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Description of Statistical Computation

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 21:04:38 +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/t12922741593cwqtlqc2ww9env.htm/, Retrieved Mon, 06 May 2024 12:41:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=109204, Retrieved Mon, 06 May 2024 12:41:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact154

Tree of Dependent Computations

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 21:04:38] [81d69fb83507cea26168920232cdff1b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
102.3
99
100.7
115.5
100.7
109.9
114.6
85.4
100.5
114.8
116.5
112.9
102
106
105.3
118.8
106.1
109.3
117.2
92.5
104.2
112.5
122.4
113.3
100
110.7
112.8
109.8
117.3
109.1
115.9
96
99.8
116.8
115.7
99.4
94.3
91
93.2
103.1
94.1
91.8
102.7
82.6
89.1
104.5
105.1
95.1
88.7
86.3
91.8
111.5
99.7
97.5
111.7
86.2
95.4
113

Tables (Output of Computation)





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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109204&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109204&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109204&T=0

As an alternative you can also use a QR Code:  
QR Code


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

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






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean103.6913793103451.3191508673328478.6046402107106
Geometric Mean103.203445308005
Harmonic Mean102.706756607467
Quadratic Mean104.168571109028
Winsorized Mean ( 1 / 19 )103.6775862068971.2922755365369380.2286998984243
Winsorized Mean ( 2 / 19 )103.6534482758621.2753733674338781.2730224125815
Winsorized Mean ( 3 / 19 )103.6534482758621.2731657755604081.4139448810092
Winsorized Mean ( 4 / 19 )103.7913793103451.2304005723985784.3557631869526
Winsorized Mean ( 5 / 19 )103.81.2182768269577585.2023101015612
Winsorized Mean ( 6 / 19 )103.9344827586211.1670681663057389.056051530921
Winsorized Mean ( 7 / 19 )104.0068965517241.1443087877614790.890586233446
Winsorized Mean ( 8 / 19 )103.9793103448281.1393892469847791.258813105349
Winsorized Mean ( 9 / 19 )103.9793103448281.1002495416798294.5052066879986
Winsorized Mean ( 10 / 19 )104.0655172413791.0725287489230497.028184415453
Winsorized Mean ( 11 / 19 )103.9896551724141.00116293436404103.868862502855
Winsorized Mean ( 12 / 19 )103.9689655172410.98394924745956105.664967767064
Winsorized Mean ( 13 / 19 )104.1258620689660.94991820052466109.615609019234
Winsorized Mean ( 14 / 19 )104.1741379310340.934003606260882111.535048936350
Winsorized Mean ( 15 / 19 )104.2517241379310.896127453244246116.335822276741
Winsorized Mean ( 16 / 19 )104.4448275862070.795423891807098131.307129018871
Winsorized Mean ( 17 / 19 )104.8258620689660.721020317686543145.385448228849
Winsorized Mean ( 18 / 19 )104.7017241379310.663655440977805157.765186078588
Winsorized Mean ( 19 / 19 )104.5379310344830.608871833621343171.691192237831
Trimmed Mean ( 1 / 19 )103.7339285714291.2687561062119481.7603383846099
Trimmed Mean ( 2 / 19 )103.7944444444441.2391652491865383.7615842702027
Trimmed Mean ( 3 / 19 )103.8730769230771.2130515581953885.6295647298008
Trimmed Mean ( 4 / 19 )103.9581.1807333936747988.0452780931794
Trimmed Mean ( 5 / 19 )104.0083333333331.1565755324123689.9278347315499
Trimmed Mean ( 6 / 19 )104.0608695652171.1291802775194292.156116819378
Trimmed Mean ( 7 / 19 )104.0886363636361.1093882278327293.825257698094
Trimmed Mean ( 8 / 19 )104.1047619047621.0891501251586195.583482478691
Trimmed Mean ( 9 / 19 )104.12751.0626043689312697.9927271565136
Trimmed Mean ( 10 / 19 )104.1526315789471.03711862065815100.424994310538
Trimmed Mean ( 11 / 19 )104.1666666666671.00916435649140103.220715234956
Trimmed Mean ( 12 / 19 )104.1941176470590.989435651607263105.306613399066
Trimmed Mean ( 13 / 19 )104.2281250.964566114799057108.057004492339
Trimmed Mean ( 14 / 19 )104.2433333333330.937356068133894111.209962656841
Trimmed Mean ( 15 / 19 )104.2535714285710.900462581633544115.777794163799
Trimmed Mean ( 16 / 19 )104.2538461538460.856526631122749121.716993220851
Trimmed Mean ( 17 / 19 )104.2250.825087830195205126.319885211907
Trimmed Mean ( 18 / 19 )104.1318181818180.799577441531402130.233561845339
Trimmed Mean ( 19 / 19 )104.040.777424899063704133.826431498787
Median103.65
Midrange102.5
Midmean - Weighted Average at Xnp103.948275862069
Midmean - Weighted Average at X(n+1)p104.243333333333
Midmean - Empirical Distribution Function104.243333333333
Midmean - Empirical Distribution Function - Averaging104.243333333333
Midmean - Empirical Distribution Function - Interpolation104.253571428571
Midmean - Closest Observation104.243333333333
Midmean - True Basic - Statistics Graphics Toolkit104.243333333333
Midmean - MS Excel (old versions)104.243333333333
Number of observations58

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 103.691379310345 & 1.31915086733284 & 78.6046402107106 \tabularnewline
Geometric Mean & 103.203445308005 &  &  \tabularnewline
Harmonic Mean & 102.706756607467 &  &  \tabularnewline
Quadratic Mean & 104.168571109028 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 103.677586206897 & 1.29227553653693 & 80.2286998984243 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 103.653448275862 & 1.27537336743387 & 81.2730224125815 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 103.653448275862 & 1.27316577556040 & 81.4139448810092 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 103.791379310345 & 1.23040057239857 & 84.3557631869526 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 103.8 & 1.21827682695775 & 85.2023101015612 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 103.934482758621 & 1.16706816630573 & 89.056051530921 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 104.006896551724 & 1.14430878776147 & 90.890586233446 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 103.979310344828 & 1.13938924698477 & 91.258813105349 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 103.979310344828 & 1.10024954167982 & 94.5052066879986 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 104.065517241379 & 1.07252874892304 & 97.028184415453 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 103.989655172414 & 1.00116293436404 & 103.868862502855 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 103.968965517241 & 0.98394924745956 & 105.664967767064 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 104.125862068966 & 0.94991820052466 & 109.615609019234 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 104.174137931034 & 0.934003606260882 & 111.535048936350 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 104.251724137931 & 0.896127453244246 & 116.335822276741 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 104.444827586207 & 0.795423891807098 & 131.307129018871 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 104.825862068966 & 0.721020317686543 & 145.385448228849 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 104.701724137931 & 0.663655440977805 & 157.765186078588 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 104.537931034483 & 0.608871833621343 & 171.691192237831 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 103.733928571429 & 1.26875610621194 & 81.7603383846099 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 103.794444444444 & 1.23916524918653 & 83.7615842702027 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 103.873076923077 & 1.21305155819538 & 85.6295647298008 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 103.958 & 1.18073339367479 & 88.0452780931794 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 104.008333333333 & 1.15657553241236 & 89.9278347315499 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 104.060869565217 & 1.12918027751942 & 92.156116819378 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 104.088636363636 & 1.10938822783272 & 93.825257698094 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 104.104761904762 & 1.08915012515861 & 95.583482478691 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 104.1275 & 1.06260436893126 & 97.9927271565136 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 104.152631578947 & 1.03711862065815 & 100.424994310538 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 104.166666666667 & 1.00916435649140 & 103.220715234956 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 104.194117647059 & 0.989435651607263 & 105.306613399066 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 104.228125 & 0.964566114799057 & 108.057004492339 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 104.243333333333 & 0.937356068133894 & 111.209962656841 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 104.253571428571 & 0.900462581633544 & 115.777794163799 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 104.253846153846 & 0.856526631122749 & 121.716993220851 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 104.225 & 0.825087830195205 & 126.319885211907 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 104.131818181818 & 0.799577441531402 & 130.233561845339 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 104.04 & 0.777424899063704 & 133.826431498787 \tabularnewline
Median & 103.65 &  &  \tabularnewline
Midrange & 102.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 103.948275862069 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 104.243333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 104.243333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 104.243333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 104.253571428571 &  &  \tabularnewline
Midmean - Closest Observation & 104.243333333333 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 104.243333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 104.243333333333 &  &  \tabularnewline
Number of observations & 58 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109204&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]103.691379310345[/C][C]1.31915086733284[/C][C]78.6046402107106[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]103.203445308005[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]102.706756607467[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]104.168571109028[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]103.677586206897[/C][C]1.29227553653693[/C][C]80.2286998984243[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]103.653448275862[/C][C]1.27537336743387[/C][C]81.2730224125815[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]103.653448275862[/C][C]1.27316577556040[/C][C]81.4139448810092[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]103.791379310345[/C][C]1.23040057239857[/C][C]84.3557631869526[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]103.8[/C][C]1.21827682695775[/C][C]85.2023101015612[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]103.934482758621[/C][C]1.16706816630573[/C][C]89.056051530921[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]104.006896551724[/C][C]1.14430878776147[/C][C]90.890586233446[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]103.979310344828[/C][C]1.13938924698477[/C][C]91.258813105349[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]103.979310344828[/C][C]1.10024954167982[/C][C]94.5052066879986[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]104.065517241379[/C][C]1.07252874892304[/C][C]97.028184415453[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]103.989655172414[/C][C]1.00116293436404[/C][C]103.868862502855[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]103.968965517241[/C][C]0.98394924745956[/C][C]105.664967767064[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]104.125862068966[/C][C]0.94991820052466[/C][C]109.615609019234[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]104.174137931034[/C][C]0.934003606260882[/C][C]111.535048936350[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]104.251724137931[/C][C]0.896127453244246[/C][C]116.335822276741[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]104.444827586207[/C][C]0.795423891807098[/C][C]131.307129018871[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]104.825862068966[/C][C]0.721020317686543[/C][C]145.385448228849[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]104.701724137931[/C][C]0.663655440977805[/C][C]157.765186078588[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]104.537931034483[/C][C]0.608871833621343[/C][C]171.691192237831[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]103.733928571429[/C][C]1.26875610621194[/C][C]81.7603383846099[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]103.794444444444[/C][C]1.23916524918653[/C][C]83.7615842702027[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]103.873076923077[/C][C]1.21305155819538[/C][C]85.6295647298008[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]103.958[/C][C]1.18073339367479[/C][C]88.0452780931794[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]104.008333333333[/C][C]1.15657553241236[/C][C]89.9278347315499[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]104.060869565217[/C][C]1.12918027751942[/C][C]92.156116819378[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]104.088636363636[/C][C]1.10938822783272[/C][C]93.825257698094[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]104.104761904762[/C][C]1.08915012515861[/C][C]95.583482478691[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]104.1275[/C][C]1.06260436893126[/C][C]97.9927271565136[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]104.152631578947[/C][C]1.03711862065815[/C][C]100.424994310538[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]104.166666666667[/C][C]1.00916435649140[/C][C]103.220715234956[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]104.194117647059[/C][C]0.989435651607263[/C][C]105.306613399066[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]104.228125[/C][C]0.964566114799057[/C][C]108.057004492339[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]104.243333333333[/C][C]0.937356068133894[/C][C]111.209962656841[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]104.253571428571[/C][C]0.900462581633544[/C][C]115.777794163799[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]104.253846153846[/C][C]0.856526631122749[/C][C]121.716993220851[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]104.225[/C][C]0.825087830195205[/C][C]126.319885211907[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]104.131818181818[/C][C]0.799577441531402[/C][C]130.233561845339[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]104.04[/C][C]0.777424899063704[/C][C]133.826431498787[/C][/ROW]
[ROW][C]Median[/C][C]103.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]102.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]103.948275862069[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]104.243333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]104.243333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]104.243333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]104.253571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]104.243333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]104.243333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]104.243333333333[/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=109204&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109204&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean103.6913793103451.3191508673328478.6046402107106
Geometric Mean103.203445308005
Harmonic Mean102.706756607467
Quadratic Mean104.168571109028
Winsorized Mean ( 1 / 19 )103.6775862068971.2922755365369380.2286998984243
Winsorized Mean ( 2 / 19 )103.6534482758621.2753733674338781.2730224125815
Winsorized Mean ( 3 / 19 )103.6534482758621.2731657755604081.4139448810092
Winsorized Mean ( 4 / 19 )103.7913793103451.2304005723985784.3557631869526
Winsorized Mean ( 5 / 19 )103.81.2182768269577585.2023101015612
Winsorized Mean ( 6 / 19 )103.9344827586211.1670681663057389.056051530921
Winsorized Mean ( 7 / 19 )104.0068965517241.1443087877614790.890586233446
Winsorized Mean ( 8 / 19 )103.9793103448281.1393892469847791.258813105349
Winsorized Mean ( 9 / 19 )103.9793103448281.1002495416798294.5052066879986
Winsorized Mean ( 10 / 19 )104.0655172413791.0725287489230497.028184415453
Winsorized Mean ( 11 / 19 )103.9896551724141.00116293436404103.868862502855
Winsorized Mean ( 12 / 19 )103.9689655172410.98394924745956105.664967767064
Winsorized Mean ( 13 / 19 )104.1258620689660.94991820052466109.615609019234
Winsorized Mean ( 14 / 19 )104.1741379310340.934003606260882111.535048936350
Winsorized Mean ( 15 / 19 )104.2517241379310.896127453244246116.335822276741
Winsorized Mean ( 16 / 19 )104.4448275862070.795423891807098131.307129018871
Winsorized Mean ( 17 / 19 )104.8258620689660.721020317686543145.385448228849
Winsorized Mean ( 18 / 19 )104.7017241379310.663655440977805157.765186078588
Winsorized Mean ( 19 / 19 )104.5379310344830.608871833621343171.691192237831
Trimmed Mean ( 1 / 19 )103.7339285714291.2687561062119481.7603383846099
Trimmed Mean ( 2 / 19 )103.7944444444441.2391652491865383.7615842702027
Trimmed Mean ( 3 / 19 )103.8730769230771.2130515581953885.6295647298008
Trimmed Mean ( 4 / 19 )103.9581.1807333936747988.0452780931794
Trimmed Mean ( 5 / 19 )104.0083333333331.1565755324123689.9278347315499
Trimmed Mean ( 6 / 19 )104.0608695652171.1291802775194292.156116819378
Trimmed Mean ( 7 / 19 )104.0886363636361.1093882278327293.825257698094
Trimmed Mean ( 8 / 19 )104.1047619047621.0891501251586195.583482478691
Trimmed Mean ( 9 / 19 )104.12751.0626043689312697.9927271565136
Trimmed Mean ( 10 / 19 )104.1526315789471.03711862065815100.424994310538
Trimmed Mean ( 11 / 19 )104.1666666666671.00916435649140103.220715234956
Trimmed Mean ( 12 / 19 )104.1941176470590.989435651607263105.306613399066
Trimmed Mean ( 13 / 19 )104.2281250.964566114799057108.057004492339
Trimmed Mean ( 14 / 19 )104.2433333333330.937356068133894111.209962656841
Trimmed Mean ( 15 / 19 )104.2535714285710.900462581633544115.777794163799
Trimmed Mean ( 16 / 19 )104.2538461538460.856526631122749121.716993220851
Trimmed Mean ( 17 / 19 )104.2250.825087830195205126.319885211907
Trimmed Mean ( 18 / 19 )104.1318181818180.799577441531402130.233561845339
Trimmed Mean ( 19 / 19 )104.040.777424899063704133.826431498787
Median103.65
Midrange102.5
Midmean - Weighted Average at Xnp103.948275862069
Midmean - Weighted Average at X(n+1)p104.243333333333
Midmean - Empirical Distribution Function104.243333333333
Midmean - Empirical Distribution Function - Averaging104.243333333333
Midmean - Empirical Distribution Function - Interpolation104.253571428571
Midmean - Closest Observation104.243333333333
Midmean - True Basic - Statistics Graphics Toolkit104.243333333333
Midmean - MS Excel (old versions)104.243333333333
Number of observations58


Figures (Output of Computation)

Input Parameters & R Code

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')