centrummaten, aantal geboortes 2000-2006, Olivier Percy MAR201b

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Wed, 22 Apr 2009 12:27:16 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Apr/22/t1240424954ld8e2uzjuvxric9.htm/, Retrieved Wed, 22 Apr 2009 20:29:16 +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/2009/Apr/22/t1240424954ld8e2uzjuvxric9.htm/}, year = {2009}, } @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 = {2009}, 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:

Dataseries X:

» Textbox « » Textfile « » CSV «

9.733 9.259 9.864 9.215 10.103 9.380 9.896 10.117 9.451 9.700 9.081 9.084 9.743 8.587 9.731 9.563 9.998 9.437 10.038 9.918 9.252 9.737 9.035 9.133 9.487 8.700 9.627 8.947 9.283 8.829 9.947 9.628 9.318 9.605 8.640 9.214 9.567 8.547 9.185 9.470 9.123 9.278 10.170 9.434 9.655 9.429 8.739 9.552 9.687 9.019 9.672 9.206 9.069 9.788 10.312 10.105 9.863 9.656 9.295 9.946 9.701 9.049 10.190 9.706 9.765 9.893 9.994 10.433 10.073 10.112 9.266 9.820 10.097 9.115 10.411 9.678 10.408 10.153 10.368 10.581 10.597 10.680 9.738 9.556

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 9.61227380952381 0.0532206093723043 180.611870530855 Geometric Mean 9.59999935251038 Harmonic Mean 9.58767819856305 Quadratic Mean 9.62449477894814 Winsorized Mean ( 1 / 28 ) 9.6117619047619 0.052877236932476 181.775040875076 Winsorized Mean ( 2 / 28 ) 9.61264285714286 0.0525039780556005 183.084086446998 Winsorized Mean ( 3 / 28 ) 9.6095 0.0509309728834287 188.676937744628 Winsorized Mean ( 4 / 28 ) 9.61030952380952 0.0503350534566155 190.926776944675 Winsorized Mean ( 5 / 28 ) 9.6154880952381 0.0492258995205285 195.333923582812 Winsorized Mean ( 6 / 28 ) 9.62105952380952 0.0471368089525607 204.109266995403 Winsorized Mean ( 7 / 28 ) 9.62239285714286 0.0452632638828815 212.587251375437 Winsorized Mean ( 8 / 28 ) 9.61229761904762 0.0430078805696858 223.500844303936 Winsorized Mean ( 9 / 28 ) 9.61165476190476 0.0424234165183565 226.564844388377 Winsorized Mean ( 10 / 28 ) 9.6120119047619 0.0417279715180727 230.349368902317 Winsorized Mean ( 11 / 28 ) 9.60886904761905 0.0407597869861745 235.743848486704 Winsorized Mean ( 12 / 28 ) 9.60858333333333 0.040585966249866 236.746447631145 Winsorized Mean ( 13 / 28 ) 9.61229761904762 0.0396881806924768 242.195471078111 Winsorized Mean ( 14 / 28 ) 9.61329761904762 0.0394378156378363 243.758369056949 Winsorized Mean ( 15 / 28 ) 9.6140119047619 0.0390113790056717 246.441221761583 Winsorized Mean ( 16 / 28 ) 9.61934523809524 0.0368926296151665 260.738942667853 Winsorized Mean ( 17 / 28 ) 9.6165119047619 0.0352578994865567 272.747725894123 Winsorized Mean ( 18 / 28 ) 9.60965476190476 0.0338058752920141 284.259900946118 Winsorized Mean ( 19 / 28 ) 9.60897619047619 0.0336489972101737 285.565008979552 Winsorized Mean ( 20 / 28 ) 9.60659523809524 0.0309030191374469 310.862676406086 Winsorized Mean ( 21 / 28 ) 9.60809523809524 0.0306286898747649 313.695926184926 Winsorized Mean ( 22 / 28 ) 9.60259523809524 0.0294151107982344 326.4510986874 Winsorized Mean ( 23 / 28 ) 9.59985714285714 0.0281921788960283 340.514905863114 Winsorized Mean ( 24 / 28 ) 9.60042857142857 0.0278875615435480 344.254859157799 Winsorized Mean ( 25 / 28 ) 9.59536904761905 0.0263206145513739 364.557181174107 Winsorized Mean ( 26 / 28 ) 9.60217857142857 0.0253113155862193 379.363077305095 Winsorized Mean ( 27 / 28 ) 9.60828571428571 0.020950660363297 458.614933738235 Winsorized Mean ( 28 / 28 ) 9.61395238095238 0.0175509086969237 547.775191984076 Trimmed Mean ( 1 / 28 ) 9.61224390243902 0.0512900090553668 187.409674505277 Trimmed Mean ( 2 / 28 ) 9.61275 0.0494462804657614 194.407949585940 Trimmed Mean ( 3 / 28 ) 9.6128076923077 0.047530133308514 202.246596488838 Trimmed Mean ( 4 / 28 ) 9.61402631578947 0.0460018877327541 208.991995538134 Trimmed Mean ( 5 / 28 ) 9.61508108108108 0.0444249728674649 216.434146392530 Trimmed Mean ( 6 / 28 ) 9.61498611111111 0.0429147009124331 224.048773652888 Trimmed Mean ( 7 / 28 ) 9.61377142857143 0.0417060757966452 230.512491164291 Trimmed Mean ( 8 / 28 ) 9.61225 0.0407347270430223 235.971877014125 Trimmed Mean ( 9 / 28 ) 9.61224242424242 0.0400839449028808 239.802805026598 Trimmed Mean ( 10 / 28 ) 9.612328125 0.0394169564489468 243.862768487719 Trimmed Mean ( 11 / 28 ) 9.61237096774193 0.0387433911995987 248.103500238810 Trimmed Mean ( 12 / 28 ) 9.61281666666667 0.0381046543686915 252.274081104512 Trimmed Mean ( 13 / 28 ) 9.6133275862069 0.0373466162411653 257.408262213876 Trimmed Mean ( 14 / 28 ) 9.61344642857143 0.0365786638509219 262.815680412808 Trimmed Mean ( 15 / 28 ) 9.61346296296296 0.0356669283573832 269.534367149195 Trimmed Mean ( 16 / 28 ) 9.61340384615385 0.0346071603896917 277.786554513654 Trimmed Mean ( 17 / 28 ) 9.61278 0.0336937260556057 285.298811539447 Trimmed Mean ( 18 / 28 ) 9.61239583333333 0.0328541498018908 292.577829324322 Trimmed Mean ( 19 / 28 ) 9.61267391304348 0.0320604961725301 299.829231004845 Trimmed Mean ( 20 / 28 ) 9.61304545454546 0.031050510485695 309.593797466685 Trimmed Mean ( 21 / 28 ) 9.61369047619048 0.0303123976218967 317.153746665222 Trimmed Mean ( 22 / 28 ) 9.61425 0.0293737792981498 327.307218537098 Trimmed Mean ( 23 / 28 ) 9.61542105263158 0.0283797062403021 338.813269285243 Trimmed Mean ( 24 / 28 ) 9.617 0.0273097459201330 352.145348701697 Trimmed Mean ( 25 / 28 ) 9.61870588235294 0.0258871997568474 371.562238198773 Trimmed Mean ( 26 / 28 ) 9.62115625 0.0243205703031190 395.597476954155 Trimmed Mean ( 27 / 28 ) 9.6232 0.0223925480215306 429.750111097104 Trimmed Mean ( 28 / 28 ) 9.62485714285714 0.0211534901047794 455.000905060225 Median 9.6555 Midrange 9.6135 Midmean - Weighted Average at Xnp 9.60527906976744 Midmean - Weighted Average at X(n+1)p 9.61369047619048 Midmean - Empirical Distribution Function 9.60527906976744 Midmean - Empirical Distribution Function - Averaging 9.61369047619048 Midmean - Empirical Distribution Function - Interpolation 9.61369047619048 Midmean - Closest Observation 9.60527906976744 Midmean - True Basic - Statistics Graphics Toolkit 9.61369047619048 Midmean - MS Excel (old versions) 9.61304545454546 Number of observations 84

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/22/t1240424954ld8e2uzjuvxric9/1ek1z1240424834.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/22/t1240424954ld8e2uzjuvxric9/1ek1z1240424834.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/22/t1240424954ld8e2uzjuvxric9/28vpe1240424834.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/22/t1240424954ld8e2uzjuvxric9/28vpe1240424834.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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