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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 07 Jan 2008 13:57:08 -0700
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/Jan/07/t1199739515wlt45r52s7n6a9i.htm/, Retrieved Mon, 06 May 2024 16:54:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7927, Retrieved Mon, 06 May 2024 16:54:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact272
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ARIMA Backward Selection] [ARMA backward sel...] [2007-12-20 15:28:14] [74be16979710d4c4e7c6647856088456]
- RMPD    [Central Tendency] [] [2008-01-07 20:57:08] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
106.8
114.3
105.7
90.1
91.6
97.7
100.8
104.6
95.9
102.7
104
107.9
113.8
113.8
123.1
125.1
137.6
134
140.3
152.1
150.6
167.3
153.2
142
154.4
158.5
180.9
181.3
172.4
192
199.3
215.4
214.3
201.5
190.5
196
215.7
209.4
214.1
237.8
239
237.8
251.5
248.8
215.4
201.2
203.1
214.2




Summary of compuational 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 compuational 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=7927&T=0

[TABLE]
[ROW][C]Summary of compuational 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=7927&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7927&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 compuational 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 Mean162.906257.1694599576102422.7222483929321
Geometric Mean155.252333803095
Harmonic Mean147.683155199118
Quadratic Mean170.159632771701
Winsorized Mean ( 1 / 16 )162.881257.1481812497670522.7863905948535
Winsorized Mean ( 2 / 16 )162.6520833333337.0114578147340723.1980406402120
Winsorized Mean ( 3 / 16 )162.6895833333336.9716219606533223.3359732141999
Winsorized Mean ( 4 / 16 )162.9479166666676.921322659323323.5428869144208
Winsorized Mean ( 5 / 16 )160.843756.4066357347976725.1058053958611
Winsorized Mean ( 6 / 16 )160.968756.3686567358617825.275149325224
Winsorized Mean ( 7 / 16 )161.056256.352056757886225.3549765278853
Winsorized Mean ( 8 / 16 )161.056256.2843304697136125.6282273467613
Winsorized Mean ( 9 / 16 )161.243756.2424840668528225.8300619229761
Winsorized Mean ( 10 / 16 )161.4520833333336.1963877815110426.0558391479434
Winsorized Mean ( 11 / 16 )161.7270833333335.7599372500024528.0779245178868
Winsorized Mean ( 12 / 16 )160.1520833333335.4900013803168229.1715925441336
Winsorized Mean ( 13 / 16 )159.8541666666675.3940126039007529.6354825999231
Winsorized Mean ( 14 / 16 )162.3333333333334.9310488049485832.9206503027151
Winsorized Mean ( 15 / 16 )162.3645833333334.7265607666360734.3515277491904
Winsorized Mean ( 16 / 16 )164.231254.0585750611561940.4652488928502
Trimmed Mean ( 1 / 16 )162.5630434782617.0473206329313323.0673545231676
Trimmed Mean ( 2 / 16 )162.2159090909096.9095683444003123.4769961024227
Trimmed Mean ( 3 / 16 )161.9666666666676.8173411347178323.7580404832375
Trimmed Mean ( 4 / 16 )161.67756.7057031673008524.1104468787690
Trimmed Mean ( 5 / 16 )161.2763157894746.5673471699606324.5573001724592
Trimmed Mean ( 6 / 16 )161.3916666666676.5615067653509324.5967385904288
Trimmed Mean ( 7 / 16 )161.4911764705886.5431658263520924.6808931267178
Trimmed Mean ( 8 / 16 )161.5843756.498539087337824.8647231059735
Trimmed Mean ( 9 / 16 )161.696.4318556161240625.1389349590899
Trimmed Mean ( 10 / 16 )161.7756.3225066712867625.5871616133978
Trimmed Mean ( 11 / 16 )161.8346153846156.1494088328946626.3171013315822
Trimmed Mean ( 12 / 16 )161.8541666666676.020812271163226.8824469817587
Trimmed Mean ( 13 / 16 )162.1636363636365.8844521290859527.5579837861347
Trimmed Mean ( 14 / 16 )162.595.6558442061473528.7472557718759
Trimmed Mean ( 15 / 16 )162.6388888888895.4549320424281329.8150165068774
Trimmed Mean ( 16 / 16 )162.693755.1446450213628331.6239020038164
Median156.45
Midrange170.8
Midmean - Weighted Average at Xnp159.932
Midmean - Weighted Average at X(n+1)p159.932
Midmean - Empirical Distribution Function159.932
Midmean - Empirical Distribution Function - Averaging159.932
Midmean - Empirical Distribution Function - Interpolation159.932
Midmean - Closest Observation159.932
Midmean - True Basic - Statistics Graphics Toolkit159.932
Midmean - MS Excel (old versions)161.834615384615
Number of observations48

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 162.90625 & 7.16945995761024 & 22.7222483929321 \tabularnewline
Geometric Mean & 155.252333803095 &  &  \tabularnewline
Harmonic Mean & 147.683155199118 &  &  \tabularnewline
Quadratic Mean & 170.159632771701 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & 162.88125 & 7.14818124976705 & 22.7863905948535 \tabularnewline
Winsorized Mean ( 2 / 16 ) & 162.652083333333 & 7.01145781473407 & 23.1980406402120 \tabularnewline
Winsorized Mean ( 3 / 16 ) & 162.689583333333 & 6.97162196065332 & 23.3359732141999 \tabularnewline
Winsorized Mean ( 4 / 16 ) & 162.947916666667 & 6.9213226593233 & 23.5428869144208 \tabularnewline
Winsorized Mean ( 5 / 16 ) & 160.84375 & 6.40663573479767 & 25.1058053958611 \tabularnewline
Winsorized Mean ( 6 / 16 ) & 160.96875 & 6.36865673586178 & 25.275149325224 \tabularnewline
Winsorized Mean ( 7 / 16 ) & 161.05625 & 6.3520567578862 & 25.3549765278853 \tabularnewline
Winsorized Mean ( 8 / 16 ) & 161.05625 & 6.28433046971361 & 25.6282273467613 \tabularnewline
Winsorized Mean ( 9 / 16 ) & 161.24375 & 6.24248406685282 & 25.8300619229761 \tabularnewline
Winsorized Mean ( 10 / 16 ) & 161.452083333333 & 6.19638778151104 & 26.0558391479434 \tabularnewline
Winsorized Mean ( 11 / 16 ) & 161.727083333333 & 5.75993725000245 & 28.0779245178868 \tabularnewline
Winsorized Mean ( 12 / 16 ) & 160.152083333333 & 5.49000138031682 & 29.1715925441336 \tabularnewline
Winsorized Mean ( 13 / 16 ) & 159.854166666667 & 5.39401260390075 & 29.6354825999231 \tabularnewline
Winsorized Mean ( 14 / 16 ) & 162.333333333333 & 4.93104880494858 & 32.9206503027151 \tabularnewline
Winsorized Mean ( 15 / 16 ) & 162.364583333333 & 4.72656076663607 & 34.3515277491904 \tabularnewline
Winsorized Mean ( 16 / 16 ) & 164.23125 & 4.05857506115619 & 40.4652488928502 \tabularnewline
Trimmed Mean ( 1 / 16 ) & 162.563043478261 & 7.04732063293133 & 23.0673545231676 \tabularnewline
Trimmed Mean ( 2 / 16 ) & 162.215909090909 & 6.90956834440031 & 23.4769961024227 \tabularnewline
Trimmed Mean ( 3 / 16 ) & 161.966666666667 & 6.81734113471783 & 23.7580404832375 \tabularnewline
Trimmed Mean ( 4 / 16 ) & 161.6775 & 6.70570316730085 & 24.1104468787690 \tabularnewline
Trimmed Mean ( 5 / 16 ) & 161.276315789474 & 6.56734716996063 & 24.5573001724592 \tabularnewline
Trimmed Mean ( 6 / 16 ) & 161.391666666667 & 6.56150676535093 & 24.5967385904288 \tabularnewline
Trimmed Mean ( 7 / 16 ) & 161.491176470588 & 6.54316582635209 & 24.6808931267178 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 161.584375 & 6.4985390873378 & 24.8647231059735 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 161.69 & 6.43185561612406 & 25.1389349590899 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 161.775 & 6.32250667128676 & 25.5871616133978 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 161.834615384615 & 6.14940883289466 & 26.3171013315822 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 161.854166666667 & 6.0208122711632 & 26.8824469817587 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 162.163636363636 & 5.88445212908595 & 27.5579837861347 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 162.59 & 5.65584420614735 & 28.7472557718759 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 162.638888888889 & 5.45493204242813 & 29.8150165068774 \tabularnewline
Trimmed Mean ( 16 / 16 ) & 162.69375 & 5.14464502136283 & 31.6239020038164 \tabularnewline
Median & 156.45 &  &  \tabularnewline
Midrange & 170.8 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 159.932 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 159.932 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 159.932 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 159.932 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 159.932 &  &  \tabularnewline
Midmean - Closest Observation & 159.932 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 159.932 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 161.834615384615 &  &  \tabularnewline
Number of observations & 48 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7927&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]162.90625[/C][C]7.16945995761024[/C][C]22.7222483929321[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]155.252333803095[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]147.683155199118[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]170.159632771701[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]162.88125[/C][C]7.14818124976705[/C][C]22.7863905948535[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]162.652083333333[/C][C]7.01145781473407[/C][C]23.1980406402120[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]162.689583333333[/C][C]6.97162196065332[/C][C]23.3359732141999[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]162.947916666667[/C][C]6.9213226593233[/C][C]23.5428869144208[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]160.84375[/C][C]6.40663573479767[/C][C]25.1058053958611[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]160.96875[/C][C]6.36865673586178[/C][C]25.275149325224[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]161.05625[/C][C]6.3520567578862[/C][C]25.3549765278853[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]161.05625[/C][C]6.28433046971361[/C][C]25.6282273467613[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]161.24375[/C][C]6.24248406685282[/C][C]25.8300619229761[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]161.452083333333[/C][C]6.19638778151104[/C][C]26.0558391479434[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]161.727083333333[/C][C]5.75993725000245[/C][C]28.0779245178868[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]160.152083333333[/C][C]5.49000138031682[/C][C]29.1715925441336[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]159.854166666667[/C][C]5.39401260390075[/C][C]29.6354825999231[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]162.333333333333[/C][C]4.93104880494858[/C][C]32.9206503027151[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]162.364583333333[/C][C]4.72656076663607[/C][C]34.3515277491904[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]164.23125[/C][C]4.05857506115619[/C][C]40.4652488928502[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]162.563043478261[/C][C]7.04732063293133[/C][C]23.0673545231676[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]162.215909090909[/C][C]6.90956834440031[/C][C]23.4769961024227[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]161.966666666667[/C][C]6.81734113471783[/C][C]23.7580404832375[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]161.6775[/C][C]6.70570316730085[/C][C]24.1104468787690[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]161.276315789474[/C][C]6.56734716996063[/C][C]24.5573001724592[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]161.391666666667[/C][C]6.56150676535093[/C][C]24.5967385904288[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]161.491176470588[/C][C]6.54316582635209[/C][C]24.6808931267178[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]161.584375[/C][C]6.4985390873378[/C][C]24.8647231059735[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]161.69[/C][C]6.43185561612406[/C][C]25.1389349590899[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]161.775[/C][C]6.32250667128676[/C][C]25.5871616133978[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]161.834615384615[/C][C]6.14940883289466[/C][C]26.3171013315822[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]161.854166666667[/C][C]6.0208122711632[/C][C]26.8824469817587[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]162.163636363636[/C][C]5.88445212908595[/C][C]27.5579837861347[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]162.59[/C][C]5.65584420614735[/C][C]28.7472557718759[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]162.638888888889[/C][C]5.45493204242813[/C][C]29.8150165068774[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]162.69375[/C][C]5.14464502136283[/C][C]31.6239020038164[/C][/ROW]
[ROW][C]Median[/C][C]156.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]170.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]159.932[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]159.932[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]159.932[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]159.932[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]159.932[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]159.932[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]159.932[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]161.834615384615[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]48[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7927&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7927&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 Mean162.906257.1694599576102422.7222483929321
Geometric Mean155.252333803095
Harmonic Mean147.683155199118
Quadratic Mean170.159632771701
Winsorized Mean ( 1 / 16 )162.881257.1481812497670522.7863905948535
Winsorized Mean ( 2 / 16 )162.6520833333337.0114578147340723.1980406402120
Winsorized Mean ( 3 / 16 )162.6895833333336.9716219606533223.3359732141999
Winsorized Mean ( 4 / 16 )162.9479166666676.921322659323323.5428869144208
Winsorized Mean ( 5 / 16 )160.843756.4066357347976725.1058053958611
Winsorized Mean ( 6 / 16 )160.968756.3686567358617825.275149325224
Winsorized Mean ( 7 / 16 )161.056256.352056757886225.3549765278853
Winsorized Mean ( 8 / 16 )161.056256.2843304697136125.6282273467613
Winsorized Mean ( 9 / 16 )161.243756.2424840668528225.8300619229761
Winsorized Mean ( 10 / 16 )161.4520833333336.1963877815110426.0558391479434
Winsorized Mean ( 11 / 16 )161.7270833333335.7599372500024528.0779245178868
Winsorized Mean ( 12 / 16 )160.1520833333335.4900013803168229.1715925441336
Winsorized Mean ( 13 / 16 )159.8541666666675.3940126039007529.6354825999231
Winsorized Mean ( 14 / 16 )162.3333333333334.9310488049485832.9206503027151
Winsorized Mean ( 15 / 16 )162.3645833333334.7265607666360734.3515277491904
Winsorized Mean ( 16 / 16 )164.231254.0585750611561940.4652488928502
Trimmed Mean ( 1 / 16 )162.5630434782617.0473206329313323.0673545231676
Trimmed Mean ( 2 / 16 )162.2159090909096.9095683444003123.4769961024227
Trimmed Mean ( 3 / 16 )161.9666666666676.8173411347178323.7580404832375
Trimmed Mean ( 4 / 16 )161.67756.7057031673008524.1104468787690
Trimmed Mean ( 5 / 16 )161.2763157894746.5673471699606324.5573001724592
Trimmed Mean ( 6 / 16 )161.3916666666676.5615067653509324.5967385904288
Trimmed Mean ( 7 / 16 )161.4911764705886.5431658263520924.6808931267178
Trimmed Mean ( 8 / 16 )161.5843756.498539087337824.8647231059735
Trimmed Mean ( 9 / 16 )161.696.4318556161240625.1389349590899
Trimmed Mean ( 10 / 16 )161.7756.3225066712867625.5871616133978
Trimmed Mean ( 11 / 16 )161.8346153846156.1494088328946626.3171013315822
Trimmed Mean ( 12 / 16 )161.8541666666676.020812271163226.8824469817587
Trimmed Mean ( 13 / 16 )162.1636363636365.8844521290859527.5579837861347
Trimmed Mean ( 14 / 16 )162.595.6558442061473528.7472557718759
Trimmed Mean ( 15 / 16 )162.6388888888895.4549320424281329.8150165068774
Trimmed Mean ( 16 / 16 )162.693755.1446450213628331.6239020038164
Median156.45
Midrange170.8
Midmean - Weighted Average at Xnp159.932
Midmean - Weighted Average at X(n+1)p159.932
Midmean - Empirical Distribution Function159.932
Midmean - Empirical Distribution Function - Averaging159.932
Midmean - Empirical Distribution Function - Interpolation159.932
Midmean - Closest Observation159.932
Midmean - True Basic - Statistics Graphics Toolkit159.932
Midmean - MS Excel (old versions)161.834615384615
Number of observations48



Parameters (Session):
par1 = 20 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 2 ; par7 = 1 ; par8 = 1 ; par9 = 0 ; par10 = FALSE ;
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')