centrummaten eigen reeks

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sun, 03 Jan 2010 04:17:49 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/03/t126251756469wcr06wcbqbtvi.htm/, Retrieved Sun, 03 Jan 2010 12:19:26 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Jan/03/t126251756469wcr06wcbqbtvi.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

203,7 173,8 167,1 151,8 144,5 128,4 121,6 124,9 122,7 148,1 176,9 234,6 254,6 279,7 275,8 283 295,4 297,6 276,8 250,1 239,1 258,9 276,1 264,1 265,5 287,7 285,1 304,5 301,5 274,2 258,6 253,9 269,6 266,9 269,6 257,9 258,2 254,7 237,2 267,2 228,8 196,3 194,8 186,6 176,7 162,1 154,9 150,1 150,5 143,6 143,8 141,5 147,9 151,4 144,6 140,4 139,5 138,1 136,7 130 128,5 130,4 125,7 121,7 129,9 129,6 128,2 119,7 112,2 105,6 101,2 94,9 95,1 93,1 91,4 89,8 85,9 89,7 91,6 88,6 86,9 86,4 82,2 81,5 81,2

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 178.716470588235 7.79460217721245 22.9282350176528 Geometric Mean 164.424800162315 Harmonic Mean 151.091330186765 Quadratic Mean 192.465752797738 Winsorized Mean ( 1 / 28 ) 178.684705882353 7.78737369670336 22.9454387116411 Winsorized Mean ( 2 / 28 ) 178.609411764706 7.76795158163284 22.9931159956022 Winsorized Mean ( 3 / 28 ) 178.662352941176 7.73492606083499 23.0981332641064 Winsorized Mean ( 4 / 28 ) 178.323529411765 7.66824322732672 23.2548087124163 Winsorized Mean ( 5 / 28 ) 178.2 7.63832570710644 23.3297199979583 Winsorized Mean ( 6 / 28 ) 178.171764705882 7.59684100862097 23.4534018157931 Winsorized Mean ( 7 / 28 ) 177.990588235294 7.54002459772222 23.606101800923 Winsorized Mean ( 8 / 28 ) 177.727058823529 7.49532018108003 23.7117367276924 Winsorized Mean ( 9 / 28 ) 177.822352941176 7.4601650571009 23.8362491419567 Winsorized Mean ( 10 / 28 ) 177.810588235294 7.45139188086812 23.8627347854074 Winsorized Mean ( 11 / 28 ) 177.797647058824 7.3925037692861 24.0510728986742 Winsorized Mean ( 12 / 28 ) 177.402352941176 7.25845801938989 24.440776879507 Winsorized Mean ( 13 / 28 ) 177.432941176471 7.25432207463687 24.4589279812686 Winsorized Mean ( 14 / 28 ) 178.042352941176 7.06173028853303 25.2122844779678 Winsorized Mean ( 15 / 28 ) 178.765882352941 6.95483036560929 25.7038450911635 Winsorized Mean ( 16 / 28 ) 179.744705882353 6.76335953719469 26.5762458573816 Winsorized Mean ( 17 / 28 ) 180.964705882353 6.54827424094963 27.6354806203274 Winsorized Mean ( 18 / 28 ) 180.265882352941 6.33914532516937 28.4369379634193 Winsorized Mean ( 19 / 28 ) 180.221176470588 6.32678692201911 28.4854190115625 Winsorized Mean ( 20 / 28 ) 180.362352941176 6.28711032483225 28.6876392527737 Winsorized Mean ( 21 / 28 ) 180.831764705882 6.21739928060495 29.0847919756390 Winsorized Mean ( 22 / 28 ) 180.210588235294 6.07366981749116 29.670791078619 Winsorized Mean ( 23 / 28 ) 180.86 5.99822037099735 30.1522766443353 Winsorized Mean ( 24 / 28 ) 180.718823529412 5.96341988578895 30.3045613071908 Winsorized Mean ( 25 / 28 ) 179.630588235294 5.79783042188392 30.9823805051762 Winsorized Mean ( 26 / 28 ) 176.602352941176 5.28163086403728 33.437087423823 Winsorized Mean ( 27 / 28 ) 176.094117647059 5.1866966092998 33.9511120298265 Winsorized Mean ( 28 / 28 ) 175.270588235294 5.06339663665433 34.6152199427745 Trimmed Mean ( 1 / 28 ) 178.375903614458 7.7468770480456 23.0255240283514 Trimmed Mean ( 2 / 28 ) 178.051851851852 7.69703127617345 23.1325358392424 Trimmed Mean ( 3 / 28 ) 177.751898734177 7.64788801201578 23.2419588852383 Trimmed Mean ( 4 / 28 ) 177.416883116883 7.60133262649094 23.3402341187621 Trimmed Mean ( 5 / 28 ) 177.16 7.56567259414533 23.4162921796397 Trimmed Mean ( 6 / 28 ) 176.917808219178 7.52818760453525 23.5007172393786 Trimmed Mean ( 7 / 28 ) 176.667605633803 7.49001448600703 23.5870846396701 Trimmed Mean ( 8 / 28 ) 176.434782608696 7.45311855807888 23.6726118380939 Trimmed Mean ( 9 / 28 ) 176.229850746269 7.41382301272884 23.7704421111346 Trimmed Mean ( 10 / 28 ) 175.998461538462 7.36873250383115 23.8844959356248 Trimmed Mean ( 11 / 28 ) 175.753968253968 7.31126018383029 24.0388064211788 Trimmed Mean ( 12 / 28 ) 175.495081967213 7.24787491984466 24.2133154763348 Trimmed Mean ( 13 / 28 ) 175.266101694915 7.19015318379015 24.3758508636567 Trimmed Mean ( 14 / 28 ) 175.017543859649 7.11485135417627 24.5989037784911 Trimmed Mean ( 15 / 28 ) 174.683636363636 7.05031974518431 24.7766970402943 Trimmed Mean ( 16 / 28 ) 174.247169811321 6.98181631801511 24.9572835884715 Trimmed Mean ( 17 / 28 ) 173.674509803922 6.9211145215698 25.0934310164441 Trimmed Mean ( 18 / 28 ) 172.930612244898 6.87078640455521 25.1689693235476 Trimmed Mean ( 19 / 28 ) 172.193617021277 6.83428222605546 25.1955671898937 Trimmed Mean ( 20 / 28 ) 171.395555555556 6.77700729185785 25.2907438599744 Trimmed Mean ( 21 / 28 ) 170.509302325581 6.69692977203569 25.4608168414093 Trimmed Mean ( 22 / 28 ) 169.490243902439 6.59069632954431 25.7165913019934 Trimmed Mean ( 23 / 28 ) 168.428205128205 6.46880081029855 26.0370059408943 Trimmed Mean ( 24 / 28 ) 167.186486486486 6.3027904613776 26.5257884600442 Trimmed Mean ( 25 / 28 ) 165.817142857143 6.0685627245186 27.3239563277805 Trimmed Mean ( 26 / 28 ) 164.393939393939 5.77855711549228 28.4489598542169 Trimmed Mean ( 27 / 28 ) 163.106451612903 5.52790173006789 29.506033134728 Trimmed Mean ( 28 / 28 ) 161.696551724138 5.17769106813166 31.2294707421556 Median 150.5 Midrange 192.85 Midmean - Weighted Average at Xnp 168.428571428571 Midmean - Weighted Average at X(n+1)p 170.509302325581 Midmean - Empirical Distribution Function 170.509302325581 Midmean - Empirical Distribution Function - Averaging 170.509302325581 Midmean - Empirical Distribution Function - Interpolation 170.509302325581 Midmean - Closest Observation 169.422727272727 Midmean - True Basic - Statistics Graphics Toolkit 170.509302325581 Midmean - MS Excel (old versions) 170.509302325581 Number of observations 85

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/03/t126251756469wcr06wcbqbtvi/1mtd61262517467.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/03/t126251756469wcr06wcbqbtvi/1mtd61262517467.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/03/t126251756469wcr06wcbqbtvi/2p21i1262517467.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/03/t126251756469wcr06wcbqbtvi/2p21i1262517467.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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