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Q8 Central tendency

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

Title produced by software: Central Tendency

Date of computation: Mon, 22 Oct 2007 02:39:06 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Oct/22/65bv0so6uu9py6p1193045825.htm/, Retrieved Mon, 22 Oct 2007 11:37:08 +0200

User-defined keywords:

Q8, central tendency, niet-voeding, associations, own data

Dataseries X:

» Textbox « » Textfile « » CSV «

92,58 93,15 93,7 93,34 93,93 94,41 94,3 94,44 96,09 95,99 96,23 95,64 94,88 95,48 95,52 96,18 96,82 96,81 96,25 96,24 96,95 96,25 96,04 95,78 95,86 96,02 96,34 96,84 96,73 96,34 96,6 96,64 97,2 97,5 96,99 97,08 97,55 98,42 98,78 97,49 96,99 97,16 97,29 97,8 98,12 98,03 98,11 98,07 98,21 98,48 98,83 99,2 99,88 99,71 100,03 100,6 100,85 101,96 101,4 100,81 100,66 101,55 102,23 102,9 102,68 103,41 104,62 104,93 105,88 105,18 104,54 104,58 104,34 104,66 104,73 105,44 105,72 105,68 105,9 105,97 105,21 104,75 104,89 105,26 104,84 105,47 105,4 105,73 105,72 105,63 105,97 105,92 106,32

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 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 99.7593548387097 0.429335864869558 232.357375662103 Geometric Mean 99.6749030686052 Harmonic Mean 99.5910569285645 Quadratic Mean 99.844314670606 Winsorized Mean ( 1 / 31 ) 99.7617204301075 0.427654283997276 233.276560444190 Winsorized Mean ( 2 / 31 ) 99.765806451613 0.426976752675600 233.656295867262 Winsorized Mean ( 3 / 31 ) 99.775806451613 0.424870118002106 234.838371125734 Winsorized Mean ( 4 / 31 ) 99.7848387096774 0.423222311706629 235.774050539299 Winsorized Mean ( 5 / 31 ) 99.8036559139785 0.420141252348394 237.547861239815 Winsorized Mean ( 6 / 31 ) 99.8010752688172 0.417630744292097 238.969655928910 Winsorized Mean ( 7 / 31 ) 99.8025806451613 0.417198489112846 239.220858295501 Winsorized Mean ( 8 / 31 ) 99.8404301075269 0.412077199530099 242.285742140980 Winsorized Mean ( 9 / 31 ) 99.894623655914 0.404227501312895 247.124758536876 Winsorized Mean ( 10 / 31 ) 99.8935483870968 0.402884226522204 247.946039608953 Winsorized Mean ( 11 / 31 ) 99.888817204301 0.398318193295746 250.776436742208 Winsorized Mean ( 12 / 31 ) 99.9030107526882 0.395658616295133 252.498003678423 Winsorized Mean ( 13 / 31 ) 99.9086021505376 0.393550761354181 253.864588666425 Winsorized Mean ( 14 / 31 ) 99.9070967741935 0.388205572648046 257.356163366493 Winsorized Mean ( 15 / 31 ) 99.903870967742 0.386469830853988 258.503673487224 Winsorized Mean ( 16 / 31 ) 99.9021505376344 0.385325125448105 259.267158925739 Winsorized Mean ( 17 / 31 ) 99.8655913978495 0.377596866641112 264.476748141999 Winsorized Mean ( 18 / 31 ) 99.8752688172043 0.374588681744168 266.626499103398 Winsorized Mean ( 19 / 31 ) 99.8752688172043 0.372012883629952 268.472607299676 Winsorized Mean ( 20 / 31 ) 99.858064516129 0.368985324451024 270.628824234942 Winsorized Mean ( 21 / 31 ) 99.855806451613 0.368094366196924 271.277736422056 Winsorized Mean ( 22 / 31 ) 99.839247311828 0.365716369270871 272.996386546431 Winsorized Mean ( 23 / 31 ) 99.8516129032258 0.361938423493807 275.880112255985 Winsorized Mean ( 24 / 31 ) 99.8412903225806 0.360461797525905 276.981613607488 Winsorized Mean ( 25 / 31 ) 99.9004301075269 0.351666503170992 284.077184510667 Winsorized Mean ( 26 / 31 ) 99.8556989247312 0.342537808843586 291.51730508771 Winsorized Mean ( 27 / 31 ) 99.6118279569892 0.302147524188088 329.679444584761 Winsorized Mean ( 28 / 31 ) 99.4823655913979 0.278918987747807 356.671183968829 Winsorized Mean ( 29 / 31 ) 99.4168817204301 0.269509795961277 368.88040141856 Winsorized Mean ( 30 / 31 ) 99.2781720430108 0.249952494141673 397.18816323049 Winsorized Mean ( 31 / 31 ) 99.2248387096774 0.234594365726567 422.963434788240 Trimmed Mean ( 1 / 31 ) 99.7661538461538 0.425461317374386 234.489364301865 Trimmed Mean ( 2 / 31 ) 99.770786516854 0.422833486035761 235.957628266972 Trimmed Mean ( 3 / 31 ) 99.773448275862 0.420104708997592 237.496619625927 Trimmed Mean ( 4 / 31 ) 99.7725882352941 0.41771286537227 238.854477576064 Trimmed Mean ( 5 / 31 ) 99.769156626506 0.415348711334969 240.205769041245 Trimmed Mean ( 6 / 31 ) 99.7612345679012 0.413296532961387 241.379316330296 Trimmed Mean ( 7 / 31 ) 99.753417721519 0.411338837548108 242.5091156384 Trimmed Mean ( 8 / 31 ) 99.744935064935 0.408966932141199 243.894865882451 Trimmed Mean ( 9 / 31 ) 99.7301333333333 0.407007248904317 245.032818461616 Trimmed Mean ( 10 / 31 ) 99.7068493150685 0.405883428537495 245.653905295761 Trimmed Mean ( 11 / 31 ) 99.6823943661972 0.404507971224616 246.428751612525 Trimmed Mean ( 12 / 31 ) 99.6571014492754 0.403348944346909 247.074159598055 Trimmed Mean ( 13 / 31 ) 99.6571014492754 0.40205689462864 247.86815692173 Trimmed Mean ( 14 / 31 ) 99.5978461538461 0.400493175077958 248.687998576902 Trimmed Mean ( 15 / 31 ) 99.5652380952381 0.399083297826838 249.484853506546 Trimmed Mean ( 16 / 31 ) 99.5308196721311 0.397256458374595 250.545504230111 Trimmed Mean ( 17 / 31 ) 99.4942372881356 0.394814592489211 252.002431472577 Trimmed Mean ( 18 / 31 ) 99.458596491228 0.392683591993392 253.279226632168 Trimmed Mean ( 19 / 31 ) 99.4194545454545 0.390059170006962 254.883007989993 Trimmed Mean ( 20 / 31 ) 99.377358490566 0.386747645108983 256.956596238775 Trimmed Mean ( 21 / 31 ) 99.3335294117647 0.382673241406531 259.577934027109 Trimmed Mean ( 22 / 31 ) 99.2863265306122 0.377221164971576 263.204548817121 Trimmed Mean ( 23 / 31 ) 99.2365957446809 0.370306180862777 267.985253482590 Trimmed Mean ( 24 / 31 ) 99.1813333333333 0.361645453923362 274.250186909169 Trimmed Mean ( 25 / 31 ) 99.1218604651163 0.350279315190739 282.979485703119 Trimmed Mean ( 26 / 31 ) 99.1218604651163 0.336469872373252 294.593568707866 Trimmed Mean ( 27 / 31 ) 98.977435897436 0.319908623498165 309.392834788661 Trimmed Mean ( 28 / 31 ) 98.9183783783784 0.308588891781863 320.550677657906 Trimmed Mean ( 29 / 31 ) 98.8648571428571 0.299079363691838 330.56395440484 Trimmed Mean ( 30 / 31 ) 98.8112121212121 0.288037954403976 343.049277397063 Trimmed Mean ( 31 / 31 ) 98.7645161290323 0.278186461297801 355.029916510940 Median 98.21 Midrange 99.45 Midmean - Weighted Average at Xnp 99.1195652173913 Midmean - Weighted Average at X(n+1)p 99.2365957446809 Midmean - Empirical Distribution Function 99.2365957446809 Midmean - Empirical Distribution Function - Averaging 99.2365957446809 Midmean - Empirical Distribution Function - Interpolation 99.2365957446809 Midmean - Closest Observation 99.114693877551 Midmean - True Basic - Statistics Graphics Toolkit 99.2365957446809 Midmean - MS Excel (old versions) 99.2365957446809 Number of observations 93

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/22/65bv0so6uu9py6p1193045825/112631193045944.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/22/65bv0so6uu9py6p1193045825/112631193045944.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/22/65bv0so6uu9py6p1193045825/2gbuq1193045944.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/22/65bv0so6uu9py6p1193045825/2gbuq1193045944.ps (open in new window)

Parameters:

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')

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Software written by Ed van Stee & Patrick Wessa

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