Duncan Huysmans Opgave 5 opdracht 2 correct

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Fri, 05 Jun 2009 12:02:27 -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/Jun/05/t1244225236k6ws5l8jin0bayh.htm/, Retrieved Fri, 05 Jun 2009 20:07:18 +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/Jun/05/t1244225236k6ws5l8jin0bayh.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:

Duncan Huysmans Opgave 5 opdracht 2 correct

Dataseries X:

» Textbox « » Textfile « » CSV «

1664.81 2397.53 2840.71 3547.29 3752.96 3714.74 4349.61 3566.34 5021.82 6423.48 7600.60 19756.21 2499.81 5198.24 7225.14 4806.03 5900.88 4951.34 6179.12 4752.15 5496.43 5835.10 12600.08 28541.72 4717.02 5702.63 9957.58 5304.78 6492.43 6630.80 7349.62 8176.62 8573.17 9690.50 15151.84 34061.01 5921.10 5814.58 12421.25 6369.77 7609.12 7224.75 8121.22 7979.25 8093.06 8476.70 17914.66 30114.41 4826.64 6470.23 9638.77 8821.17 8722.37 10209.48 11276.55 12552.22 11637.39 13606.89 21822.11 45060.69 7615.03 9849.69 14558.40 11587.33 9332.56 13082.09 16732.78 19888.61 23933.38 25391.35 36024.80 80721.71 10243.24 11266.88 21826.84 17357.33 15997.79 18601.53 26155.15 28586.52 30505.41 30821.33 46634.38 104660.67

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 14315.5871428571 1718.33935550022 8.33105934344952 Geometric Mean 10097.0517117205 Harmonic Mean 7683.59818323638 Quadratic Mean 21213.4230363606 Winsorized Mean ( 1 / 28 ) 14039.3223809524 1552.72980033024 9.04170344252198 Winsorized Mean ( 2 / 28 ) 13230.1545238095 1196.50801992656 11.0573053447829 Winsorized Mean ( 3 / 28 ) 13186.1263095238 1176.57832729262 11.2071810296437 Winsorized Mean ( 4 / 28 ) 12789.4925 1044.36626775497 12.2461754030921 Winsorized Mean ( 5 / 28 ) 12673.7341666667 1013.70923905591 12.5023366448450 Winsorized Mean ( 6 / 28 ) 12452.9284523810 956.288501074286 13.0221459720486 Winsorized Mean ( 7 / 28 ) 12429.7867857143 949.87356393492 13.0857276775058 Winsorized Mean ( 8 / 28 ) 12449.3725 935.274835696301 13.3109242597462 Winsorized Mean ( 9 / 28 ) 12325.0353571429 894.636897074858 13.7765784056541 Winsorized Mean ( 10 / 28 ) 12323.8841666667 893.041593075116 13.7998994248749 Winsorized Mean ( 11 / 28 ) 12018.4128571429 825.814646790899 14.5534023934380 Winsorized Mean ( 12 / 28 ) 11912.2428571429 803.21729180703 14.8306603688068 Winsorized Mean ( 13 / 28 ) 11705.9034523810 756.343686695218 15.4769632619384 Winsorized Mean ( 14 / 28 ) 11366.5601190476 688.645532408226 16.5056761194663 Winsorized Mean ( 15 / 28 ) 11397.2190476190 685.024835441704 16.6376727644774 Winsorized Mean ( 16 / 28 ) 11049.2266666667 617.138462081812 17.9039670115422 Winsorized Mean ( 17 / 28 ) 11061.2177380952 608.205823987403 18.1866356779976 Winsorized Mean ( 18 / 28 ) 10857.9720238095 561.42888229635 19.3398885703891 Winsorized Mean ( 19 / 28 ) 10727.9305952381 533.088497060777 20.124108200397 Winsorized Mean ( 20 / 28 ) 10600.1186904762 511.195200179313 20.7359511332618 Winsorized Mean ( 21 / 28 ) 10460.4261904762 484.728939528037 21.5799498182657 Winsorized Mean ( 22 / 28 ) 10273.2245238095 454.499444189855 22.6033819295897 Winsorized Mean ( 23 / 28 ) 10112.2436904762 411.676794707236 24.5635503882785 Winsorized Mean ( 24 / 28 ) 9997.16083333333 380.6614595874 26.2626031124067 Winsorized Mean ( 25 / 28 ) 9729.95845238095 338.788379598264 28.7198706871787 Winsorized Mean ( 26 / 28 ) 9581.9905952381 314.993855111787 30.4196111757087 Winsorized Mean ( 27 / 28 ) 9434.19452380952 293.696518230264 32.1222552472104 Winsorized Mean ( 28 / 28 ) 9464.36452380952 286.087843097132 33.0820227149471 Trimmed Mean ( 1 / 28 ) 13368.0956097561 1354.74368180895 9.86761982303994 Trimmed Mean ( 2 / 28 ) 12663.3075 1088.90143379063 11.6294341315331 Trimmed Mean ( 3 / 28 ) 12358.0821794872 1018.40103875913 12.1347894485112 Trimmed Mean ( 4 / 28 ) 12053.0132894737 942.37036643622 12.7901021920445 Trimmed Mean ( 5 / 28 ) 11844.0124324324 903.70566310265 13.1060509145964 Trimmed Mean ( 6 / 28 ) 11650.4106944444 867.48257980767 13.4301379251068 Trimmed Mean ( 7 / 28 ) 11489.9071428571 840.808387094548 13.6653098603845 Trimmed Mean ( 8 / 28 ) 11324.0460294118 810.28430702172 13.9753984265528 Trimmed Mean ( 9 / 28 ) 11145.0168181818 776.618458409133 14.3506978201521 Trimmed Mean ( 10 / 28 ) 10972.93078125 745.361645779332 14.7216198249334 Trimmed Mean ( 11 / 28 ) 10789.8983870968 707.031328410599 15.2608490649946 Trimmed Mean ( 12 / 28 ) 10633.542 675.903241865158 15.7323435387833 Trimmed Mean ( 13 / 28 ) 10479.2160344828 642.405871923308 16.3124536877424 Trimmed Mean ( 14 / 28 ) 10337.6751785714 611.48206717639 16.9059335236227 Trimmed Mean ( 15 / 28 ) 10223.3546296296 588.344400449576 17.3764798676040 Trimmed Mean ( 16 / 28 ) 10096.9384615385 559.460289418564 18.0476410077863 Trimmed Mean ( 17 / 28 ) 9996.9482 538.601130548666 18.5609491569694 Trimmed Mean ( 18 / 28 ) 9887.39104166667 513.406004972455 19.2584250006915 Trimmed Mean ( 19 / 28 ) 9788.92630434783 491.844095205815 19.9024983724804 Trimmed Mean ( 20 / 28 ) 9694.5765909091 470.335847859266 20.6120299675943 Trimmed Mean ( 21 / 28 ) 9604.02238095238 447.332109588318 21.4695573492165 Trimmed Mean ( 22 / 28 ) 9518.382 423.475198571479 22.4768346106422 Trimmed Mean ( 23 / 28 ) 9442.53657894737 399.693141950993 23.6244648403428 Trimmed Mean ( 24 / 28 ) 9374.59527777778 379.225158651223 24.7203938449655 Trimmed Mean ( 25 / 28 ) 9310.50764705882 359.691782823887 25.8846826412419 Trimmed Mean ( 26 / 28 ) 9266.4653125 345.341134515576 26.8327876014494 Trimmed Mean ( 27 / 28 ) 9232.48566666667 331.998222239972 27.8088406750363 Trimmed Mean ( 28 / 28 ) 9210.07357142857 319.207003376835 28.8529808995317 Median 8771.77 Midrange 53162.74 Midmean - Weighted Average at Xnp 9516.37302325582 Midmean - Weighted Average at X(n+1)p 9604.02238095238 Midmean - Empirical Distribution Function 9516.37302325582 Midmean - Empirical Distribution Function - Averaging 9604.02238095238 Midmean - Empirical Distribution Function - Interpolation 9604.02238095238 Midmean - Closest Observation 9516.37302325582 Midmean - True Basic - Statistics Graphics Toolkit 9604.02238095238 Midmean - MS Excel (old versions) 9694.5765909091 Number of observations 84

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244225236k6ws5l8jin0bayh/1godj1244224945.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244225236k6ws5l8jin0bayh/1godj1244224945.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244225236k6ws5l8jin0bayh/25qp31244224945.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244225236k6ws5l8jin0bayh/25qp31244224945.ps (open in new window)

Parameters (Session):

par1 = 9 ;

Parameters (R input):

par1 = 9 ;

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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