Centrummaten - Prijsevolutie slagroom - Van Hal Elien

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Fri, 13 Mar 2009 01:37:15 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Mar/13/t1236929909t3kka9jx5xtu75c.htm/, Retrieved Fri, 13 Mar 2009 08:38:32 +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/2009/Mar/13/t1236929909t3kka9jx5xtu75c.htm/}, year = {2009}, } @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 = {2009}, 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:

» Textbox « » Textfile « » CSV «

4,2 4,19 4,19 4,19 4,19 4,18 4,2 4,19 4,17 4,21 4,22 4,23 4,21 4,23 4,23 4,22 4,25 4,28 4,3 4,32 4,33 4,32 4,34 4,33 4,31 4,31 4,3 4,3 4,29 4,33 4,32 4,32 4,35 4,37 4,39 4,4 4,41 4,44 4,47 4,47 4,47 4,48 4,47 4,48 4,46 4,44 4,43 4,41 4,41 4,38 4,35 4,37 4,4 4,39 4,36 4,34 4,33 4,33 4,34 4,34 4,35 4,37 4,39 4,4 4,38 4,37 4,36 4,33 4,33 4,33 4,32 4,33 4,34

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 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 4.32986301369863 0.00986494252237418 438.914165376867 Geometric Mean 4.32905168770462 Harmonic Mean 4.32823819694739 Quadratic Mean 4.33067206654408 Winsorized Mean ( 1 / 24 ) 4.33 0.00983501649552635 440.263623550564 Winsorized Mean ( 2 / 24 ) 4.33 0.00972216786242684 445.37391878761 Winsorized Mean ( 3 / 24 ) 4.33 0.00972216786242684 445.37391878761 Winsorized Mean ( 4 / 24 ) 4.33 0.00972216786242684 445.37391878761 Winsorized Mean ( 5 / 24 ) 4.33 0.00972216786242684 445.37391878761 Winsorized Mean ( 6 / 24 ) 4.32917808219178 0.00956184990161433 452.755285508182 Winsorized Mean ( 7 / 24 ) 4.32821917808219 0.00902251214935675 479.713311152567 Winsorized Mean ( 8 / 24 ) 4.32821917808219 0.00902251214935675 479.713311152567 Winsorized Mean ( 9 / 24 ) 4.32821917808219 0.00857490601444254 504.754124510783 Winsorized Mean ( 10 / 24 ) 4.32547945205480 0.00815106863760496 530.664093797369 Winsorized Mean ( 11 / 24 ) 4.32698630136986 0.00786028330979911 550.487320981876 Winsorized Mean ( 12 / 24 ) 4.32698630136986 0.00786028330979911 550.487320981876 Winsorized Mean ( 13 / 24 ) 4.32698630136986 0.00727185974295882 595.031594986357 Winsorized Mean ( 14 / 24 ) 4.32698630136986 0.00727185974295882 595.031594986357 Winsorized Mean ( 15 / 24 ) 4.32698630136986 0.00727185974295882 595.031594986357 Winsorized Mean ( 16 / 24 ) 4.32917808219178 0.00617093343891476 701.543473940487 Winsorized Mean ( 17 / 24 ) 4.33616438356164 0.00499478471153132 868.138395144612 Winsorized Mean ( 18 / 24 ) 4.3386301369863 0.0046215820744767 938.77595746854 Winsorized Mean ( 19 / 24 ) 4.3386301369863 0.00385385152231582 1125.79068286968 Winsorized Mean ( 20 / 24 ) 4.3386301369863 0.00385385152231582 1125.79068286968 Winsorized Mean ( 21 / 24 ) 4.33575342465753 0.00343961725010413 1260.53369005702 Winsorized Mean ( 22 / 24 ) 4.33876712328767 0.00302164443042298 1435.89599080667 Winsorized Mean ( 23 / 24 ) 4.33876712328767 0.00302164443042298 1435.89599080667 Winsorized Mean ( 24 / 24 ) 4.34205479452055 0.00260954010269032 1663.91571834596 Trimmed Mean ( 1 / 24 ) 4.33 0.0096560569913251 448.423202544271 Trimmed Mean ( 2 / 24 ) 4.33 0.00944314886722427 458.533489292832 Trimmed Mean ( 3 / 24 ) 4.33 0.00926029442929499 467.587724457445 Trimmed Mean ( 4 / 24 ) 4.33 0.00904050713349473 478.955432041806 Trimmed Mean ( 5 / 24 ) 4.33 0.00877551870960525 493.418126413496 Trimmed Mean ( 6 / 24 ) 4.33 0.00845431309072863 512.164613911503 Trimmed Mean ( 7 / 24 ) 4.33016949152542 0.0081104716367717 533.898604847227 Trimmed Mean ( 8 / 24 ) 4.33052631578947 0.00783772227855536 552.523572778043 Trimmed Mean ( 9 / 24 ) 4.33090909090909 0.00749982144466568 577.468293460439 Trimmed Mean ( 10 / 24 ) 4.33132075471698 0.00719335756253142 602.127826549018 Trimmed Mean ( 11 / 24 ) 4.3321568627451 0.00690730630786007 627.18470408868 Trimmed Mean ( 12 / 24 ) 4.33285714285714 0.00661759148080347 654.748356018355 Trimmed Mean ( 13 / 24 ) 4.33361702127660 0.00624377974956233 694.069489171262 Trimmed Mean ( 14 / 24 ) 4.33444444444444 0.00590801164278373 733.655366055126 Trimmed Mean ( 15 / 24 ) 4.3353488372093 0.00546152187351611 793.798676927795 Trimmed Mean ( 16 / 24 ) 4.33634146341463 0.00484838541846382 894.388768454917 Trimmed Mean ( 17 / 24 ) 4.33717948717949 0.00436135522816907 994.456828273598 Trimmed Mean ( 18 / 24 ) 4.3372972972973 0.0040760165858968 1064.10197453674 Trimmed Mean ( 19 / 24 ) 4.33714285714286 0.00379232813731624 1143.66233619546 Trimmed Mean ( 20 / 24 ) 4.3369696969697 0.00362767269509482 1195.52397955691 Trimmed Mean ( 21 / 24 ) 4.33677419354839 0.00338837661432016 1279.89733349594 Trimmed Mean ( 22 / 24 ) 4.33689655172414 0.00318182369693697 1363.02226798396 Trimmed Mean ( 23 / 24 ) 4.33666666666667 0.00301940542438558 1436.26511088657 Trimmed Mean ( 24 / 24 ) 4.3364 0.00276164202362772 1570.22523661617 Median 4.33 Midrange 4.325 Midmean - Weighted Average at Xnp 4.33583333333333 Midmean - Weighted Average at X(n+1)p 4.34 Midmean - Empirical Distribution Function 4.34 Midmean - Empirical Distribution Function - Averaging 4.34 Midmean - Empirical Distribution Function - Interpolation 4.34 Midmean - Closest Observation 4.3385 Midmean - True Basic - Statistics Graphics Toolkit 4.34 Midmean - MS Excel (old versions) 4.34 Number of observations 73

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/13/t1236929909t3kka9jx5xtu75c/1rbjl1236929832.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/13/t1236929909t3kka9jx5xtu75c/1rbjl1236929832.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/13/t1236929909t3kka9jx5xtu75c/29irg1236929832.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/13/t1236929909t3kka9jx5xtu75c/29irg1236929832.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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