Descriptive Statistics – Central Tendency - consumptieprijs bloemkool

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

Title produced by software: Central Tendency

Date of computation: Sun, 17 Aug 2008 13:33:36 -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/Aug/17/t1219001715793e5km5ot7jl8m.htm/, Retrieved Sun, 17 Aug 2008 19:35:17 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

100,58 118,48 79,58 81,97 127,13 120,76 120,26 74,9 67,59 87,73 102,87 144,94 110,48 96,34 100,43 90,88 128,28 101,21 73,76 73,64 66,4 57,34 113,59 123,53 102,87 102,99 95,8 98,43 102,65 129,55 100,37 101,93 101,94 93,87 100,91 92,64 101,67 88,67 129,86 98,07 166,45 176,52 82,07 92,18 95,02 84,69 103,01 107,9 204,13 101,99 119,23 95,65 160,95 111,06 150,41 94,79 160,34 104,08 101,07 111,5 136,9 141,71 153,98 134,27 124,71 72,89 101,2 73,28 174,05 111,9 97,06 105,23 109,13 84,04 118,82 90,84 144,28 110,16 86,09 59,87 108,97 94,93 87,36 143,52 108,7 121,13 210,25 110,2 161,46 99,41 132,72 174,29 69,93 83,43 127,53 187,58

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 111.247395833333 3.13066742661529 35.5347217298032 Geometric Mean 107.440920929119 Harmonic Mean 103.922142187034 Quadratic Mean 115.356341570912 Winsorized Mean ( 1 / 32 ) 111.21 3.10533274342194 35.8125873098712 Winsorized Mean ( 2 / 32 ) 111.00125 2.98169842704933 37.2275240825902 Winsorized Mean ( 3 / 32 ) 110.6928125 2.88757661363814 38.3341560453126 Winsorized Mean ( 4 / 32 ) 110.697395833333 2.85051569759059 38.8341646134069 Winsorized Mean ( 5 / 32 ) 110.8390625 2.82506875043701 39.2341115531629 Winsorized Mean ( 6 / 32 ) 110.3884375 2.71392571201822 40.6748191415708 Winsorized Mean ( 7 / 32 ) 110.050833333333 2.63314652624099 41.7944205674111 Winsorized Mean ( 8 / 32 ) 110.018333333333 2.62298059193592 41.9440134904441 Winsorized Mean ( 9 / 32 ) 110.068020833333 2.59591036164525 42.4005475919337 Winsorized Mean ( 10 / 32 ) 109.893020833333 2.39681035815892 45.8496937228469 Winsorized Mean ( 11 / 32 ) 109.7578125 2.28305363187846 48.0750040066702 Winsorized Mean ( 12 / 32 ) 109.0865625 2.15742522805586 50.5633108769671 Winsorized Mean ( 13 / 32 ) 109.181354166667 2.11788501657113 51.552068838672 Winsorized Mean ( 14 / 32 ) 109.159479166667 2.08728666506174 52.2973106635729 Winsorized Mean ( 15 / 32 ) 108.978229166667 2.02588570620917 53.7928812235841 Winsorized Mean ( 16 / 32 ) 108.409895833333 1.86362820824595 58.1714181796857 Winsorized Mean ( 17 / 32 ) 108.1690625 1.76164186573684 61.4024136255164 Winsorized Mean ( 18 / 32 ) 107.9478125 1.70815398846654 63.1955978377031 Winsorized Mean ( 19 / 32 ) 107.5678125 1.60023853898332 67.2198612141543 Winsorized Mean ( 20 / 32 ) 107.9553125 1.53608260121127 70.2796271599409 Winsorized Mean ( 21 / 32 ) 107.68625 1.49433998111764 72.0627510209958 Winsorized Mean ( 22 / 32 ) 107.812291666667 1.43471040142136 75.1456820553177 Winsorized Mean ( 23 / 32 ) 107.826666666667 1.40828900065176 76.5657238086532 Winsorized Mean ( 24 / 32 ) 107.529166666667 1.28746338447906 83.520174603005 Winsorized Mean ( 25 / 32 ) 107.461458333333 1.21803444787485 88.2253030863168 Winsorized Mean ( 26 / 32 ) 106.849375 1.12522929254461 94.9578683277694 Winsorized Mean ( 27 / 32 ) 106.770625 1.10854289153798 96.3161875061664 Winsorized Mean ( 28 / 32 ) 106.808541666667 1.06884615581771 99.928826132096 Winsorized Mean ( 29 / 32 ) 106.542708333333 1.02292504440597 104.154951446325 Winsorized Mean ( 30 / 32 ) 106.583333333333 0.98766556092329 107.914396887239 Winsorized Mean ( 31 / 32 ) 106.706041666667 0.948186432358131 112.536984315721 Winsorized Mean ( 32 / 32 ) 105.412708333333 0.70464907402592 149.596036124864 Trimmed Mean ( 1 / 32 ) 110.767659574468 2.96121268072834 37.4061816955422 Trimmed Mean ( 2 / 32 ) 110.306086956522 2.79345483973294 39.4873349615587 Trimmed Mean ( 3 / 32 ) 109.935333333333 2.67738033312224 41.0607831742499 Trimmed Mean ( 4 / 32 ) 109.659886363636 2.58566110530193 42.4107730664228 Trimmed Mean ( 5 / 32 ) 109.370348837209 2.49274077370990 43.8755405257945 Trimmed Mean ( 6 / 32 ) 109.034642857143 2.39222123072003 45.5788291889395 Trimmed Mean ( 7 / 32 ) 108.770487804878 2.30594916744835 47.1695080448101 Trimmed Mean ( 8 / 32 ) 108.551 2.22557030523511 48.7744645696702 Trimmed Mean ( 9 / 32 ) 108.325256410256 2.1337225262421 50.7682020871937 Trimmed Mean ( 10 / 32 ) 108.080657894737 2.03118750450064 53.2105764018612 Trimmed Mean ( 11 / 32 ) 107.845540540541 1.95248498041271 55.235016720971 Trimmed Mean ( 12 / 32 ) 107.61375 1.88210553934896 57.177319629602 Trimmed Mean ( 13 / 32 ) 107.445428571429 1.82350826393587 58.922369970245 Trimmed Mean ( 14 / 32 ) 107.256911764706 1.76074949194067 60.9154864196435 Trimmed Mean ( 15 / 32 ) 107.059242424242 1.69106195942402 63.3088822249346 Trimmed Mean ( 16 / 32 ) 106.86734375 1.61870404638743 66.0203104999353 Trimmed Mean ( 17 / 32 ) 106.718064516129 1.56218006287613 68.313549156203 Trimmed Mean ( 18 / 32 ) 106.5815 1.51215926404282 70.482985843072 Trimmed Mean ( 19 / 32 ) 106.455862068966 1.46083566390330 72.8732633652433 Trimmed Mean ( 20 / 32 ) 106.355535714286 1.41770859386535 75.0193207366472 Trimmed Mean ( 21 / 32 ) 106.213333333333 1.37496303234722 77.2481374659326 Trimmed Mean ( 22 / 32 ) 106.083846153846 1.32952279267707 79.7909195225158 Trimmed Mean ( 23 / 32 ) 105.933 1.28307106870467 82.562067358393 Trimmed Mean ( 24 / 32 ) 105.768333333333 1.22872798398541 86.0795348619565 Trimmed Mean ( 25 / 32 ) 105.615217391304 1.18456481089906 89.1595093991897 Trimmed Mean ( 26 / 32 ) 105.454090909091 1.14150601156447 92.3815466942331 Trimmed Mean ( 27 / 32 ) 105.331428571429 1.10647484999066 95.1955017977296 Trimmed Mean ( 28 / 32 ) 105.2035 1.06313533342632 98.9558870750215 Trimmed Mean ( 29 / 32 ) 105.058684210526 1.01357641593128 103.651468758769 Trimmed Mean ( 30 / 32 ) 104.922222222222 0.958345226519254 109.482699259956 Trimmed Mean ( 31 / 32 ) 104.765882352941 0.890423612624498 117.658472739898 Trimmed Mean ( 32 / 32 ) 104.578125 0.803844522047019 130.097453091660 Median 102.87 Midrange 133.795 Midmean - Weighted Average at Xnp 105.500408163265 Midmean - Weighted Average at X(n+1)p 105.768333333333 Midmean - Empirical Distribution Function 105.500408163265 Midmean - Empirical Distribution Function - Averaging 105.768333333333 Midmean - Empirical Distribution Function - Interpolation 105.768333333333 Midmean - Closest Observation 105.500408163265 Midmean - True Basic - Statistics Graphics Toolkit 105.768333333333 Midmean - MS Excel (old versions) 105.933 Number of observations 96

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/17/t1219001715793e5km5ot7jl8m/1p0l61219001613.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/17/t1219001715793e5km5ot7jl8m/1p0l61219001613.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/17/t1219001715793e5km5ot7jl8m/2s6o61219001613.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/17/t1219001715793e5km5ot7jl8m/2s6o61219001613.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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