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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, 26 Oct 2008 03:36:42 -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/26/t1225013855foqi7q7y5ndr30q.htm/, Retrieved Fri, 17 May 2024 22:38:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18821, Retrieved Fri, 17 May 2024 22:38:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact163
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Q1 central tenden...] [2007-10-18 09:35:57] [b731da8b544846036771bbf9bf2f34ce]
-    D    [Central Tendency] [Central Tendency ...] [2008-10-26 09:36:42] [35348cd8592af0baf5f138bd59921307] [Current]
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Dataseries X:
72.50
59.40
85.70
88.20
62.80
87.00
79.20
112.00
79.20
40.10
69.00
59.40
73.80
57.40
81.10
46.60
41.40
71.20
67.90
72.00
39.70
51.90
73.70
70.90
60.80
61.00
54.50
39.10
66.60
58.50
59.80
37.30
44.60
48.70
54.00
49.50
61.60
35.00
35.70
51.30
49.00
41.50
42.10
44.10
45.10
50.30
40.90
47.20
36.90
40.90
38.30
46.30
28.40
36.80
50.70
42.80




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18821&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18821&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18821&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean56.09642857142862.2714003408357624.6968478268292
Geometric Mean53.7612768515018
Harmonic Mean51.6151720310031
Quadratic Mean58.5710557479424
Winsorized Mean ( 1 / 18 )55.78928571428572.0911558951299026.6786832317062
Winsorized Mean ( 2 / 18 )55.77142857142862.0747941758124226.8804632390055
Winsorized Mean ( 3 / 18 )55.76071428571432.0458489467215027.2555382815879
Winsorized Mean ( 4 / 18 )55.43928571428571.9617522623347528.2600850161913
Winsorized Mean ( 5 / 18 )55.30535714285711.9162182379215728.8617215139568
Winsorized Mean ( 6 / 18 )55.41251.8982836788332429.1908425583992
Winsorized Mean ( 7 / 18 )54.83751.7375541895688631.5601667730471
Winsorized Mean ( 8 / 18 )54.90892857142861.7207731514840331.9094521692613
Winsorized Mean ( 9 / 18 )54.78035714285711.6727522612601732.7486373275551
Winsorized Mean ( 10 / 18 )54.83392857142861.6331395085701333.5757773807319
Winsorized Mean ( 11 / 18 )54.67678571428571.6033993739589334.1005407650149
Winsorized Mean ( 12 / 18 )54.71964285714291.5747632673929934.7478532108073
Winsorized Mean ( 13 / 18 )54.30178571428571.4903771227432036.4349297138549
Winsorized Mean ( 14 / 18 )54.17678571428571.4181911633445338.2013279412350
Winsorized Mean ( 15 / 18 )54.01607142857141.3286473367157240.6549352381901
Winsorized Mean ( 16 / 18 )53.30178571428571.0915629538794448.8307023656767
Winsorized Mean ( 17 / 18 )53.08928571428571.0116358058662152.4786542809526
Winsorized Mean ( 18 / 18 )53.05714285714290.95794306538126855.3865305512972
Trimmed Mean ( 1 / 18 )55.57407407407412.0462407542161627.159108213228
Trimmed Mean ( 2 / 18 )55.34230769230771.9891245528702927.8224446088352
Trimmed Mean ( 3 / 18 )55.1021.9274631524575628.5878357413700
Trimmed Mean ( 4 / 18 )54.84583333333331.8627173544774329.4439911677958
Trimmed Mean ( 5 / 18 )54.66521739130431.8144407780674630.1278598078729
Trimmed Mean ( 6 / 18 )54.50227272727271.7674185635609730.8372186707502
Trimmed Mean ( 7 / 18 )54.31.7101120311597431.7523057031389
Trimmed Mean ( 8 / 18 )54.19251.684051842721732.1798288064672
Trimmed Mean ( 9 / 18 )54.06052631578951.6511065278593532.7419978079057
Trimmed Mean ( 10 / 18 )53.93611111111111.6177348105012733.3405146263734
Trimmed Mean ( 11 / 18 )53.78823529411761.5798743418176434.0458945818655
Trimmed Mean ( 12 / 18 )53.6468751.5327735795838134.9998693313638
Trimmed Mean ( 13 / 18 )53.481.4708305574523636.3604085657787
Trimmed Mean ( 14 / 18 )53.35357142857141.4073078556608337.9117981996328
Trimmed Mean ( 15 / 18 )53.22692307692311.3350950146805539.8675169120146
Trimmed Mean ( 16 / 18 )53.10416666666671.2559204599379842.2830651785776
Trimmed Mean ( 17 / 18 )53.07272727272731.2270257888493543.2531473706811
Trimmed Mean ( 18 / 18 )53.071.2042490562477944.0689571020767
Median51.6
Midrange70.2
Midmean - Weighted Average at Xnp52.9448275862069
Midmean - Weighted Average at X(n+1)p53.3535714285714
Midmean - Empirical Distribution Function52.9448275862069
Midmean - Empirical Distribution Function - Averaging53.3535714285714
Midmean - Empirical Distribution Function - Interpolation53.3535714285714
Midmean - Closest Observation52.9448275862069
Midmean - True Basic - Statistics Graphics Toolkit53.3535714285714
Midmean - MS Excel (old versions)53.48
Number of observations56

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 56.0964285714286 & 2.27140034083576 & 24.6968478268292 \tabularnewline
Geometric Mean & 53.7612768515018 &  &  \tabularnewline
Harmonic Mean & 51.6151720310031 &  &  \tabularnewline
Quadratic Mean & 58.5710557479424 &  &  \tabularnewline
Winsorized Mean ( 1 / 18 ) & 55.7892857142857 & 2.09115589512990 & 26.6786832317062 \tabularnewline
Winsorized Mean ( 2 / 18 ) & 55.7714285714286 & 2.07479417581242 & 26.8804632390055 \tabularnewline
Winsorized Mean ( 3 / 18 ) & 55.7607142857143 & 2.04584894672150 & 27.2555382815879 \tabularnewline
Winsorized Mean ( 4 / 18 ) & 55.4392857142857 & 1.96175226233475 & 28.2600850161913 \tabularnewline
Winsorized Mean ( 5 / 18 ) & 55.3053571428571 & 1.91621823792157 & 28.8617215139568 \tabularnewline
Winsorized Mean ( 6 / 18 ) & 55.4125 & 1.89828367883324 & 29.1908425583992 \tabularnewline
Winsorized Mean ( 7 / 18 ) & 54.8375 & 1.73755418956886 & 31.5601667730471 \tabularnewline
Winsorized Mean ( 8 / 18 ) & 54.9089285714286 & 1.72077315148403 & 31.9094521692613 \tabularnewline
Winsorized Mean ( 9 / 18 ) & 54.7803571428571 & 1.67275226126017 & 32.7486373275551 \tabularnewline
Winsorized Mean ( 10 / 18 ) & 54.8339285714286 & 1.63313950857013 & 33.5757773807319 \tabularnewline
Winsorized Mean ( 11 / 18 ) & 54.6767857142857 & 1.60339937395893 & 34.1005407650149 \tabularnewline
Winsorized Mean ( 12 / 18 ) & 54.7196428571429 & 1.57476326739299 & 34.7478532108073 \tabularnewline
Winsorized Mean ( 13 / 18 ) & 54.3017857142857 & 1.49037712274320 & 36.4349297138549 \tabularnewline
Winsorized Mean ( 14 / 18 ) & 54.1767857142857 & 1.41819116334453 & 38.2013279412350 \tabularnewline
Winsorized Mean ( 15 / 18 ) & 54.0160714285714 & 1.32864733671572 & 40.6549352381901 \tabularnewline
Winsorized Mean ( 16 / 18 ) & 53.3017857142857 & 1.09156295387944 & 48.8307023656767 \tabularnewline
Winsorized Mean ( 17 / 18 ) & 53.0892857142857 & 1.01163580586621 & 52.4786542809526 \tabularnewline
Winsorized Mean ( 18 / 18 ) & 53.0571428571429 & 0.957943065381268 & 55.3865305512972 \tabularnewline
Trimmed Mean ( 1 / 18 ) & 55.5740740740741 & 2.04624075421616 & 27.159108213228 \tabularnewline
Trimmed Mean ( 2 / 18 ) & 55.3423076923077 & 1.98912455287029 & 27.8224446088352 \tabularnewline
Trimmed Mean ( 3 / 18 ) & 55.102 & 1.92746315245756 & 28.5878357413700 \tabularnewline
Trimmed Mean ( 4 / 18 ) & 54.8458333333333 & 1.86271735447743 & 29.4439911677958 \tabularnewline
Trimmed Mean ( 5 / 18 ) & 54.6652173913043 & 1.81444077806746 & 30.1278598078729 \tabularnewline
Trimmed Mean ( 6 / 18 ) & 54.5022727272727 & 1.76741856356097 & 30.8372186707502 \tabularnewline
Trimmed Mean ( 7 / 18 ) & 54.3 & 1.71011203115974 & 31.7523057031389 \tabularnewline
Trimmed Mean ( 8 / 18 ) & 54.1925 & 1.6840518427217 & 32.1798288064672 \tabularnewline
Trimmed Mean ( 9 / 18 ) & 54.0605263157895 & 1.65110652785935 & 32.7419978079057 \tabularnewline
Trimmed Mean ( 10 / 18 ) & 53.9361111111111 & 1.61773481050127 & 33.3405146263734 \tabularnewline
Trimmed Mean ( 11 / 18 ) & 53.7882352941176 & 1.57987434181764 & 34.0458945818655 \tabularnewline
Trimmed Mean ( 12 / 18 ) & 53.646875 & 1.53277357958381 & 34.9998693313638 \tabularnewline
Trimmed Mean ( 13 / 18 ) & 53.48 & 1.47083055745236 & 36.3604085657787 \tabularnewline
Trimmed Mean ( 14 / 18 ) & 53.3535714285714 & 1.40730785566083 & 37.9117981996328 \tabularnewline
Trimmed Mean ( 15 / 18 ) & 53.2269230769231 & 1.33509501468055 & 39.8675169120146 \tabularnewline
Trimmed Mean ( 16 / 18 ) & 53.1041666666667 & 1.25592045993798 & 42.2830651785776 \tabularnewline
Trimmed Mean ( 17 / 18 ) & 53.0727272727273 & 1.22702578884935 & 43.2531473706811 \tabularnewline
Trimmed Mean ( 18 / 18 ) & 53.07 & 1.20424905624779 & 44.0689571020767 \tabularnewline
Median & 51.6 &  &  \tabularnewline
Midrange & 70.2 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 52.9448275862069 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 53.3535714285714 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 52.9448275862069 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 53.3535714285714 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 53.3535714285714 &  &  \tabularnewline
Midmean - Closest Observation & 52.9448275862069 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 53.3535714285714 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 53.48 &  &  \tabularnewline
Number of observations & 56 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18821&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]56.0964285714286[/C][C]2.27140034083576[/C][C]24.6968478268292[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]53.7612768515018[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]51.6151720310031[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]58.5710557479424[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 18 )[/C][C]55.7892857142857[/C][C]2.09115589512990[/C][C]26.6786832317062[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 18 )[/C][C]55.7714285714286[/C][C]2.07479417581242[/C][C]26.8804632390055[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 18 )[/C][C]55.7607142857143[/C][C]2.04584894672150[/C][C]27.2555382815879[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 18 )[/C][C]55.4392857142857[/C][C]1.96175226233475[/C][C]28.2600850161913[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 18 )[/C][C]55.3053571428571[/C][C]1.91621823792157[/C][C]28.8617215139568[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 18 )[/C][C]55.4125[/C][C]1.89828367883324[/C][C]29.1908425583992[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 18 )[/C][C]54.8375[/C][C]1.73755418956886[/C][C]31.5601667730471[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 18 )[/C][C]54.9089285714286[/C][C]1.72077315148403[/C][C]31.9094521692613[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 18 )[/C][C]54.7803571428571[/C][C]1.67275226126017[/C][C]32.7486373275551[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 18 )[/C][C]54.8339285714286[/C][C]1.63313950857013[/C][C]33.5757773807319[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 18 )[/C][C]54.6767857142857[/C][C]1.60339937395893[/C][C]34.1005407650149[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 18 )[/C][C]54.7196428571429[/C][C]1.57476326739299[/C][C]34.7478532108073[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 18 )[/C][C]54.3017857142857[/C][C]1.49037712274320[/C][C]36.4349297138549[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 18 )[/C][C]54.1767857142857[/C][C]1.41819116334453[/C][C]38.2013279412350[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 18 )[/C][C]54.0160714285714[/C][C]1.32864733671572[/C][C]40.6549352381901[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 18 )[/C][C]53.3017857142857[/C][C]1.09156295387944[/C][C]48.8307023656767[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 18 )[/C][C]53.0892857142857[/C][C]1.01163580586621[/C][C]52.4786542809526[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 18 )[/C][C]53.0571428571429[/C][C]0.957943065381268[/C][C]55.3865305512972[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 18 )[/C][C]55.5740740740741[/C][C]2.04624075421616[/C][C]27.159108213228[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 18 )[/C][C]55.3423076923077[/C][C]1.98912455287029[/C][C]27.8224446088352[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 18 )[/C][C]55.102[/C][C]1.92746315245756[/C][C]28.5878357413700[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 18 )[/C][C]54.8458333333333[/C][C]1.86271735447743[/C][C]29.4439911677958[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 18 )[/C][C]54.6652173913043[/C][C]1.81444077806746[/C][C]30.1278598078729[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 18 )[/C][C]54.5022727272727[/C][C]1.76741856356097[/C][C]30.8372186707502[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 18 )[/C][C]54.3[/C][C]1.71011203115974[/C][C]31.7523057031389[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 18 )[/C][C]54.1925[/C][C]1.6840518427217[/C][C]32.1798288064672[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 18 )[/C][C]54.0605263157895[/C][C]1.65110652785935[/C][C]32.7419978079057[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 18 )[/C][C]53.9361111111111[/C][C]1.61773481050127[/C][C]33.3405146263734[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 18 )[/C][C]53.7882352941176[/C][C]1.57987434181764[/C][C]34.0458945818655[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 18 )[/C][C]53.646875[/C][C]1.53277357958381[/C][C]34.9998693313638[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 18 )[/C][C]53.48[/C][C]1.47083055745236[/C][C]36.3604085657787[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 18 )[/C][C]53.3535714285714[/C][C]1.40730785566083[/C][C]37.9117981996328[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 18 )[/C][C]53.2269230769231[/C][C]1.33509501468055[/C][C]39.8675169120146[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 18 )[/C][C]53.1041666666667[/C][C]1.25592045993798[/C][C]42.2830651785776[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 18 )[/C][C]53.0727272727273[/C][C]1.22702578884935[/C][C]43.2531473706811[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 18 )[/C][C]53.07[/C][C]1.20424905624779[/C][C]44.0689571020767[/C][/ROW]
[ROW][C]Median[/C][C]51.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]70.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]52.9448275862069[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]53.3535714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]52.9448275862069[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]53.3535714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]53.3535714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]52.9448275862069[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]53.3535714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]53.48[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]56[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18821&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18821&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 Mean56.09642857142862.2714003408357624.6968478268292
Geometric Mean53.7612768515018
Harmonic Mean51.6151720310031
Quadratic Mean58.5710557479424
Winsorized Mean ( 1 / 18 )55.78928571428572.0911558951299026.6786832317062
Winsorized Mean ( 2 / 18 )55.77142857142862.0747941758124226.8804632390055
Winsorized Mean ( 3 / 18 )55.76071428571432.0458489467215027.2555382815879
Winsorized Mean ( 4 / 18 )55.43928571428571.9617522623347528.2600850161913
Winsorized Mean ( 5 / 18 )55.30535714285711.9162182379215728.8617215139568
Winsorized Mean ( 6 / 18 )55.41251.8982836788332429.1908425583992
Winsorized Mean ( 7 / 18 )54.83751.7375541895688631.5601667730471
Winsorized Mean ( 8 / 18 )54.90892857142861.7207731514840331.9094521692613
Winsorized Mean ( 9 / 18 )54.78035714285711.6727522612601732.7486373275551
Winsorized Mean ( 10 / 18 )54.83392857142861.6331395085701333.5757773807319
Winsorized Mean ( 11 / 18 )54.67678571428571.6033993739589334.1005407650149
Winsorized Mean ( 12 / 18 )54.71964285714291.5747632673929934.7478532108073
Winsorized Mean ( 13 / 18 )54.30178571428571.4903771227432036.4349297138549
Winsorized Mean ( 14 / 18 )54.17678571428571.4181911633445338.2013279412350
Winsorized Mean ( 15 / 18 )54.01607142857141.3286473367157240.6549352381901
Winsorized Mean ( 16 / 18 )53.30178571428571.0915629538794448.8307023656767
Winsorized Mean ( 17 / 18 )53.08928571428571.0116358058662152.4786542809526
Winsorized Mean ( 18 / 18 )53.05714285714290.95794306538126855.3865305512972
Trimmed Mean ( 1 / 18 )55.57407407407412.0462407542161627.159108213228
Trimmed Mean ( 2 / 18 )55.34230769230771.9891245528702927.8224446088352
Trimmed Mean ( 3 / 18 )55.1021.9274631524575628.5878357413700
Trimmed Mean ( 4 / 18 )54.84583333333331.8627173544774329.4439911677958
Trimmed Mean ( 5 / 18 )54.66521739130431.8144407780674630.1278598078729
Trimmed Mean ( 6 / 18 )54.50227272727271.7674185635609730.8372186707502
Trimmed Mean ( 7 / 18 )54.31.7101120311597431.7523057031389
Trimmed Mean ( 8 / 18 )54.19251.684051842721732.1798288064672
Trimmed Mean ( 9 / 18 )54.06052631578951.6511065278593532.7419978079057
Trimmed Mean ( 10 / 18 )53.93611111111111.6177348105012733.3405146263734
Trimmed Mean ( 11 / 18 )53.78823529411761.5798743418176434.0458945818655
Trimmed Mean ( 12 / 18 )53.6468751.5327735795838134.9998693313638
Trimmed Mean ( 13 / 18 )53.481.4708305574523636.3604085657787
Trimmed Mean ( 14 / 18 )53.35357142857141.4073078556608337.9117981996328
Trimmed Mean ( 15 / 18 )53.22692307692311.3350950146805539.8675169120146
Trimmed Mean ( 16 / 18 )53.10416666666671.2559204599379842.2830651785776
Trimmed Mean ( 17 / 18 )53.07272727272731.2270257888493543.2531473706811
Trimmed Mean ( 18 / 18 )53.071.2042490562477944.0689571020767
Median51.6
Midrange70.2
Midmean - Weighted Average at Xnp52.9448275862069
Midmean - Weighted Average at X(n+1)p53.3535714285714
Midmean - Empirical Distribution Function52.9448275862069
Midmean - Empirical Distribution Function - Averaging53.3535714285714
Midmean - Empirical Distribution Function - Interpolation53.3535714285714
Midmean - Closest Observation52.9448275862069
Midmean - True Basic - Statistics Graphics Toolkit53.3535714285714
Midmean - MS Excel (old versions)53.48
Number of observations56



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')