Huishoudbrood - centrummaten - Joris Hoefnagels

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Mon, 01 Jun 2009 04:43:42 -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/Jun/01/t12438530659o7gq8y6zpk2aev.htm/, Retrieved Mon, 01 Jun 2009 12:44:27 +0200

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/Jun/01/t12438530659o7gq8y6zpk2aev.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 «

40,04 40,04 40,03 40,03 41,63 42,03 42,03 42,03 42,03 42,03 42,03 42,03 42,03 42,03 42,03 42,03 42,03 42,03 42,03 42,03 42,03 42,38 42,06 42,06 42,05 42,05 42,05 42,05 44,36 44,48 44,49 44,49 44,49 44,49 44,49 44,48 44,48 44,48 44,48 44,48 44,48 44,49 44,49 44,49 44,49 44,49 44,49 44,49 44,49 45,5 45,94 45,95 45,96 45,96 45,96 45,96 45,96 45,96 45,96 45,96 45,97 46,06 47,9 47,93 47,94 47,94 47,94 47,94 47,94 47,94 47,94 47,94

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 44.1595833333333 0.266294152774773 165.830090045885 Geometric Mean 44.1026951725576 Harmonic Mean 44.0459556524679 Quadratic Mean 44.2165533828176 Winsorized Mean ( 1 / 24 ) 44.1595833333333 0.266294152774773 165.830090045885 Winsorized Mean ( 2 / 24 ) 44.1598611111111 0.266233545933386 165.868883863945 Winsorized Mean ( 3 / 24 ) 44.1598611111111 0.266233545933386 165.868883863945 Winsorized Mean ( 4 / 24 ) 44.2481944444444 0.249994548171298 176.996637599174 Winsorized Mean ( 5 / 24 ) 44.2759722222222 0.246158963910293 179.867397550298 Winsorized Mean ( 6 / 24 ) 44.2759722222222 0.246158963910293 179.867397550298 Winsorized Mean ( 7 / 24 ) 44.2759722222222 0.246158963910293 179.867397550298 Winsorized Mean ( 8 / 24 ) 44.2748611111111 0.24592619739261 180.033122052582 Winsorized Mean ( 9 / 24 ) 44.2711111111111 0.245142764092668 180.593179141832 Winsorized Mean ( 10 / 24 ) 44.0155555555556 0.199184653448407 220.978648673637 Winsorized Mean ( 11 / 24 ) 44.0018055555556 0.197224315463114 223.105378524105 Winsorized Mean ( 12 / 24 ) 44.0001388888889 0.196990412794641 223.361828957424 Winsorized Mean ( 13 / 24 ) 44.0001388888889 0.196990412794641 223.361828957424 Winsorized Mean ( 14 / 24 ) 44.0001388888889 0.196990412794641 223.361828957424 Winsorized Mean ( 15 / 24 ) 44.0001388888889 0.196990412794641 223.361828957424 Winsorized Mean ( 16 / 24 ) 44.0001388888889 0.196990412794641 223.361828957424 Winsorized Mean ( 17 / 24 ) 44.0001388888889 0.196990412794641 223.361828957424 Winsorized Mean ( 18 / 24 ) 44.0001388888889 0.196990412794641 223.361828957424 Winsorized Mean ( 19 / 24 ) 44.0001388888889 0.196990412794641 223.361828957424 Winsorized Mean ( 20 / 24 ) 43.9973611111111 0.196601504388942 223.789544479120 Winsorized Mean ( 21 / 24 ) 44.0002777777778 0.195372419560216 225.212329748603 Winsorized Mean ( 22 / 24 ) 43.8658333333333 0.177208703204422 247.537691660275 Winsorized Mean ( 23 / 24 ) 43.5431944444444 0.140265624715657 310.43382534184 Winsorized Mean ( 24 / 24 ) 43.5431944444444 0.140265624715657 310.43382534184 Trimmed Mean ( 1 / 24 ) 44.1645714285714 0.261844997510146 168.666851948776 Trimmed Mean ( 2 / 24 ) 44.1698529411765 0.256524988869056 172.185380987281 Trimmed Mean ( 3 / 24 ) 44.175303030303 0.250191648657851 176.565857682623 Trimmed Mean ( 4 / 24 ) 44.18109375 0.242578546147361 182.131084762793 Trimmed Mean ( 5 / 24 ) 44.1616129032258 0.239313887234724 184.534267582688 Trimmed Mean ( 6 / 24 ) 44.1341666666667 0.236341141408792 186.739246512858 Trimmed Mean ( 7 / 24 ) 44.1048275862069 0.232540643154378 189.665027962131 Trimmed Mean ( 8 / 24 ) 44.0733928571429 0.227709982554381 193.550552166141 Trimmed Mean ( 9 / 24 ) 44.0398148148148 0.22164014291602 198.699631914159 Trimmed Mean ( 10 / 24 ) 44.0042307692308 0.214120380667824 205.511640844207 Trimmed Mean ( 11 / 24 ) 44.0026 0.215201625439579 204.471503921584 Trimmed Mean ( 12 / 24 ) 44.0027083333333 0.216457155847691 203.285995147676 Trimmed Mean ( 13 / 24 ) 44.0030434782609 0.21756155652106 202.255601503758 Trimmed Mean ( 14 / 24 ) 44.0034090909091 0.218413446793346 201.468406533336 Trimmed Mean ( 15 / 24 ) 44.0038095238095 0.218927528561429 200.997151034217 Trimmed Mean ( 16 / 24 ) 44.00425 0.218988902511239 200.942830871266 Trimmed Mean ( 17 / 24 ) 44.0047368421053 0.218440332316770 201.449688230158 Trimmed Mean ( 18 / 24 ) 44.0052777777778 0.217062453930950 202.730951303888 Trimmed Mean ( 19 / 24 ) 44.0058823529412 0.214541802369201 205.115655163614 Trimmed Mean ( 20 / 24 ) 44.0065625 0.210416546064854 209.140218880108 Trimmed Mean ( 21 / 24 ) 44.0076666666667 0.204087925233350 215.630917979832 Trimmed Mean ( 22 / 24 ) 44.0085714285714 0.194741528797914 225.984522665629 Trimmed Mean ( 23 / 24 ) 44.0265384615385 0.186473295516619 236.101037092545 Trimmed Mean ( 24 / 24 ) 44.0895833333333 0.182500227483148 241.586456857455 Median 44.485 Midrange 43.985 Midmean - Weighted Average at Xnp 43.7516363636364 Midmean - Weighted Average at X(n+1)p 43.7516363636364 Midmean - Empirical Distribution Function 43.7516363636364 Midmean - Empirical Distribution Function - Averaging 43.7516363636364 Midmean - Empirical Distribution Function - Interpolation 43.7516363636364 Midmean - Closest Observation 43.7516363636364 Midmean - True Basic - Statistics Graphics Toolkit 43.7516363636364 Midmean - MS Excel (old versions) 43.7516363636364 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t12438530659o7gq8y6zpk2aev/1yx3w1243853020.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t12438530659o7gq8y6zpk2aev/1yx3w1243853020.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t12438530659o7gq8y6zpk2aev/2loab1243853020.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t12438530659o7gq8y6zpk2aev/2loab1243853020.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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