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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, 13 Dec 2010 21:08:56 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/13/t1292274414hx3udeo4qm23myy.htm/, Retrieved Mon, 06 May 2024 13:20:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=109206, Retrieved Mon, 06 May 2024 13:20:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact145
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [] [2010-12-13 08:35:23] [21eff0c210342db4afbdafe426a7c254]
-   PD  [(Partial) Autocorrelation Function] [] [2010-12-13 09:29:04] [21eff0c210342db4afbdafe426a7c254]
-    D    [(Partial) Autocorrelation Function] [] [2010-12-13 10:05:17] [21eff0c210342db4afbdafe426a7c254]
- RM D      [ARIMA Forecasting] [] [2010-12-13 10:48:48] [21eff0c210342db4afbdafe426a7c254]
- RMPD          [Central Tendency] [] [2010-12-13 21:08:56] [81d69fb83507cea26168920232cdff1b] [Current]
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Dataseries X:
56.47
62.36
59.71
60.93
68.00
68.61
68.29
72.51
71.81
61.97
57.95
58.13
61.00
53.40
57.58
60.60
65.10
65.10
68.19
73.67
70.13
76.91
82.15
91.27
89.43
90.82
93.75
101.84
109.05
122.77
131.52
132.55
114.57
99.29
72.69
54.04
41.53
43.91
41.76
46.95
50.28
58.10
69.13
64.65
71.63
68.38
74.08
77.56
74.88
77.09
74.70
79.30
84.19
75.56
74.73
74.49
75.93
76.14




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109206&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109206&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109206&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean73.77810344827592.6246151154692128.110065743901
Geometric Mean71.3847482516828
Harmonic Mean69.1842770792747
Quadratic Mean76.3927941966545
Winsorized Mean ( 1 / 19 )73.76431034482762.6168358202892728.1883600694038
Winsorized Mean ( 2 / 19 )73.5367241379312.4902474432008729.5298864129782
Winsorized Mean ( 3 / 19 )73.26982758620692.3180457600916731.6084474463996
Winsorized Mean ( 4 / 19 )73.11879310344832.1585791365018833.8735753843809
Winsorized Mean ( 5 / 19 )72.76620689655171.9368711527946037.5689455602462
Winsorized Mean ( 6 / 19 )72.56862068965521.8572121228400939.0739538026931
Winsorized Mean ( 7 / 19 )72.1932758620691.6452030655565243.8810730258688
Winsorized Mean ( 8 / 19 )72.00431034482761.5429621089630346.6662855338807
Winsorized Mean ( 9 / 19 )71.99189655172411.5183519310832147.4144992856592
Winsorized Mean ( 10 / 19 )71.77810344827591.4626811490522849.0729667875896
Winsorized Mean ( 11 / 19 )70.791.2630987017286256.0447096518427
Winsorized Mean ( 12 / 19 )70.69482758620691.1294994646372462.5895184544527
Winsorized Mean ( 13 / 19 )70.25551724137930.98681131030936971.1944791343686
Winsorized Mean ( 14 / 19 )69.91517241379310.90817018991615776.9846590320783
Winsorized Mean ( 15 / 19 )69.8117241379310.88729781190611178.6790220838707
Winsorized Mean ( 16 / 19 )70.02965517241380.83412266182727683.9560635110943
Winsorized Mean ( 17 / 19 )69.9182758620690.78266372139142789.3337380423966
Winsorized Mean ( 18 / 19 )70.56379310344830.656764919098632107.441477234035
Winsorized Mean ( 19 / 19 )70.590.616334568282923114.531950068386
Trimmed Mean ( 1 / 19 )73.30446428571432.4353383044496430.1003208267938
Trimmed Mean ( 2 / 19 )72.81055555555562.2014077259806933.0745434824527
Trimmed Mean ( 3 / 19 )72.40557692307691.9926426024214836.3364593505574
Trimmed Mean ( 4 / 19 )72.07141.8181272717624939.6404592348114
Trimmed Mean ( 5 / 19 )71.7551.6646619681139843.1048473350398
Trimmed Mean ( 6 / 19 )71.51.5551994761534745.9748097246300
Trimmed Mean ( 7 / 19 )71.26522727272731.4406942583159949.4658924760543
Trimmed Mean ( 8 / 19 )71.08214285714291.3634441570173752.1342531641635
Trimmed Mean ( 9 / 19 )70.9151.2935214804991954.8232101817379
Trimmed Mean ( 10 / 19 )70.73236842105261.2059067779356758.6549223499146
Trimmed Mean ( 11 / 19 )70.56388888888891.1035371900420963.9433718461245
Trimmed Mean ( 12 / 19 )70.52882352941181.0316327301735868.3662135434038
Trimmed Mean ( 13 / 19 )70.503750.974466225891572.3511478661037
Trimmed Mean ( 14 / 19 )70.54066666666670.93862738292928375.1530031507522
Trimmed Mean ( 15 / 19 )70.63321428571430.90895952692061277.7077660707365
Trimmed Mean ( 16 / 19 )70.75538461538460.86800908020228181.5145673348207
Trimmed Mean ( 17 / 19 )70.8650.82354966940131586.0482404801593
Trimmed Mean ( 18 / 19 )71.01181818181820.76976176568792792.251682724662
Trimmed Mean ( 19 / 19 )71.0840.74159302216668495.8531133320491
Median71.72
Midrange87.04
Midmean - Weighted Average at Xnp70.2986206896552
Midmean - Weighted Average at X(n+1)p70.5406666666667
Midmean - Empirical Distribution Function70.5406666666667
Midmean - Empirical Distribution Function - Averaging70.5406666666667
Midmean - Empirical Distribution Function - Interpolation70.6332142857143
Midmean - Closest Observation70.5406666666667
Midmean - True Basic - Statistics Graphics Toolkit70.5406666666667
Midmean - MS Excel (old versions)70.5406666666667
Number of observations58

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 73.7781034482759 & 2.62461511546921 & 28.110065743901 \tabularnewline
Geometric Mean & 71.3847482516828 &  &  \tabularnewline
Harmonic Mean & 69.1842770792747 &  &  \tabularnewline
Quadratic Mean & 76.3927941966545 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 73.7643103448276 & 2.61683582028927 & 28.1883600694038 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 73.536724137931 & 2.49024744320087 & 29.5298864129782 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 73.2698275862069 & 2.31804576009167 & 31.6084474463996 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 73.1187931034483 & 2.15857913650188 & 33.8735753843809 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 72.7662068965517 & 1.93687115279460 & 37.5689455602462 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 72.5686206896552 & 1.85721212284009 & 39.0739538026931 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 72.193275862069 & 1.64520306555652 & 43.8810730258688 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 72.0043103448276 & 1.54296210896303 & 46.6662855338807 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 71.9918965517241 & 1.51835193108321 & 47.4144992856592 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 71.7781034482759 & 1.46268114905228 & 49.0729667875896 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 70.79 & 1.26309870172862 & 56.0447096518427 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 70.6948275862069 & 1.12949946463724 & 62.5895184544527 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 70.2555172413793 & 0.986811310309369 & 71.1944791343686 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 69.9151724137931 & 0.908170189916157 & 76.9846590320783 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 69.811724137931 & 0.887297811906111 & 78.6790220838707 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 70.0296551724138 & 0.834122661827276 & 83.9560635110943 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 69.918275862069 & 0.782663721391427 & 89.3337380423966 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 70.5637931034483 & 0.656764919098632 & 107.441477234035 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 70.59 & 0.616334568282923 & 114.531950068386 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 73.3044642857143 & 2.43533830444964 & 30.1003208267938 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 72.8105555555556 & 2.20140772598069 & 33.0745434824527 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 72.4055769230769 & 1.99264260242148 & 36.3364593505574 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 72.0714 & 1.81812727176249 & 39.6404592348114 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 71.755 & 1.66466196811398 & 43.1048473350398 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 71.5 & 1.55519947615347 & 45.9748097246300 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 71.2652272727273 & 1.44069425831599 & 49.4658924760543 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 71.0821428571429 & 1.36344415701737 & 52.1342531641635 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 70.915 & 1.29352148049919 & 54.8232101817379 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 70.7323684210526 & 1.20590677793567 & 58.6549223499146 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 70.5638888888889 & 1.10353719004209 & 63.9433718461245 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 70.5288235294118 & 1.03163273017358 & 68.3662135434038 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 70.50375 & 0.9744662258915 & 72.3511478661037 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 70.5406666666667 & 0.938627382929283 & 75.1530031507522 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 70.6332142857143 & 0.908959526920612 & 77.7077660707365 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 70.7553846153846 & 0.868009080202281 & 81.5145673348207 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 70.865 & 0.823549669401315 & 86.0482404801593 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 71.0118181818182 & 0.769761765687927 & 92.251682724662 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 71.084 & 0.741593022166684 & 95.8531133320491 \tabularnewline
Median & 71.72 &  &  \tabularnewline
Midrange & 87.04 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 70.2986206896552 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 70.5406666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 70.5406666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 70.5406666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 70.6332142857143 &  &  \tabularnewline
Midmean - Closest Observation & 70.5406666666667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 70.5406666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 70.5406666666667 &  &  \tabularnewline
Number of observations & 58 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109206&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]73.7781034482759[/C][C]2.62461511546921[/C][C]28.110065743901[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]71.3847482516828[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]69.1842770792747[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]76.3927941966545[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]73.7643103448276[/C][C]2.61683582028927[/C][C]28.1883600694038[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]73.536724137931[/C][C]2.49024744320087[/C][C]29.5298864129782[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]73.2698275862069[/C][C]2.31804576009167[/C][C]31.6084474463996[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]73.1187931034483[/C][C]2.15857913650188[/C][C]33.8735753843809[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]72.7662068965517[/C][C]1.93687115279460[/C][C]37.5689455602462[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]72.5686206896552[/C][C]1.85721212284009[/C][C]39.0739538026931[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]72.193275862069[/C][C]1.64520306555652[/C][C]43.8810730258688[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]72.0043103448276[/C][C]1.54296210896303[/C][C]46.6662855338807[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]71.9918965517241[/C][C]1.51835193108321[/C][C]47.4144992856592[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]71.7781034482759[/C][C]1.46268114905228[/C][C]49.0729667875896[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]70.79[/C][C]1.26309870172862[/C][C]56.0447096518427[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]70.6948275862069[/C][C]1.12949946463724[/C][C]62.5895184544527[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]70.2555172413793[/C][C]0.986811310309369[/C][C]71.1944791343686[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]69.9151724137931[/C][C]0.908170189916157[/C][C]76.9846590320783[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]69.811724137931[/C][C]0.887297811906111[/C][C]78.6790220838707[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]70.0296551724138[/C][C]0.834122661827276[/C][C]83.9560635110943[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]69.918275862069[/C][C]0.782663721391427[/C][C]89.3337380423966[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]70.5637931034483[/C][C]0.656764919098632[/C][C]107.441477234035[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]70.59[/C][C]0.616334568282923[/C][C]114.531950068386[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]73.3044642857143[/C][C]2.43533830444964[/C][C]30.1003208267938[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]72.8105555555556[/C][C]2.20140772598069[/C][C]33.0745434824527[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]72.4055769230769[/C][C]1.99264260242148[/C][C]36.3364593505574[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]72.0714[/C][C]1.81812727176249[/C][C]39.6404592348114[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]71.755[/C][C]1.66466196811398[/C][C]43.1048473350398[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]71.5[/C][C]1.55519947615347[/C][C]45.9748097246300[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]71.2652272727273[/C][C]1.44069425831599[/C][C]49.4658924760543[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]71.0821428571429[/C][C]1.36344415701737[/C][C]52.1342531641635[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]70.915[/C][C]1.29352148049919[/C][C]54.8232101817379[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]70.7323684210526[/C][C]1.20590677793567[/C][C]58.6549223499146[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]70.5638888888889[/C][C]1.10353719004209[/C][C]63.9433718461245[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]70.5288235294118[/C][C]1.03163273017358[/C][C]68.3662135434038[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]70.50375[/C][C]0.9744662258915[/C][C]72.3511478661037[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]70.5406666666667[/C][C]0.938627382929283[/C][C]75.1530031507522[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]70.6332142857143[/C][C]0.908959526920612[/C][C]77.7077660707365[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]70.7553846153846[/C][C]0.868009080202281[/C][C]81.5145673348207[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]70.865[/C][C]0.823549669401315[/C][C]86.0482404801593[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]71.0118181818182[/C][C]0.769761765687927[/C][C]92.251682724662[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]71.084[/C][C]0.741593022166684[/C][C]95.8531133320491[/C][/ROW]
[ROW][C]Median[/C][C]71.72[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]87.04[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]70.2986206896552[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]70.5406666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]70.5406666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]70.5406666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]70.6332142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]70.5406666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]70.5406666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]70.5406666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]58[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109206&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109206&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 Mean73.77810344827592.6246151154692128.110065743901
Geometric Mean71.3847482516828
Harmonic Mean69.1842770792747
Quadratic Mean76.3927941966545
Winsorized Mean ( 1 / 19 )73.76431034482762.6168358202892728.1883600694038
Winsorized Mean ( 2 / 19 )73.5367241379312.4902474432008729.5298864129782
Winsorized Mean ( 3 / 19 )73.26982758620692.3180457600916731.6084474463996
Winsorized Mean ( 4 / 19 )73.11879310344832.1585791365018833.8735753843809
Winsorized Mean ( 5 / 19 )72.76620689655171.9368711527946037.5689455602462
Winsorized Mean ( 6 / 19 )72.56862068965521.8572121228400939.0739538026931
Winsorized Mean ( 7 / 19 )72.1932758620691.6452030655565243.8810730258688
Winsorized Mean ( 8 / 19 )72.00431034482761.5429621089630346.6662855338807
Winsorized Mean ( 9 / 19 )71.99189655172411.5183519310832147.4144992856592
Winsorized Mean ( 10 / 19 )71.77810344827591.4626811490522849.0729667875896
Winsorized Mean ( 11 / 19 )70.791.2630987017286256.0447096518427
Winsorized Mean ( 12 / 19 )70.69482758620691.1294994646372462.5895184544527
Winsorized Mean ( 13 / 19 )70.25551724137930.98681131030936971.1944791343686
Winsorized Mean ( 14 / 19 )69.91517241379310.90817018991615776.9846590320783
Winsorized Mean ( 15 / 19 )69.8117241379310.88729781190611178.6790220838707
Winsorized Mean ( 16 / 19 )70.02965517241380.83412266182727683.9560635110943
Winsorized Mean ( 17 / 19 )69.9182758620690.78266372139142789.3337380423966
Winsorized Mean ( 18 / 19 )70.56379310344830.656764919098632107.441477234035
Winsorized Mean ( 19 / 19 )70.590.616334568282923114.531950068386
Trimmed Mean ( 1 / 19 )73.30446428571432.4353383044496430.1003208267938
Trimmed Mean ( 2 / 19 )72.81055555555562.2014077259806933.0745434824527
Trimmed Mean ( 3 / 19 )72.40557692307691.9926426024214836.3364593505574
Trimmed Mean ( 4 / 19 )72.07141.8181272717624939.6404592348114
Trimmed Mean ( 5 / 19 )71.7551.6646619681139843.1048473350398
Trimmed Mean ( 6 / 19 )71.51.5551994761534745.9748097246300
Trimmed Mean ( 7 / 19 )71.26522727272731.4406942583159949.4658924760543
Trimmed Mean ( 8 / 19 )71.08214285714291.3634441570173752.1342531641635
Trimmed Mean ( 9 / 19 )70.9151.2935214804991954.8232101817379
Trimmed Mean ( 10 / 19 )70.73236842105261.2059067779356758.6549223499146
Trimmed Mean ( 11 / 19 )70.56388888888891.1035371900420963.9433718461245
Trimmed Mean ( 12 / 19 )70.52882352941181.0316327301735868.3662135434038
Trimmed Mean ( 13 / 19 )70.503750.974466225891572.3511478661037
Trimmed Mean ( 14 / 19 )70.54066666666670.93862738292928375.1530031507522
Trimmed Mean ( 15 / 19 )70.63321428571430.90895952692061277.7077660707365
Trimmed Mean ( 16 / 19 )70.75538461538460.86800908020228181.5145673348207
Trimmed Mean ( 17 / 19 )70.8650.82354966940131586.0482404801593
Trimmed Mean ( 18 / 19 )71.01181818181820.76976176568792792.251682724662
Trimmed Mean ( 19 / 19 )71.0840.74159302216668495.8531133320491
Median71.72
Midrange87.04
Midmean - Weighted Average at Xnp70.2986206896552
Midmean - Weighted Average at X(n+1)p70.5406666666667
Midmean - Empirical Distribution Function70.5406666666667
Midmean - Empirical Distribution Function - Averaging70.5406666666667
Midmean - Empirical Distribution Function - Interpolation70.6332142857143
Midmean - Closest Observation70.5406666666667
Midmean - True Basic - Statistics Graphics Toolkit70.5406666666667
Midmean - MS Excel (old versions)70.5406666666667
Number of observations58



Parameters (Session):
par1 = Olieprijs ; par4 = 12 ;
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')