taak 3 task 2 verbetering (1)

*The author of this computation has been verified*

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

Title produced by software: Central Tendency

Date of computation: Tue, 28 Oct 2008 13:19:05 -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/Oct/28/t1225221589cty1nnflw42dang.htm/, Retrieved Tue, 28 Oct 2008 19:19:49 +0000

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/2008/Oct/28/t1225221589cty1nnflw42dang.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Dataseries X:

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0.904891304 1.03526971 0.97939156 0.944444444 1.233333333 1.054910243 0.99009901 0.914990859 0.978494624 1.104740904 1.042619543 1.046826223 0.943396226 0.970902037 0.982352941 0.955109838 1.163953488 1.086862106 0.936389149 0.892539964 0.98820059 1.092391304 0.988706366 0.992783505 0.918406072 0.94255112 0.987767584 0.926315789 1.107551487 1.076751947 0.881602914 0.868397493 0.983772819 1.001031992 1.01787592 0.998969072 0.862466726 0.945578231 0.998973306 0.872531418 1.113272311 1.005165289 0.852760736 0.882139619 0.936477382 0.957677165 1.036997886 1.009384776 0.924546323 0.941634241 0.986748216 0.849868306 1.196538937 1.011494253 0.855123675 0.914069877 0.889705882 0.946236559 0.978787879 0.964250248 0.840692641

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 3 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 1.7653899566875e-16 0.0108613552660899 1.62538643975600e-14 Geometric Mean NaN Harmonic Mean -0.00162882846536965 Quadratic Mean 0.0841316961256171 Winsorized Mean ( 1 / 20 ) -0.000452766081967039 0.0106088911329880 -0.0426779836168905 Winsorized Mean ( 2 / 20 ) -0.00142630768852441 0.0102440990508508 -0.139232125875038 Winsorized Mean ( 3 / 20 ) -0.00380261447540966 0.00953803572767026 -0.398678992612505 Winsorized Mean ( 4 / 20 ) -0.00369623893442605 0.0093496255896929 -0.395335502899796 Winsorized Mean ( 5 / 20 ) -0.0034404861475408 0.00919950165594475 -0.373986143620893 Winsorized Mean ( 6 / 20 ) -0.00424858532786868 0.0088436374652073 -0.480411521230205 Winsorized Mean ( 7 / 20 ) -0.00384209211475391 0.0085082580954819 -0.451572116364706 Winsorized Mean ( 8 / 20 ) -0.00509762706557359 0.00821120888717081 -0.620813224413049 Winsorized Mean ( 9 / 20 ) -0.00720383967213099 0.00736127621302734 -0.978612874134822 Winsorized Mean ( 10 / 20 ) -0.00806448524590145 0.00703053051174702 -1.14706638886309 Winsorized Mean ( 11 / 20 ) -0.0065957760655736 0.00649413968457744 -1.01565047657314 Winsorized Mean ( 12 / 20 ) -0.00589605488524574 0.00599149761323075 -0.984070305264872 Winsorized Mean ( 13 / 20 ) -0.00606807983606542 0.00589402037935933 -1.02953153289318 Winsorized Mean ( 14 / 20 ) -0.00927627783606538 0.00509323821834484 -1.82129274901261 Winsorized Mean ( 15 / 20 ) -0.00933564242622935 0.00460005258703251 -2.02946428320111 Winsorized Mean ( 16 / 20 ) -0.00942482563934406 0.00444110821049579 -2.12217878795885 Winsorized Mean ( 17 / 20 ) -0.00779341840983587 0.00382552159135442 -2.03721720652389 Winsorized Mean ( 18 / 20 ) -0.00898704385245887 0.00364372706833431 -2.46644265169048 Winsorized Mean ( 19 / 20 ) -0.00802203914754079 0.00331190064623736 -2.42218593020132 Winsorized Mean ( 20 / 20 ) -0.00772281127868837 0.00326776643390957 -2.36333025474185 Trimmed Mean ( 1 / 20 ) -0.0019728129174769 0.0100797475614187 -0.195720468737536 Trimmed Mean ( 2 / 20 ) -0.00359952970635588 0.0094182244942701 -0.382187715799913 Trimmed Mean ( 3 / 20 ) -0.00480468009806241 0.00884666885461018 -0.543106131474402 Trimmed Mean ( 4 / 20 ) -0.00518912036838831 0.0084954306342108 -0.610813105517207 Trimmed Mean ( 5 / 20 ) -0.00563552118932801 0.00813138160085245 -0.693058260694249 Trimmed Mean ( 6 / 20 ) -0.00618204011809952 0.00772348649091372 -0.80042091422991 Trimmed Mean ( 7 / 20 ) -0.0066002697003835 0.00732272691754123 -0.901340412486621 Trimmed Mean ( 8 / 20 ) -0.0071343929788705 0.00691083605029858 -1.03234875302276 Trimmed Mean ( 9 / 20 ) -0.0074955636786121 0.00646572583903224 -1.15927644710250 Trimmed Mean ( 10 / 20 ) -0.00754378905637727 0.0061412560410803 -1.22837885375811 Trimmed Mean ( 11 / 20 ) -0.00746234683186195 0.00580527555918704 -1.28544231118410 Trimmed Mean ( 12 / 20 ) -0.00759222598848011 0.00551060333614026 -1.37774859218916 Trimmed Mean ( 13 / 20 ) -0.00783857464871177 0.00525433529518376 -1.49182992868703 Trimmed Mean ( 14 / 20 ) -0.00809032332836544 0.00492206933194985 -1.64368333372511 Trimmed Mean ( 15 / 20 ) -0.00792363386990992 0.00470896284300525 -1.68267071414245 Trimmed Mean ( 16 / 20 ) -0.00772562807235708 0.00455190824857457 -1.69722842607304 Trimmed Mean ( 17 / 20 ) -0.0074856950825742 0.00436114795739127 -1.71645061247863 Trimmed Mean ( 18 / 20 ) -0.00744152773442605 0.00427902445678365 -1.73907109192349 Trimmed Mean ( 19 / 20 ) -0.007213806760513 0.00419096348192655 -1.72127645388045 Trimmed Mean ( 20 / 20 ) -0.00709024241061653 0.00415185014910060 -1.70773080819221 Median -2.71269344260805e-05 Midrange 0.058197981065574 Midmean - Weighted Average at Xnp -0.00927706323442605 Midmean - Weighted Average at X(n+1)p -0.00792363386990992 Midmean - Empirical Distribution Function -0.00792363386990992 Midmean - Empirical Distribution Function - Averaging -0.00792363386990992 Midmean - Empirical Distribution Function - Interpolation -0.00792363386990992 Midmean - Closest Observation -0.00956379949692605 Midmean - True Basic - Statistics Graphics Toolkit -0.00792363386990992 Midmean - MS Excel (old versions) -0.00792363386990992 Number of observations 61

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/28/t1225221589cty1nnflw42dang/17g2o1225221539.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/28/t1225221589cty1nnflw42dang/17g2o1225221539.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/28/t1225221589cty1nnflw42dang/2rlqv1225221539.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/28/t1225221589cty1nnflw42dang/2rlqv1225221539.ps (open in new window)

Parameters (Session):

Parameters (R input):

R code (references can be found in the software module):

x <- x-0.978815005934426 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')

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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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