export van petroleum

*The author of this computation has been verified*

R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Fri, 12 Nov 2010 17:22:47 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/12/t1289582531q76ye9wv7sotko5.htm/, Retrieved Fri, 12 Nov 2010 18:22:13 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/12/t1289582531q76ye9wv7sotko5.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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0,163174 0,201921 0,232752 0,228971 0,245583 0,254378 0,224034 0,230488 0,145256 0,151829 0,165472 0,196739 0,187848 0,204079 0,207498 0,240080 0,239256 0,228852 0,245555 0,222047 0,266542 0,267053 0,231662 0,206036 0,257087 0,216368 0,225624 0,231318 0,253926 0,227463 0,263592 0,260886 0,232007 0,233059 0,299560 0,270942 0,283427 0,301381 0,316548 0,292079 0,312963 0,361612 0,358814 0,358174 0,220870 0,288982 0,291079 0,327455 0,335642 0,284180 0,325792 0,326291 0,356246 0,335943 0,414564 0,374787 0,361182 0,393189 0,344907 0,352865

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.26796515 0.00815221157026373 32.8702398963048 Geometric Mean 0.260595398573290 Harmonic Mean 0.253172469078432 Quadratic Mean 0.275184258761683 Winsorized Mean ( 1 / 20 ) 0.26771845 0.0080232622125136 33.3677802007329 Winsorized Mean ( 2 / 20 ) 0.267483216666667 0.00778082811534246 34.3772170136024 Winsorized Mean ( 3 / 20 ) 0.266939366666667 0.00760824729762309 35.0855270898019 Winsorized Mean ( 4 / 20 ) 0.268402433333333 0.00729329686834505 36.8012488972271 Winsorized Mean ( 5 / 20 ) 0.268946016666667 0.00711778938638011 37.7850484282796 Winsorized Mean ( 6 / 20 ) 0.269400216666667 0.00701728391611554 38.3909529508954 Winsorized Mean ( 7 / 20 ) 0.26942705 0.00692863867937942 38.8860009112398 Winsorized Mean ( 8 / 20 ) 0.269237183333333 0.00679228852455803 39.6386552720612 Winsorized Mean ( 9 / 20 ) 0.268262783333333 0.00651396590641948 41.1827122197495 Winsorized Mean ( 10 / 20 ) 0.268247116666667 0.0059961909044629 44.7362535550716 Winsorized Mean ( 11 / 20 ) 0.2690173 0.00586765521958096 45.8474961347869 Winsorized Mean ( 12 / 20 ) 0.2676153 0.00552682185312813 48.4211916200143 Winsorized Mean ( 13 / 20 ) 0.267793616666667 0.00542107947633609 49.3985778728444 Winsorized Mean ( 14 / 20 ) 0.268048183333333 0.0053494645992985 50.1074786752461 Winsorized Mean ( 15 / 20 ) 0.266196933333333 0.00487343160155818 54.6220723090117 Winsorized Mean ( 16 / 20 ) 0.265611333333333 0.00465760409763648 57.0274604207169 Winsorized Mean ( 17 / 20 ) 0.262363483333333 0.00410479620546665 63.9163237833648 Winsorized Mean ( 18 / 20 ) 0.262272283333333 0.00395475312807343 66.3182441077175 Winsorized Mean ( 19 / 20 ) 0.260166133333333 0.00354843727165708 73.3185099286929 Winsorized Mean ( 20 / 20 ) 0.259947466666667 0.00348197999808203 74.6550717723402 Trimmed Mean ( 1 / 20 ) 0.267553258620690 0.00775269367673895 34.5110060808222 Trimmed Mean ( 2 / 20 ) 0.267376267857143 0.00741896663961158 36.0395565643279 Trimmed Mean ( 3 / 20 ) 0.267316851851852 0.00716997180475123 37.2828316667455 Trimmed Mean ( 4 / 20 ) 0.267462038461538 0.00694369918793217 38.5186672438770 Trimmed Mean ( 5 / 20 ) 0.26717992 0.00678354142226791 39.3864949542351 Trimmed Mean ( 6 / 20 ) 0.266738395833333 0.00663686308191088 40.1904322179469 Trimmed Mean ( 7 / 20 ) 0.266159739130435 0.00647533452480639 41.1036276366576 Trimmed Mean ( 8 / 20 ) 0.26552325 0.00628799796561398 42.2269936237286 Trimmed Mean ( 9 / 20 ) 0.264860047619048 0.00607836198946507 43.5742471537726 Trimmed Mean ( 10 / 20 ) 0.264292925 0.00587863701120176 44.9581977074599 Trimmed Mean ( 11 / 20 ) 0.263668578947368 0.00574875319918479 45.865350244077 Trimmed Mean ( 12 / 20 ) 0.262858166666667 0.00559408575980877 46.9885836493955 Trimmed Mean ( 13 / 20 ) 0.262158588235294 0.00547032508021924 47.923767672101 Trimmed Mean ( 14 / 20 ) 0.26134584375 0.00531162487974478 49.2026168388905 Trimmed Mean ( 15 / 20 ) 0.260388366666667 0.00508895490309246 51.167355896283 Trimmed Mean ( 16 / 20 ) 0.259558571428571 0.00491643503286179 52.7940610815894 Trimmed Mean ( 17 / 20 ) 0.258685576923077 0.00471638493410858 54.8482747988359 Trimmed Mean ( 18 / 20 ) 0.258144708333333 0.00461289746038181 55.9615102114077 Trimmed Mean ( 19 / 20 ) 0.257519318181818 0.00447629298904244 57.5295939770257 Trimmed Mean ( 20 / 20 ) 0.2571014 0.00440478570743471 58.368651071049 Median 0.2557325 Midrange 0.27991 Midmean - Weighted Average at Xnp 0.259266935483871 Midmean - Weighted Average at X(n+1)p 0.260388366666667 Midmean - Empirical Distribution Function 0.259266935483871 Midmean - Empirical Distribution Function - Averaging 0.260388366666667 Midmean - Empirical Distribution Function - Interpolation 0.260388366666667 Midmean - Closest Observation 0.259266935483871 Midmean - True Basic - Statistics Graphics Toolkit 0.260388366666667 Midmean - MS Excel (old versions) 0.26134584375 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/12/t1289582531q76ye9wv7sotko5/1wqqp1289582566.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289582531q76ye9wv7sotko5/1wqqp1289582566.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289582531q76ye9wv7sotko5/2wqqp1289582566.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289582531q76ye9wv7sotko5/2wqqp1289582566.ps (open in new window)

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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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