Tijdreeks 2 stap 9

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Wed, 11 Aug 2010 17:04:45 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Aug/11/t1281546287rz9w4h1nmrnqphn.htm/, Retrieved Wed, 11 Aug 2010 19:04:47 +0200

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/Aug/11/t1281546287rz9w4h1nmrnqphn.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:

Marianne Nykjaer

Dataseries X:

» Textbox « » Textfile « » CSV «

190 189 188 186 184 183 184 186 187 187 188 190 190 190 197 187 185 182 182 191 183 192 178 181 179 175 183 179 178 175 170 179 169 178 161 168 167 165 181 181 184 181 177 183 162 166 151 162 159 152 164 158 160 161 151 149 131 138 130 147 151 140 149 143 145 139 136 133 118 130 121 142 148 131 137 128 130 119 107 113 93 106 98 118

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 160.821428571429 2.84643090195424 56.4993263883607 Geometric Mean 158.502176262835 Harmonic Mean 155.937021127630 Quadratic Mean 162.898778094748 Winsorized Mean ( 1 / 28 ) 160.821428571429 2.82137773471416 57.001027048837 Winsorized Mean ( 2 / 28 ) 160.988095238095 2.76988425082041 58.1208746143137 Winsorized Mean ( 3 / 28 ) 160.988095238095 2.75680423793864 58.3966365919663 Winsorized Mean ( 4 / 28 ) 161.273809523810 2.69220156751192 59.9040619654848 Winsorized Mean ( 5 / 28 ) 161.571428571429 2.63032568865985 61.426396460337 Winsorized Mean ( 6 / 28 ) 161.571428571429 2.63032568865985 61.426396460337 Winsorized Mean ( 7 / 28 ) 161.571428571429 2.60308335389004 62.0692488890058 Winsorized Mean ( 8 / 28 ) 161.666666666667 2.55408132621531 63.2973840759516 Winsorized Mean ( 9 / 28 ) 162.416666666667 2.41761609142148 67.1805036552229 Winsorized Mean ( 10 / 28 ) 162.535714285714 2.36241890270954 68.800547650248 Winsorized Mean ( 11 / 28 ) 162.535714285714 2.36241890270954 68.800547650248 Winsorized Mean ( 12 / 28 ) 162.535714285714 2.36241890270954 68.800547650248 Winsorized Mean ( 13 / 28 ) 162.535714285714 2.31779803488438 70.1250548319764 Winsorized Mean ( 14 / 28 ) 162.535714285714 2.31779803488438 70.1250548319764 Winsorized Mean ( 15 / 28 ) 162.714285714286 2.23834851657034 72.6939011104495 Winsorized Mean ( 16 / 28 ) 163.095238095238 2.12602235186394 76.7137927558702 Winsorized Mean ( 17 / 28 ) 163.297619047619 2.09518064060901 77.9396372239069 Winsorized Mean ( 18 / 28 ) 163.511904761905 2.06301293958017 79.258787778219 Winsorized Mean ( 19 / 28 ) 163.511904761905 2.00268709674374 81.646256685713 Winsorized Mean ( 20 / 28 ) 163.75 1.96781875975824 83.2139642881125 Winsorized Mean ( 21 / 28 ) 164.25 1.8961018531507 86.6250933340266 Winsorized Mean ( 22 / 28 ) 164.511904761905 1.85933118713673 88.479075648295 Winsorized Mean ( 23 / 28 ) 164.785714285714 1.75124506389883 94.0963190604796 Winsorized Mean ( 24 / 28 ) 165.357142857143 1.67459184511253 98.7447438847588 Winsorized Mean ( 25 / 28 ) 165.357142857143 1.60013292415639 103.339629077579 Winsorized Mean ( 26 / 28 ) 165.666666666667 1.55998195457638 106.197809648160 Winsorized Mean ( 27 / 28 ) 165.666666666667 1.55998195457638 106.197809648160 Winsorized Mean ( 28 / 28 ) 166.333333333333 1.47530186272306 112.74528795505 Trimmed Mean ( 1 / 28 ) 161.207317073171 2.75921918599701 58.4249768526166 Trimmed Mean ( 2 / 28 ) 161.6125 2.68643414248307 60.158742566688 Trimmed Mean ( 3 / 28 ) 161.948717948718 2.63325497819441 61.5013431246846 Trimmed Mean ( 4 / 28 ) 162.302631578947 2.57620826612891 63.0005864482488 Trimmed Mean ( 5 / 28 ) 162.594594594595 2.53176187376634 64.2219145012691 Trimmed Mean ( 6 / 28 ) 162.833333333333 2.49733817605290 65.2027566369467 Trimmed Mean ( 7 / 28 ) 163.085714285714 2.45579914147056 66.40840919427 Trimmed Mean ( 8 / 28 ) 163.352941176471 2.41217688505522 67.7201337051743 Trimmed Mean ( 9 / 28 ) 163.621212121212 2.37034565668699 69.0284185598077 Trimmed Mean ( 10 / 28 ) 163.796875 2.34850295184642 69.7452284959749 Trimmed Mean ( 11 / 28 ) 163.967741935484 2.33135205446746 70.331609342862 Trimmed Mean ( 12 / 28 ) 164.15 2.30876798412482 71.0985257629619 Trimmed Mean ( 13 / 28 ) 164.344827586207 2.27954842697768 72.0953438151353 Trimmed Mean ( 14 / 28 ) 164.553571428571 2.25024091680724 73.1270906148347 Trimmed Mean ( 15 / 28 ) 164.777777777778 2.21229438540750 74.4827536808243 Trimmed Mean ( 16 / 28 ) 165 2.17849769038864 75.7402685015305 Trimmed Mean ( 17 / 28 ) 165.2 2.15539191000483 76.6449939953748 Trimmed Mean ( 18 / 28 ) 165.395833333333 2.12960797497299 77.6649201529362 Trimmed Mean ( 19 / 28 ) 165.586956521739 2.10051203487475 78.8317104460738 Trimmed Mean ( 20 / 28 ) 165.795454545455 2.07180293083136 80.02472246669 Trimmed Mean ( 21 / 28 ) 166 2.03882182279058 81.4195719039303 Trimmed Mean ( 22 / 28 ) 166.175 2.00828013548013 82.744930383067 Trimmed Mean ( 23 / 28 ) 166.342105263158 1.97252692481429 84.3294472539678 Trimmed Mean ( 24 / 28 ) 166.5 1.94548724871705 85.5826734972426 Trimmed Mean ( 25 / 28 ) 166.617647058824 1.92275737176164 86.6555757402545 Trimmed Mean ( 26 / 28 ) 166.75 1.90341374140457 87.6057561068944 Trimmed Mean ( 27 / 28 ) 166.866666666667 1.88016466222725 88.7510918692597 Trimmed Mean ( 28 / 28 ) 167 1.83873662631503 90.8232302603776 Median 166.5 Midrange 145 Midmean - Weighted Average at Xnp 166.177777777778 Midmean - Weighted Average at X(n+1)p 166.772727272727 Midmean - Empirical Distribution Function 166.177777777778 Midmean - Empirical Distribution Function - Averaging 166.772727272727 Midmean - Empirical Distribution Function - Interpolation 166.772727272727 Midmean - Closest Observation 166.177777777778 Midmean - True Basic - Statistics Graphics Toolkit 166.772727272727 Midmean - MS Excel (old versions) 166.177777777778 Number of observations 84

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/11/t1281546287rz9w4h1nmrnqphn/1i54n1281546280.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/11/t1281546287rz9w4h1nmrnqphn/1i54n1281546280.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/11/t1281546287rz9w4h1nmrnqphn/2lpol1281546281.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/11/t1281546287rz9w4h1nmrnqphn/2lpol1281546281.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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