Cijferreeks - Oliezaden - Tim Deelstra

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

Title produced by software: Central Tendency

Date of computation: Thu, 24 Apr 2008 11:57:09 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Apr/24/t120905988740avmvr2zd2bsyr.htm/, Retrieved Thu, 24 Apr 2008 19:58:09 +0200

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

90,2 94,3 96 99 103,3 113,1 112,8 112,1 107,4 111 110,5 110,8 112,4 111,5 116,2 122,5 121,3 113,9 110,7 120,8 141,1 147,4 148 158,1 165 187 190,3 182,4 168,8 151,2 120,1 112,5 106,2 107,1 108,5 106,5 108,3 125,6 124 127,2 136,9 135,8 124,3 115,4 113,6 114,4 118,4 117 116,5 115,4 113,6 117,4 116,9 116,4 111,1 110,2 118,9 131,8 130,6 138,3 148,4 148,7 144,3 152,5 162,9 167,2 166,5 185,6 193,2 207,8 223,4 246,4

Text written by user:

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 132.429166666667 3.72012588630243 35.5980336994168 Geometric Mean 129.272300875257 Harmonic Mean 126.583629411952 Quadratic Mean 136.088489900261 Winsorized Mean ( 1 / 24 ) 132.166666666667 3.58494613776018 36.8671275907209 Winsorized Mean ( 2 / 24 ) 131.780555555556 3.4325011747852 38.3919913920502 Winsorized Mean ( 3 / 24 ) 131.297222222222 3.23735711838847 40.5569164663492 Winsorized Mean ( 4 / 24 ) 131.375 3.16277914947548 41.5378354893315 Winsorized Mean ( 5 / 24 ) 131.347222222222 3.07934837795179 42.6542261871608 Winsorized Mean ( 6 / 24 ) 131.255555555556 3.04697693179370 43.0773053074240 Winsorized Mean ( 7 / 24 ) 131.002777777778 2.96323255123001 44.2094150603873 Winsorized Mean ( 8 / 24 ) 129.525 2.61330018033728 49.563766525774 Winsorized Mean ( 9 / 24 ) 129.4375 2.55808151832225 50.5994430094993 Winsorized Mean ( 10 / 24 ) 129.368055555556 2.53471733444338 51.0384545833253 Winsorized Mean ( 11 / 24 ) 129.398611111111 2.45834586059954 52.6364549370418 Winsorized Mean ( 12 / 24 ) 129.098611111111 2.38216713075962 54.1937672819558 Winsorized Mean ( 13 / 24 ) 128.268055555556 2.20897729683265 58.0667151896368 Winsorized Mean ( 14 / 24 ) 127.198611111111 2.00617249098816 63.4036263992725 Winsorized Mean ( 15 / 24 ) 126.969444444444 1.95366078158084 64.9905273430862 Winsorized Mean ( 16 / 24 ) 126.436111111111 1.85558235036364 68.1382376192215 Winsorized Mean ( 17 / 24 ) 126.459722222222 1.83269905771759 69.0019027890553 Winsorized Mean ( 18 / 24 ) 126.509722222222 1.79876844466876 70.3312995050447 Winsorized Mean ( 19 / 24 ) 126.430555555556 1.76328363181649 71.7017689464456 Winsorized Mean ( 20 / 24 ) 125.597222222222 1.61783749798411 77.6327797932246 Winsorized Mean ( 21 / 24 ) 124.751388888889 1.45799827546738 85.5634680698767 Winsorized Mean ( 22 / 24 ) 123.9875 1.31407889978164 94.3531625236527 Winsorized Mean ( 23 / 24 ) 123.7 1.22731050668207 100.789489967304 Winsorized Mean ( 24 / 24 ) 123.333333333333 1.17206664447562 105.227235938032 Trimmed Mean ( 1 / 24 ) 131.404285714286 3.40200004242681 38.6255979057981 Trimmed Mean ( 2 / 24 ) 130.597058823529 3.17807248734252 41.0931655409577 Trimmed Mean ( 3 / 24 ) 129.951515151515 3.00859316488864 43.1934489076476 Trimmed Mean ( 4 / 24 ) 129.446875 2.89776354714266 44.6713035394627 Trimmed Mean ( 5 / 24 ) 128.887096774194 2.79052988289772 46.1873200369944 Trimmed Mean ( 6 / 24 ) 128.296666666667 2.68590794827212 47.7665910885746 Trimmed Mean ( 7 / 24 ) 127.684482758621 2.56538312402724 49.7720911791827 Trimmed Mean ( 8 / 24 ) 127.075 2.43880326464362 52.1054739602251 Trimmed Mean ( 9 / 24 ) 126.666666666667 2.37783410658411 53.2697660934094 Trimmed Mean ( 10 / 24 ) 126.240384615385 2.31333966797403 54.570622015894 Trimmed Mean ( 11 / 24 ) 125.79 2.2357562752789 56.262841075693 Trimmed Mean ( 12 / 24 ) 125.297916666667 2.15269188563115 58.2052255146262 Trimmed Mean ( 13 / 24 ) 124.802173913043 2.06305080861849 60.4939894798891 Trimmed Mean ( 14 / 24 ) 124.365909090909 1.99023765189308 62.4879691993639 Trimmed Mean ( 15 / 24 ) 124.019047619048 1.94489784311510 63.7663556767636 Trimmed Mean ( 16 / 24 ) 123.665 1.89472462649758 65.2680596803114 Trimmed Mean ( 17 / 24 ) 123.336842105263 1.84992568784135 66.6712413995304 Trimmed Mean ( 18 / 24 ) 122.969444444444 1.79029934290705 68.6865271618597 Trimmed Mean ( 19 / 24 ) 122.552941176471 1.71185046124878 71.5909151825498 Trimmed Mean ( 20 / 24 ) 122.09375 1.60667042947569 75.9917826083616 Trimmed Mean ( 21 / 24 ) 121.673333333333 1.50488807643803 80.852081452679 Trimmed Mean ( 22 / 24 ) 121.296428571429 1.41335731245435 85.8214886657308 Trimmed Mean ( 23 / 24 ) 120.957692307692 1.33063516443404 90.9022213907442 Trimmed Mean ( 24 / 24 ) 120.6 1.23323540543458 97.7915485304298 Median 118.65 Midrange 168.3 Midmean - Weighted Average at Xnp 122.659459459459 Midmean - Weighted Average at X(n+1)p 122.969444444444 Midmean - Empirical Distribution Function 122.659459459459 Midmean - Empirical Distribution Function - Averaging 122.969444444444 Midmean - Empirical Distribution Function - Interpolation 122.969444444444 Midmean - Closest Observation 122.659459459459 Midmean - True Basic - Statistics Graphics Toolkit 122.969444444444 Midmean - MS Excel (old versions) 123.336842105263 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/24/t120905988740avmvr2zd2bsyr/1dven1209059826.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/24/t120905988740avmvr2zd2bsyr/1dven1209059826.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/24/t120905988740avmvr2zd2bsyr/2v0q91209059826.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/24/t120905988740avmvr2zd2bsyr/2v0q91209059826.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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