Alexander De Raeymaeker - Volvo verkoopcijfers - Opgave 5

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Wed, 27 Apr 2011 12:34:49 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Apr/27/t13039075344isfm6u5csuhoy6.htm/, Retrieved Wed, 27 Apr 2011 14:32:16 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

2435 1379 1511 2021 1614 1680 1630 870 1877 2428 1711 127 3192 1934 2075 1700 1198 1582 1705 911 1817 1168 920 84 2254 1485 1886 1358 1167 1781 1218 779 1418 1641 1196 132 2926 1777 2094 1648 1646 1537 1917 977 1475 2124 1209 135 2917 1981 1398 1171 903 1390 1280 781 1828 1631 1063 186 2275 1342 1070 950 1121 1305 1586 548 1225 1419 880 124 2044 1143 897 1264 1326 1529 1373 587 1137 1426 1016 176 2614

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' @ www.wessa.org Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 1414.76470588235 69.2070243983 20.4425015839448 Geometric Mean 1185.43790004489 Harmonic Mean 762.594633326986 Quadratic Mean 1550.44722580293 Winsorized Mean ( 1 / 28 ) 1412.10588235294 68.207990577202 20.702939207022 Winsorized Mean ( 2 / 28 ) 1411.96470588235 68.1363118166199 20.7226465336497 Winsorized Mean ( 3 / 28 ) 1401.44705882353 65.5073423854885 21.3937401181151 Winsorized Mean ( 4 / 28 ) 1393.16470588235 63.7251403653402 21.8620892460221 Winsorized Mean ( 5 / 28 ) 1395.16470588235 63.084037247775 22.1159704855694 Winsorized Mean ( 6 / 28 ) 1385.07058823529 60.9266923888377 22.7333953958257 Winsorized Mean ( 7 / 28 ) 1413.15294117647 54.2570846446869 26.0455007936895 Winsorized Mean ( 8 / 28 ) 1404.58823529412 51.4104570723846 27.3210610307645 Winsorized Mean ( 9 / 28 ) 1421.74117647059 47.2967719477577 30.0600044764364 Winsorized Mean ( 10 / 28 ) 1419.74117647059 46.8835680212555 30.2822766353219 Winsorized Mean ( 11 / 28 ) 1427.24705882353 44.4221911444437 32.1291458627666 Winsorized Mean ( 12 / 28 ) 1425.41176470588 43.6799196027596 32.6331132856716 Winsorized Mean ( 13 / 28 ) 1421.89411764706 42.3167991604364 33.6011736676068 Winsorized Mean ( 14 / 28 ) 1415.14117647059 40.9776674606515 34.5344492296802 Winsorized Mean ( 15 / 28 ) 1413.55294117647 40.3187874755238 35.0594110012507 Winsorized Mean ( 16 / 28 ) 1409.41176470588 39.2111939303653 35.9441175703254 Winsorized Mean ( 17 / 28 ) 1413.61176470588 38.0697027471958 37.1321986434478 Winsorized Mean ( 18 / 28 ) 1408.95294117647 35.7678200122181 39.3916358529868 Winsorized Mean ( 19 / 28 ) 1415.21176470588 34.1913756146124 41.3908987066628 Winsorized Mean ( 20 / 28 ) 1417.8 31.5062032040697 45.0006619590665 Winsorized Mean ( 21 / 28 ) 1418.54117647059 31.139527660141 45.5543575340206 Winsorized Mean ( 22 / 28 ) 1414.65882352941 27.1217999335624 52.1594741866234 Winsorized Mean ( 23 / 28 ) 1417.36470588235 26.3575333633948 53.774557973273 Winsorized Mean ( 24 / 28 ) 1417.64705882353 25.9604779658146 54.6078951508645 Winsorized Mean ( 25 / 28 ) 1418.82352941176 24.3237107895649 58.3308830501494 Winsorized Mean ( 26 / 28 ) 1409.34117647059 23.0565165626972 61.1255031799009 Winsorized Mean ( 27 / 28 ) 1409.65882352941 22.8596837440915 61.665718533563 Winsorized Mean ( 28 / 28 ) 1416.24705882353 21.6456302049593 65.4287745569564 Trimmed Mean ( 1 / 28 ) 1409.38554216867 65.5745305071027 21.4928804105737 Trimmed Mean ( 2 / 28 ) 1406.53086419753 62.5005360135528 22.5043008253967 Trimmed Mean ( 3 / 28 ) 1403.60759493671 58.9224109217816 23.8212858737225 Trimmed Mean ( 4 / 28 ) 1404.4025974026 55.9383059605146 25.1062768757053 Trimmed Mean ( 5 / 28 ) 1407.58666666667 53.0802285626604 26.5180973176299 Trimmed Mean ( 6 / 28 ) 1410.47945205479 49.8828998221694 28.2758110912377 Trimmed Mean ( 7 / 28 ) 1415.54929577465 46.6804574327388 30.3242378850784 Trimmed Mean ( 8 / 28 ) 1415.97101449275 44.6982397748067 31.6784513579624 Trimmed Mean ( 9 / 28 ) 1417.77611940299 43.0244627695204 32.952790764592 Trimmed Mean ( 10 / 28 ) 1417.2 41.9484814522987 33.7842980469163 Trimmed Mean ( 11 / 28 ) 1416.85714285714 40.7394205614409 34.778529574821 Trimmed Mean ( 12 / 28 ) 1415.54098360656 39.7750613424118 35.5886562039611 Trimmed Mean ( 13 / 28 ) 1414.35593220339 38.7443762078241 36.5048058747109 Trimmed Mean ( 14 / 28 ) 1413.49122807018 37.7469738766765 37.4464780326021 Trimmed Mean ( 15 / 28 ) 1413.30909090909 36.7745783288423 38.4316871908395 Trimmed Mean ( 16 / 28 ) 1413.28301886792 35.6899584345697 39.5988978653167 Trimmed Mean ( 17 / 28 ) 1413.6862745098 34.5487491921491 40.9185949583105 Trimmed Mean ( 18 / 28 ) 1413.69387755102 33.3379444610153 42.4049502873269 Trimmed Mean ( 19 / 28 ) 1414.17021276596 32.2720758819276 43.8202431705948 Trimmed Mean ( 20 / 28 ) 1414.06666666667 31.2280856495132 45.2818876743637 Trimmed Mean ( 21 / 28 ) 1413.6976744186 30.4360072442131 46.4481974614918 Trimmed Mean ( 22 / 28 ) 1413.21951219512 29.4550404025525 47.9788685698986 Trimmed Mean ( 23 / 28 ) 1413.07692307692 29.028311942271 48.6792661553014 Trimmed Mean ( 24 / 28 ) 1412.64864864865 28.5715007477609 49.4425778022652 Trimmed Mean ( 25 / 28 ) 1412.14285714286 27.9865256551666 50.457955179662 Trimmed Mean ( 26 / 28 ) 1411.45454545455 27.5276063538087 51.2741473891085 Trimmed Mean ( 27 / 28 ) 1411.67741935484 27.1392025737152 52.0161716439699 Trimmed Mean ( 28 / 28 ) 1411.89655172414 26.5445227263075 53.1897509057434 Median 1398 Midrange 1638 Midmean - Weighted Average at Xnp 1405.04761904762 Midmean - Weighted Average at X(n+1)p 1413.6976744186 Midmean - Empirical Distribution Function 1413.6976744186 Midmean - Empirical Distribution Function - Averaging 1413.6976744186 Midmean - Empirical Distribution Function - Interpolation 1413.6976744186 Midmean - Closest Observation 1405.72727272727 Midmean - True Basic - Statistics Graphics Toolkit 1413.6976744186 Midmean - MS Excel (old versions) 1413.6976744186 Number of observations 85

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Apr/27/t13039075344isfm6u5csuhoy6/11cdj1303907687.png (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/27/t13039075344isfm6u5csuhoy6/11cdj1303907687.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/27/t13039075344isfm6u5csuhoy6/28rnf1303907687.png (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/27/t13039075344isfm6u5csuhoy6/28rnf1303907687.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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