
Winsorized Mean ( 11 / 20 )68.99183333333332.6982860273523425.568762034109
Winsorized Mean ( 12 / 20 )68.67783333333332.6169455509196926.2435087001323
Winsorized Mean ( 13 / 20 )68.7062.582643689977126.6029728632869
Winsorized Mean ( 14 / 20 )67.98966666666672.404803114750928.272446193047
Winsorized Mean ( 15 / 20 )68.12716666666672.3457049232799529.0433660221021
Winsorized Mean ( 16 / 20 )65.94051.9312403207663434.1441193470081
Winsorized Mean ( 17 / 20 )65.52116666666671.8273000998457935.8568177565339
Winsorized Mean ( 18 / 20 )65.19116666666671.5979869944894540.7958055300036
Winsorized Mean ( 19 / 20 )64.85233333333331.5191039837256042.6911745529644
Winsorized Mean ( 20 / 20 )64.8091.4617814512776644.3356289295872
Trimmed Mean ( 1 / 20 )78.6015517241386.6300899441848411.8552768342273
Trimmed Mean ( 2 / 20 )75.23678571428575.4447622579795313.8181948356006
Trimmed Mean ( 3 / 20 )72.01944444444444.0034802244452117.9892094894573
Trimmed Mean ( 4 / 20 )71.03442307692313.7949211357226618.7182870305936
Trimmed Mean ( 5 / 20 )70.02723.5497020632666019.7276274887019
Trimmed Mean ( 6 / 20 )69.10395833333333.3192359218008320.8192367042839
Trimmed Mean ( 7 / 20 )68.21152173913043.072908706674322.1977052526736
Trimmed Mean ( 8 / 20 )67.29727272727272.7959797921784524.0692986821765
Trimmed Mean ( 9 / 20 )66.96833333333332.7460111270622524.3874952557012
Trimmed Mean ( 10 / 20 )66.604252.6774696696192024.8758186715417
Trimmed Mean ( 11 / 20 )66.24578947368422.6155442068699425.3277269409878
Trimmed Mean ( 12 / 20 )65.82972222222222.5358570601556925.9595555508877
Trimmed Mean ( 13 / 20 )65.41088235294122.4456529650801926.7457743542925
Trimmed Mean ( 14 / 20 )64.9356252.3230754234167827.9524394022871
Trimmed Mean ( 15 / 20 )64.49933333333332.2044684470637429.2584515869319
Trimmed Mean ( 16 / 20 )63.98107142857142.0415876135836131.3388810761176
Trimmed Mean ( 17 / 20 )63.69846153846151.9636474454292532.4388482702082
Trimmed Mean ( 18 / 20 )63.43041666666671.8771226129493833.7913017663792
Trimmed Mean ( 19 / 20 )63.16363636363641.8251356523687334.6076393180202
Trimmed Mean ( 20 / 20 )62.8971.7618713287148335.6989747065577
Median60.48
Midrange185.435
Midmean - Weighted Average at Xnp63.9909677419355
Midmean - Weighted Average at X(n+1)p64.4993333333333
Midmean - Empirical Distribution Function63.9909677419355
Midmean - Empirical Distribution Function - Averaging64.4993333333333
Midmean - Empirical Distribution Function - Interpolation64.4993333333333
Midmean - Closest Observation63.9909677419355
Midmean - True Basic - Statistics Graphics Toolkit64.4993333333333
Midmean - MS Excel (old versions)64.935625
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')