Central Tendency_Gem consumptieprijs roze zalm_Dominique Van Santfoort

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

Title produced by software: Central Tendency

Date of computation: Tue, 15 Jul 2008 08:07:06 -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/Jul/15/t1216130869l3d42sql8lo2xid.htm/, Retrieved Tue, 15 Jul 2008 14:07:51 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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11,73 11,74 11,65 11,38 11,53 11,75 11,82 11,83 11,63 11,55 11,4 11,4 11,63 11,46 11,35 11,7 11,52 11,64 11,9 11,73 11,7 11,54 11,97 11,64 11,98 11,79 11,66 11,96 11,83 12,36 12,53 12,55 12,53 12,24 12,34 12,05 12,22 12,23 11,92 12,13 12,1 12,15 12,23 12,08 12,02 11,93 12,16 11,87 11,93 11,79 11,43 11,63 11,93 11,89 11,83 11,59 12,04 11,81 11,9 11,72 11,91 11,94 11,91 11,84 12,01 11,89 11,8 11,7 11,5 11,76 11,61 11,27 11,64 11,39 11,54 11,62 11,59 11,44 11,31 11,56 11,4 11,51 11,5 11,24 11,8 11,87 11,86 12,11 11,92 12,61 13,34 13,31 13,47 13,3 13,18 13,24

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 11.9003125 0.0477170601744135 249.393245445182 Geometric Mean 11.8915777070126 Harmonic Mean 11.8831771429469 Quadratic Mean 11.9093973311695 Winsorized Mean ( 1 / 32 ) 11.8992708333333 0.0472203784416022 251.994397885846 Winsorized Mean ( 2 / 32 ) 11.8994791666667 0.0469075167431642 253.679580435278 Winsorized Mean ( 3 / 32 ) 11.9004166666667 0.046648394762501 255.108814081487 Winsorized Mean ( 4 / 32 ) 11.8991666666667 0.0457152386074455 260.288845232642 Winsorized Mean ( 5 / 32 ) 11.8965625 0.0446982642538011 266.152672785014 Winsorized Mean ( 6 / 32 ) 11.8615625 0.0350658303606457 338.265553047112 Winsorized Mean ( 7 / 32 ) 11.8571875 0.0341062912615608 347.653968268415 Winsorized Mean ( 8 / 32 ) 11.8555208333333 0.0337528003359574 351.245547490276 Winsorized Mean ( 9 / 32 ) 11.8583333333333 0.0333629254610808 355.434458143263 Winsorized Mean ( 10 / 32 ) 11.8416666666667 0.0297012414334832 398.692650379158 Winsorized Mean ( 11 / 32 ) 11.8416666666667 0.0289610547124665 408.882438303234 Winsorized Mean ( 12 / 32 ) 11.8341666666667 0.0261170050583212 453.121123200769 Winsorized Mean ( 13 / 32 ) 11.8328125 0.0258969377402074 456.919370881001 Winsorized Mean ( 14 / 32 ) 11.8342708333333 0.0257014509077721 460.451469288632 Winsorized Mean ( 15 / 32 ) 11.8342708333333 0.0252430052808046 468.813863551042 Winsorized Mean ( 16 / 32 ) 11.8259375 0.0234677728468287 503.922446206823 Winsorized Mean ( 17 / 32 ) 11.8259375 0.0229700310688217 514.842033281005 Winsorized Mean ( 18 / 32 ) 11.8221875 0.0224205239254596 527.293097132994 Winsorized Mean ( 19 / 32 ) 11.8202083333333 0.0215933201002814 547.401153617841 Winsorized Mean ( 20 / 32 ) 11.8202083333333 0.0210273314030971 562.135446801983 Winsorized Mean ( 21 / 32 ) 11.8223958333333 0.0195798773312930 603.803365736032 Winsorized Mean ( 22 / 32 ) 11.8155208333333 0.0186483324307787 633.596643409899 Winsorized Mean ( 23 / 32 ) 11.8179166666667 0.0177308808982211 666.516048159365 Winsorized Mean ( 24 / 32 ) 11.8154166666667 0.0167724167008903 704.455230118357 Winsorized Mean ( 25 / 32 ) 11.8154166666667 0.016122418647366 732.856336576834 Winsorized Mean ( 26 / 32 ) 11.8072916666667 0.0151168541691306 781.068040649476 Winsorized Mean ( 27 / 32 ) 11.8044791666667 0.0147819456257936 798.574116391592 Winsorized Mean ( 28 / 32 ) 11.8044791666667 0.0140798706879425 838.394004340937 Winsorized Mean ( 29 / 32 ) 11.7984375 0.0133921357888442 880.997451491513 Winsorized Mean ( 30 / 32 ) 11.7953125 0.0130484531625097 903.962512115215 Winsorized Mean ( 31 / 32 ) 11.7985416666667 0.0126464917528527 932.949777475266 Winsorized Mean ( 32 / 32 ) 11.801875 0.012236980639661 964.44338252438 Trimmed Mean ( 1 / 32 ) 11.8906382978723 0.0451955785760513 263.092954499161 Trimmed Mean ( 2 / 32 ) 11.8816304347826 0.0428380647223033 277.361512752852 Trimmed Mean ( 3 / 32 ) 11.8721111111111 0.040267983225136 294.827556789592 Trimmed Mean ( 4 / 32 ) 11.8618181818182 0.0373276413274070 317.775722226224 Trimmed Mean ( 5 / 32 ) 11.8513953488372 0.0341530965284477 347.007930568334 Trimmed Mean ( 6 / 32 ) 11.8410714285714 0.0306264755669874 386.62860186678 Trimmed Mean ( 7 / 32 ) 11.8370731707317 0.0294292223294454 402.221745387003 Trimmed Mean ( 8 / 32 ) 11.833625 0.0282737766806065 418.537117756783 Trimmed Mean ( 9 / 32 ) 11.8302564102564 0.0270000643546885 438.156600474995 Trimmed Mean ( 10 / 32 ) 11.8263157894737 0.0255719433050208 462.472313832782 Trimmed Mean ( 11 / 32 ) 11.8243243243243 0.024689917840833 478.913068911428 Trimmed Mean ( 12 / 32 ) 11.8222222222222 0.02379343669959 496.869047186695 Trimmed Mean ( 13 / 32 ) 11.8208571428571 0.0232706133000390 507.97359701892 Trimmed Mean ( 14 / 32 ) 11.8195588235294 0.0226875500309318 520.971140886295 Trimmed Mean ( 15 / 32 ) 11.8180303030303 0.0220226834711693 536.629894286121 Trimmed Mean ( 16 / 32 ) 11.81640625 0.0213046300433667 554.640293023023 Trimmed Mean ( 17 / 32 ) 11.8154838709677 0.0207598611756306 569.150427886174 Trimmed Mean ( 18 / 32 ) 11.8145 0.0201833754379142 585.357986147681 Trimmed Mean ( 19 / 32 ) 11.8137931034483 0.0195778613475258 603.426129838296 Trimmed Mean ( 20 / 32 ) 11.8132142857143 0.0189824032370262 622.324483270485 Trimmed Mean ( 21 / 32 ) 11.8125925925926 0.0183474982160681 643.825793221636 Trimmed Mean ( 22 / 32 ) 11.8117307692308 0.0178220658090419 662.758789906283 Trimmed Mean ( 23 / 32 ) 11.8114 0.0173370194929220 681.282039558304 Trimmed Mean ( 24 / 32 ) 11.8108333333333 0.0168899056400428 699.283559366492 Trimmed Mean ( 25 / 32 ) 11.8104347826087 0.0164975668583378 715.889493524904 Trimmed Mean ( 26 / 32 ) 11.81 0.016109430221826 733.110969002436 Trimmed Mean ( 27 / 32 ) 11.8102380952381 0.0157966465193971 747.642107502756 Trimmed Mean ( 28 / 32 ) 11.81075 0.0154355047760774 765.167720222848 Trimmed Mean ( 29 / 32 ) 11.8113157894737 0.0150918056040821 782.631058160389 Trimmed Mean ( 30 / 32 ) 11.8125 0.0147539341000484 800.633913632652 Trimmed Mean ( 31 / 32 ) 11.8141176470588 0.0143369040471625 824.035482709186 Trimmed Mean ( 32 / 32 ) 11.815625 0.013846345010915 853.338912953983 Median 11.825 Midrange 12.355 Midmean - Weighted Average at Xnp 11.8067346938775 Midmean - Weighted Average at X(n+1)p 11.8108333333333 Midmean - Empirical Distribution Function 11.8067346938775 Midmean - Empirical Distribution Function - Averaging 11.8108333333333 Midmean - Empirical Distribution Function - Interpolation 11.8108333333333 Midmean - Closest Observation 11.8067346938775 Midmean - True Basic - Statistics Graphics Toolkit 11.8108333333333 Midmean - MS Excel (old versions) 11.8114 Number of observations 96

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jul/15/t1216130869l3d42sql8lo2xid/1rsqf1216130823.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jul/15/t1216130869l3d42sql8lo2xid/1rsqf1216130823.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jul/15/t1216130869l3d42sql8lo2xid/2256f1216130823.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jul/15/t1216130869l3d42sql8lo2xid/2256f1216130823.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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