CVWS1TIQ1

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

Title produced by software: Central Tendency

Date of computation: Sun, 06 Jan 2008 06:29:42 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Jan/06/t1199626183p8dfm7op4i0ti6q.htm/, Retrieved Sun, 06 Jan 2008 14:29:45 +0100

User-defined keywords:

Investigating associations Totale Industrie BE Q1

Dataseries X:

» Textbox « » Textfile « » CSV «

72,8 71,2 93,5 97,2 89,8 86,1 87,3 97,6 107,1 96,1 109,5 105,0 83,9 89,2 107,0 113,6 108,1 91,9 104,9 99,2 104,3 104,0 101,5 105,4 88,7 83,6 98,0 108,9 92,8 82,0 101,3 106,3 94,0 102,8 102,0 105,1 92,4 81,4 105,8 120,3 100,7 88,8 94,3 99,9 103,4 103,3 98,8 104,2 91,2 74,7 108,5 114,5 96,9 89,6 97,1 100,3 122,6 115,4 109,0 129,1 102,8 96,2 127,7 128,9 126,5 119,8 113,2 114,1 134,1 130,0 121,8 132,1 105,3 103,0 117,1 126,3 138,1 119,5 138,0 135,5 178,6 162,2 176,9 204,9 132,2 142,5 164,3 174,9 175,4 143,0 158,7 155,4 176,6 163,3 178,9 182,7 158,7 115,5 169,1

Text written by user:

Output produced by software:

Summary of compuational 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 115.936363636364 2.87143411891858 40.3757700281233 Geometric Mean 112.827770036479 Harmonic Mean 110.060306087473 Quadratic Mean 119.370279112321 Winsorized Mean ( 1 / 33 ) 115.728282828283 2.80604121978943 41.2425455521167 Winsorized Mean ( 2 / 33 ) 115.689898989899 2.78190974705389 41.5865033408856 Winsorized Mean ( 3 / 33 ) 115.883838383838 2.75154112738610 42.1159753821035 Winsorized Mean ( 4 / 33 ) 115.839393939394 2.73264046084240 42.3910117702362 Winsorized Mean ( 5 / 33 ) 115.905050505051 2.71918346516905 42.6249467863121 Winsorized Mean ( 6 / 33 ) 115.850505050505 2.70051888618905 42.8993500630512 Winsorized Mean ( 7 / 33 ) 115.970707070707 2.67430964569668 43.3647267650250 Winsorized Mean ( 8 / 33 ) 115.598989898990 2.5606002950993 45.1452693027621 Winsorized Mean ( 9 / 33 ) 115.289898989899 2.45538986385627 46.9538058647975 Winsorized Mean ( 10 / 33 ) 115.198989898990 2.43380028514514 47.3329675413856 Winsorized Mean ( 11 / 33 ) 115.121212121212 2.4043608052308 47.880173337862 Winsorized Mean ( 12 / 33 ) 114.745454545455 2.31551339745856 49.5550812495388 Winsorized Mean ( 13 / 33 ) 114.771717171717 2.31261142311431 49.6286215767102 Winsorized Mean ( 14 / 33 ) 114.503030303030 2.20152607934037 52.0107535302685 Winsorized Mean ( 15 / 33 ) 112.730303030303 1.85326626956155 60.8279041613234 Winsorized Mean ( 16 / 33 ) 112.730303030303 1.83061441977180 61.5805828976022 Winsorized Mean ( 17 / 33 ) 112.043434343434 1.70088385818174 65.8736537503563 Winsorized Mean ( 18 / 33 ) 112.152525252525 1.68349656221306 66.6188026574251 Winsorized Mean ( 19 / 33 ) 111.768686868687 1.59867604369725 69.9132806232586 Winsorized Mean ( 20 / 33 ) 111.546464646465 1.54936519084487 71.9949469018588 Winsorized Mean ( 21 / 33 ) 111.525252525253 1.44757087484949 77.0430342741237 Winsorized Mean ( 22 / 33 ) 111.525252525253 1.44192056199372 77.3449352653996 Winsorized Mean ( 23 / 33 ) 111.2 1.35423475163030 82.1127945994084 Winsorized Mean ( 24 / 33 ) 111.030303030303 1.31829448121391 84.2226866701775 Winsorized Mean ( 25 / 33 ) 111.005050505051 1.30851781409144 84.8326628110344 Winsorized Mean ( 26 / 33 ) 110.794949494950 1.25354115908199 88.3855697056554 Winsorized Mean ( 27 / 33 ) 110.576767676768 1.19709917738353 92.3705986653942 Winsorized Mean ( 28 / 33 ) 110.746464646465 1.16544357933523 95.0251617582675 Winsorized Mean ( 29 / 33 ) 109.779797979798 1.00872403568314 108.830358052737 Winsorized Mean ( 30 / 33 ) 109.749494949495 0.95487268601655 114.936259625708 Winsorized Mean ( 31 / 33 ) 109.405050505050 0.881806505023254 124.069225937685 Winsorized Mean ( 32 / 33 ) 109.372727272727 0.847917912900025 128.989759042422 Winsorized Mean ( 33 / 33 ) 109.472727272727 0.814686641104936 134.374030147656 Trimmed Mean ( 1 / 33 ) 115.480412371134 2.74288858667572 42.1017510270412 Trimmed Mean ( 2 / 33 ) 115.222105263158 2.67106396546561 43.1371568606642 Trimmed Mean ( 3 / 33 ) 114.973118279570 2.60383125665788 44.155364517416 Trimmed Mean ( 4 / 33 ) 114.642857142857 2.53964133818838 45.1413573322271 Trimmed Mean ( 5 / 33 ) 114.310112359551 2.47232694507622 46.23583971659 Trimmed Mean ( 6 / 33 ) 113.947126436782 2.39836766143193 47.5102830434056 Trimmed Mean ( 7 / 33 ) 113.577647058824 2.31747796877812 49.0091593486461 Trimmed Mean ( 8 / 33 ) 113.169879518072 2.22907795392041 50.7698168738485 Trimmed Mean ( 9 / 33 ) 112.798765432099 2.15197977598691 52.4162757897521 Trimmed Mean ( 10 / 33 ) 112.451898734177 2.08417310754767 53.9551625183827 Trimmed Mean ( 11 / 33 ) 112.098701298701 2.00868797657581 55.8069260163515 Trimmed Mean ( 12 / 33 ) 111.736 1.92505775273142 58.0429339542984 Trimmed Mean ( 13 / 33 ) 111.395890410959 1.8435471384219 60.4247583852481 Trimmed Mean ( 14 / 33 ) 111.033802816901 1.74593629204020 63.595563780368 Trimmed Mean ( 15 / 33 ) 110.678260869565 1.65036081921843 67.0630686215513 Trimmed Mean ( 16 / 33 ) 110.476119402985 1.60417688850313 68.8677914479064 Trimmed Mean ( 17 / 33 ) 110.261538461538 1.55231169474211 71.0305403450923 Trimmed Mean ( 18 / 33 ) 110.096825396825 1.51309689149152 72.7625745687035 Trimmed Mean ( 19 / 33 ) 109.911475409836 1.46791755839861 74.8757822133697 Trimmed Mean ( 20 / 33 ) 109.747457627119 1.42788534250054 76.8601332057422 Trimmed Mean ( 21 / 33 ) 109.591228070175 1.38736529455559 78.9923378509196 Trimmed Mean ( 22 / 33 ) 109.425454545455 1.3545315345137 80.7847228043606 Trimmed Mean ( 23 / 33 ) 109.247169811321 1.31399910247981 83.1409774977373 Trimmed Mean ( 24 / 33 ) 109.082352941176 1.27939540219422 85.260860523725 Trimmed Mean ( 25 / 33 ) 108.918367346939 1.24204500514584 87.6927703067813 Trimmed Mean ( 26 / 33 ) 108.742553191489 1.19556977727350 90.9545852183361 Trimmed Mean ( 27 / 33 ) 108.742553191489 1.14711681713052 94.796407451776 Trimmed Mean ( 28 / 33 ) 108.397674418605 1.09639239471569 98.8675906008213 Trimmed Mean ( 29 / 33 ) 108.195121951220 1.03495582101724 104.540812036669 Trimmed Mean ( 30 / 33 ) 108.056410256410 0.995094546344503 108.589088999992 Trimmed Mean ( 31 / 33 ) 107.905405405405 0.953592432707447 113.156734160568 Trimmed Mean ( 32 / 33 ) 107.768571428571 0.916292964678245 117.613662423365 Trimmed Mean ( 33 / 33 ) 107.618181818182 0.872371099984493 123.362846178759 Median 105.8 Midrange 138.05 Midmean - Weighted Average at Xnp 108.682 Midmean - Weighted Average at X(n+1)p 109.082352941177 Midmean - Empirical Distribution Function 109.082352941177 Midmean - Empirical Distribution Function - Averaging 109.082352941177 Midmean - Empirical Distribution Function - Interpolation 108.918367346939 Midmean - Closest Observation 108.682 Midmean - True Basic - Statistics Graphics Toolkit 109.082352941177 Midmean - MS Excel (old versions) 109.082352941177 Number of observations 99

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/06/t1199626183p8dfm7op4i0ti6q/119w21199626179.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/06/t1199626183p8dfm7op4i0ti6q/119w21199626179.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/06/t1199626183p8dfm7op4i0ti6q/2v32v1199626179.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/06/t1199626183p8dfm7op4i0ti6q/2v32v1199626179.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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As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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