centrummaten

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

Title produced by software: Central Tendency

Date of computation: Mon, 21 Apr 2008 06:57:06 -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/21/t1208782744mpv6am4t8ziv2em.htm/, Retrieved Mon, 21 Apr 2008 14:59:04 +0200

User-defined keywords:

mediaan rekenkundg gemiddelde weekend aan zee

Dataseries X:

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104,7 104,7 104,7 104,7 106 107 107 107 107 107 107 107 107 107 107 107 107,6 109,9 109,9 109,9 109,9 109,9 109,9 109,9 109,9 109,9 109,9 109,9 110,6 114,3 114,3 114,3 114,3 114,3 114,3 114,3 114,3 114,3 114,3 114,3 114,3 119,01 119,01 119,01 119,01 119,01 119,01 119,01 119,01 119,01 119,01 119,01 121,27 123,54 123,54 123,54 123,54 123,54 123,54 123,54 123,54 123,54 123,54 123,54 123,54 125,24 125,24 125,24 125,24 125,24 125,24 125,24 125,24 125,24 125,24 125,24 125,24 128,35 128,35 128,35 128,35 128,35 128,35 128,35

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 116.841547619048 0.837296048483972 139.546278560139 Geometric Mean 116.591316412589 Harmonic Mean 116.340357740236 Quadratic Mean 117.090288315714 Winsorized Mean ( 1 / 28 ) 116.841547619048 0.837296048483972 139.546278560139 Winsorized Mean ( 2 / 28 ) 116.841547619048 0.837296048483972 139.546278560139 Winsorized Mean ( 3 / 28 ) 116.841547619048 0.837296048483972 139.546278560139 Winsorized Mean ( 4 / 28 ) 116.903452380952 0.826968426466205 141.363864253564 Winsorized Mean ( 5 / 28 ) 116.962976190476 0.8178706063533 143.009145067565 Winsorized Mean ( 6 / 28 ) 116.962976190476 0.8178706063533 143.009145067565 Winsorized Mean ( 7 / 28 ) 116.703809523810 0.778910965490822 149.829460226266 Winsorized Mean ( 8 / 28 ) 116.703809523810 0.778910965490822 149.829460226266 Winsorized Mean ( 9 / 28 ) 116.703809523810 0.778910965490822 149.829460226266 Winsorized Mean ( 10 / 28 ) 116.703809523810 0.778910965490822 149.829460226266 Winsorized Mean ( 11 / 28 ) 116.703809523810 0.778910965490822 149.829460226266 Winsorized Mean ( 12 / 28 ) 116.703809523810 0.778910965490822 149.829460226266 Winsorized Mean ( 13 / 28 ) 116.703809523810 0.778910965490822 149.829460226266 Winsorized Mean ( 14 / 28 ) 116.703809523810 0.778910965490822 149.829460226266 Winsorized Mean ( 15 / 28 ) 116.703809523810 0.778910965490822 149.829460226266 Winsorized Mean ( 16 / 28 ) 116.818095238095 0.76200264718315 153.304054349325 Winsorized Mean ( 17 / 28 ) 117.283571428571 0.69824311619051 167.969534835445 Winsorized Mean ( 18 / 28 ) 117.283571428571 0.69824311619051 167.969534835445 Winsorized Mean ( 19 / 28 ) 116.899047619048 0.648009610218389 180.397089450033 Winsorized Mean ( 20 / 28 ) 116.899047619048 0.648009610218389 180.397089450033 Winsorized Mean ( 21 / 28 ) 116.899047619048 0.648009610218389 180.397089450033 Winsorized Mean ( 22 / 28 ) 116.899047619048 0.648009610218389 180.397089450033 Winsorized Mean ( 23 / 28 ) 116.899047619048 0.648009610218389 180.397089450033 Winsorized Mean ( 24 / 28 ) 116.899047619048 0.648009610218389 180.397089450033 Winsorized Mean ( 25 / 28 ) 116.899047619048 0.648009610218389 180.397089450033 Winsorized Mean ( 26 / 28 ) 116.899047619048 0.648009610218389 180.397089450033 Winsorized Mean ( 27 / 28 ) 116.899047619048 0.648009610218389 180.397089450033 Winsorized Mean ( 28 / 28 ) 117.132380952381 0.617961401944181 189.546435398503 Trimmed Mean ( 1 / 28 ) 116.849268292683 0.832922785600015 140.288235971967 Trimmed Mean ( 2 / 28 ) 116.857375 0.827540158185577 141.210518721189 Trimmed Mean ( 3 / 28 ) 116.865897435897 0.820990005992749 142.347527476394 Trimmed Mean ( 4 / 28 ) 116.874868421053 0.813082924352998 143.742864252197 Trimmed Mean ( 5 / 28 ) 116.866756756757 0.807034238235814 144.810159494879 Trimmed Mean ( 6 / 28 ) 116.844305555556 0.802125936650117 145.668280025363 Trimmed Mean ( 7 / 28 ) 116.820571428571 0.795921380620571 146.774008429687 Trimmed Mean ( 8 / 28 ) 116.841176470588 0.796778179050844 146.642038578133 Trimmed Mean ( 9 / 28 ) 116.863030303030 0.796990404509977 146.630410657055 Trimmed Mean ( 10 / 28 ) 116.88625 0.796428893960359 146.762945049326 Trimmed Mean ( 11 / 28 ) 116.910967741935 0.794935805877941 147.069696543379 Trimmed Mean ( 12 / 28 ) 116.937333333333 0.792316701312618 147.589130886179 Trimmed Mean ( 13 / 28 ) 116.965517241379 0.78832985150505 148.371290289304 Trimmed Mean ( 14 / 28 ) 116.995714285714 0.782671534542622 149.482521239366 Trimmed Mean ( 15 / 28 ) 117.028148148148 0.774955379526298 151.012756656626 Trimmed Mean ( 16 / 28 ) 117.063076923077 0.764682602481956 153.087145625023 Trimmed Mean ( 17 / 28 ) 117.0888 0.754384227333114 155.211092381836 Trimmed Mean ( 18 / 28 ) 117.06875 0.752108126150746 155.654148558602 Trimmed Mean ( 19 / 28 ) 117.046956521739 0.74793169684564 156.494178566543 Trimmed Mean ( 20 / 28 ) 117.061818181818 0.750163285447742 156.048450320984 Trimmed Mean ( 21 / 28 ) 117.078095238095 0.751090514819118 155.877478051085 Trimmed Mean ( 22 / 28 ) 117.096 0.750277623830348 156.070228247241 Trimmed Mean ( 23 / 28 ) 117.115789473684 0.747126941935189 156.754873770626 Trimmed Mean ( 24 / 28 ) 117.137777777778 0.740801701195285 158.122987013631 Trimmed Mean ( 25 / 28 ) 117.162352941176 0.73009987093354 160.474419467253 Trimmed Mean ( 26 / 28 ) 117.19 0.713236602827494 164.307327379753 Trimmed Mean ( 27 / 28 ) 117.221333333333 0.687441321773158 170.518311338890 Trimmed Mean ( 28 / 28 ) 117.257142857143 0.648132616162026 180.915355797848 Median 119.01 Midrange 116.525 Midmean - Weighted Average at Xnp 116.749166666667 Midmean - Weighted Average at X(n+1)p 116.749166666667 Midmean - Empirical Distribution Function 116.749166666667 Midmean - Empirical Distribution Function - Averaging 116.749166666667 Midmean - Empirical Distribution Function - Interpolation 116.749166666667 Midmean - Closest Observation 116.749166666667 Midmean - True Basic - Statistics Graphics Toolkit 116.749166666667 Midmean - MS Excel (old versions) 116.749166666667 Number of observations 84

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208782744mpv6am4t8ziv2em/10ovr1208782621.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208782744mpv6am4t8ziv2em/10ovr1208782621.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208782744mpv6am4t8ziv2em/2gkrf1208782621.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208782744mpv6am4t8ziv2em/2gkrf1208782621.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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