Plantaardige stof - Joyce Pauwels

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

Title produced by software: Central Tendency

Date of computation: Wed, 16 Apr 2008 08:44:29 -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/Apr/16/t1208357172hvakoiy9ghg1eld.htm/, Retrieved Wed, 16 Apr 2008 16:46:14 +0200

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Dataseries X:

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79,2 81,5 81,5 82 85,8 88,2 88 88,8 89 90,4 90,9 94,6 97,9 101,7 102,3 103,5 103,6 102,3 101,6 104,3 110,8 112,1 111,1 114,4 115 115,3 114,1 114,8 114,5 114,1 112,3 113 112,2 113,7 113,6 115,8 117,9 120,1 118,8 114,7 110,9 112,9 113,3 114,3 116,5 114,3 115,9 120,1 122,6 122,4 123,1 127,9 130,9 135 134,9 130,2 130,8 132,6 138,6 146,2 149,3 149,9 156,8 158,8 156,7 159,9 158,2 157,5 159,1 160,6 161,6 161,3

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 118.451388888889 2.65672294596961 44.5855255884268 Geometric Mean 116.375124707461 Harmonic Mean 114.339822234113 Quadratic Mean 120.548173289077 Winsorized Mean ( 1 / 24 ) 118.479166666667 2.64930818729782 44.7207943699107 Winsorized Mean ( 2 / 24 ) 118.459722222222 2.64491322378534 44.7877537746533 Winsorized Mean ( 3 / 24 ) 118.451388888889 2.6343285641289 44.9645463750485 Winsorized Mean ( 4 / 24 ) 118.618055555556 2.58504057352679 45.8863418896843 Winsorized Mean ( 5 / 24 ) 118.75 2.55382434386994 46.4988910788015 Winsorized Mean ( 6 / 24 ) 118.716666666667 2.54000542185169 46.7387453764256 Winsorized Mean ( 7 / 24 ) 118.706944444444 2.51534362386582 47.1931323092964 Winsorized Mean ( 8 / 24 ) 118.651388888889 2.49479975036616 47.5594840313233 Winsorized Mean ( 9 / 24 ) 118.813888888889 2.46323380077077 48.2349214482648 Winsorized Mean ( 10 / 24 ) 117.938888888889 2.2548110236924 52.3054427398338 Winsorized Mean ( 11 / 24 ) 118.4125 2.1443341086598 55.2211054806228 Winsorized Mean ( 12 / 24 ) 118.445833333333 1.95647968160231 60.5402828596353 Winsorized Mean ( 13 / 24 ) 117.741666666667 1.59470189668167 73.8330260418382 Winsorized Mean ( 14 / 24 ) 117.061111111111 1.46694880389649 79.7990432932457 Winsorized Mean ( 15 / 24 ) 117.165277777778 1.4450798285781 81.0787580455425 Winsorized Mean ( 16 / 24 ) 116.654166666667 1.35860144175657 85.8634203389637 Winsorized Mean ( 17 / 24 ) 116.536111111111 1.25105636983898 93.1501680664556 Winsorized Mean ( 18 / 24 ) 116.536111111111 1.24334898093899 93.7275961115133 Winsorized Mean ( 19 / 24 ) 116.5625 1.19085495106488 97.8813581752907 Winsorized Mean ( 20 / 24 ) 117.729166666667 0.846077290843678 139.147058951637 Winsorized Mean ( 21 / 24 ) 116.358333333333 0.614224799931857 189.439327989105 Winsorized Mean ( 22 / 24 ) 116.266666666667 0.58308847979862 199.397982801549 Winsorized Mean ( 23 / 24 ) 116.522222222222 0.53466025594654 217.936943930751 Winsorized Mean ( 24 / 24 ) 115.788888888889 0.414824828480371 279.127190416877 Trimmed Mean ( 1 / 24 ) 118.395714285714 2.60111095528727 45.5173640497925 Trimmed Mean ( 2 / 24 ) 118.307352941176 2.54356710334190 46.5123773560904 Trimmed Mean ( 3 / 24 ) 118.224242424242 2.47750726347829 47.719029593585 Trimmed Mean ( 4 / 24 ) 118.1390625 2.40301317255601 49.1628859338875 Trimmed Mean ( 5 / 24 ) 118 2.33146118644114 50.6120370719621 Trimmed Mean ( 6 / 24 ) 117.82 2.25439157111896 52.262438127162 Trimmed Mean ( 7 / 24 ) 117.634482758621 2.16398160917895 54.3602044766236 Trimmed Mean ( 8 / 24 ) 117.4375 2.0590733045175 57.0341520830502 Trimmed Mean ( 9 / 24 ) 117.235185185185 1.93339687130359 60.6368960895957 Trimmed Mean ( 10 / 24 ) 116.992307692308 1.78158386612871 65.6675837251074 Trimmed Mean ( 11 / 24 ) 116.856 1.64786853051982 70.9134241207566 Trimmed Mean ( 12 / 24 ) 116.64375 1.50395432161588 77.558040376303 Trimmed Mean ( 13 / 24 ) 116.408695652174 1.36826638819081 85.0775087781667 Trimmed Mean ( 14 / 24 ) 116.240909090909 1.29284221604165 89.9111335076984 Trimmed Mean ( 15 / 24 ) 116.140476190476 1.22843800201024 94.5432134144509 Trimmed Mean ( 16 / 24 ) 116.0175 1.14760557583706 101.095273883954 Trimmed Mean ( 17 / 24 ) 115.942105263158 1.06380802059356 108.987808907914 Trimmed Mean ( 18 / 24 ) 115.872222222222 0.980942299737585 118.123382234836 Trimmed Mean ( 19 / 24 ) 115.794117647059 0.864624027556484 133.924242163735 Trimmed Mean ( 20 / 24 ) 115.703125 0.709149370824743 163.157622018950 Trimmed Mean ( 21 / 24 ) 115.46 0.610532083749377 189.113730585527 Trimmed Mean ( 22 / 24 ) 115.35 0.569031015232295 202.713027782696 Trimmed Mean ( 23 / 24 ) 115.234615384615 0.517120498015168 222.839001406661 Trimmed Mean ( 24 / 24 ) 115.066666666667 0.450388989148151 255.482859126506 Median 114.45 Midrange 120.4 Midmean - Weighted Average at Xnp 115.537837837838 Midmean - Weighted Average at X(n+1)p 115.872222222222 Midmean - Empirical Distribution Function 115.537837837838 Midmean - Empirical Distribution Function - Averaging 115.872222222222 Midmean - Empirical Distribution Function - Interpolation 115.872222222222 Midmean - Closest Observation 115.537837837838 Midmean - True Basic - Statistics Graphics Toolkit 115.872222222222 Midmean - MS Excel (old versions) 115.942105263158 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/16/t1208357172hvakoiy9ghg1eld/1181o1208357067.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/16/t1208357172hvakoiy9ghg1eld/1181o1208357067.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/16/t1208357172hvakoiy9ghg1eld/2fkqz1208357067.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/16/t1208357172hvakoiy9ghg1eld/2fkqz1208357067.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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