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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 computationMon, 20 Oct 2008 12:02:19 -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/20/t1224525783336e6719cmm2gg2.htm/, Retrieved Sun, 19 May 2024 14:11:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17813, Retrieved Sun, 19 May 2024 14:11:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact136
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Central tendency ...] [2008-10-20 13:35:29] [1ce0d16c8f4225c977b42c8fa93bc163]
F    D    [Central Tendency] [Central tendency ...] [2008-10-20 18:02:19] [8758b22b4a10c08c31202f233362e983] [Current]
Feedback Forum
2008-10-25 12:46:57 [Stéphanie Claes] [reply
Door het weglaten van de extreme waarden maakt de student de juiste conclusie, namelijk dat Central Tendency bij de dataset Investments robuust is. We zien dan ook dat de twee grafieken (trimmed mean en winsorized mean gelijkaardig verlopen.
  2008-10-26 09:22:32 [Stéphanie Claes] [reply
Mijn vorige post is niet correct. Daar moest komen dat de central tendency bij investeringen niet robuust is omdat bij het verwijderen van de outliers de trimmed mean en winsorized mean

Ik denk niet dat central tendency bij de investeringen robust is aangezien de trimmed mean en de winsorized mean indien we de outliers substitueren, beiden ongeveer gelijk lopen met hun tegenhangers bij de niet gewijzigde gegevens.
    2008-10-26 09:24:37 [Stéphanie Claes] [reply
Excuses, de vorige post moet absoluut weg ! de eerste is correct, ik wou cancellen maar heb save gedrukt.
2008-10-27 23:12:50 [a7e076854c32462fd499d2de3f6d4e86] [reply
De eerste post is inderdaad correct: de Central Tendency bij de dataset Investments is robuust.

Post a new message
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 time1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17813&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]1 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=17813&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17813&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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







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=17813&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=17813&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17813&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')