Opgave 5-2 poging 3

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

Title produced by software: Central Tendency

Date of computation: Sun, 25 May 2008 22:54:23 -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/May/26/t1211777716gniksztmy0sjhb9.htm/, Retrieved Mon, 26 May 2008 06:55:18 +0200

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

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Text written by user:

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 4 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.702708333333333 0.007051625367363 99.6519662808058 Geometric Mean 0.699361299258429 Harmonic Mean 0.696038932601245 Quadratic Mean 0.706061553029668 Winsorized Mean ( 1 / 32 ) 0.702708333333333 0.007051625367363 99.6519662808058 Winsorized Mean ( 2 / 32 ) 0.702708333333333 0.00697658861784827 100.723773727404 Winsorized Mean ( 3 / 32 ) 0.702708333333333 0.00687207540133528 102.255620361324 Winsorized Mean ( 4 / 32 ) 0.702708333333333 0.00687207540133528 102.255620361324 Winsorized Mean ( 5 / 32 ) 0.703229166666667 0.00679346756609888 103.515496294699 Winsorized Mean ( 6 / 32 ) 0.703229166666667 0.00679346756609888 103.515496294699 Winsorized Mean ( 7 / 32 ) 0.703958333333333 0.00669262353605234 105.184212071872 Winsorized Mean ( 8 / 32 ) 0.703958333333333 0.00669262353605234 105.184212071872 Winsorized Mean ( 9 / 32 ) 0.703020833333333 0.006541231896939 107.475295847914 Winsorized Mean ( 10 / 32 ) 0.703020833333333 0.006541231896939 107.475295847914 Winsorized Mean ( 11 / 32 ) 0.704166666666667 0.00639467066122229 110.117737718188 Winsorized Mean ( 12 / 32 ) 0.704166666666667 0.00639467066122229 110.117737718188 Winsorized Mean ( 13 / 32 ) 0.704166666666667 0.00639467066122229 110.117737718188 Winsorized Mean ( 14 / 32 ) 0.70125 0.00596085549611916 117.642509612345 Winsorized Mean ( 15 / 32 ) 0.70125 0.00596085549611916 117.642509612345 Winsorized Mean ( 16 / 32 ) 0.70125 0.00596085549611916 117.642509612345 Winsorized Mean ( 17 / 32 ) 0.70125 0.00596085549611916 117.642509612345 Winsorized Mean ( 18 / 32 ) 0.70125 0.00596085549611916 117.642509612345 Winsorized Mean ( 19 / 32 ) 0.70125 0.00596085549611916 117.642509612345 Winsorized Mean ( 20 / 32 ) 0.70125 0.00596085549611916 117.642509612345 Winsorized Mean ( 21 / 32 ) 0.6990625 0.00566436639006316 123.414068204759 Winsorized Mean ( 22 / 32 ) 0.6990625 0.00566436639006316 123.414068204759 Winsorized Mean ( 23 / 32 ) 0.696666666666667 0.00535712893342663 130.044782443019 Winsorized Mean ( 24 / 32 ) 0.699166666666667 0.00503859374236352 138.762262332883 Winsorized Mean ( 25 / 32 ) 0.699166666666667 0.00503859374236352 138.762262332883 Winsorized Mean ( 26 / 32 ) 0.701875 0.00471399674913732 148.891702169385 Winsorized Mean ( 27 / 32 ) 0.701875 0.00471399674913732 148.891702169384 Winsorized Mean ( 28 / 32 ) 0.698958333333333 0.00434397941566747 160.902772884327 Winsorized Mean ( 29 / 32 ) 0.698958333333333 0.00434397941566747 160.902772884327 Winsorized Mean ( 30 / 32 ) 0.695833333333333 0.00396715314722878 175.398656797356 Winsorized Mean ( 31 / 32 ) 0.695833333333333 0.00396715314722878 175.398656797356 Winsorized Mean ( 32 / 32 ) 0.699166666666667 0.0035715329976379 195.760942746175 Trimmed Mean ( 1 / 32 ) 0.702659574468085 0.00694979138997005 101.105131800382 Trimmed Mean ( 2 / 32 ) 0.702608695652174 0.00683375304840947 102.814469688176 Trimmed Mean ( 3 / 32 ) 0.702555555555556 0.00674589829807475 104.145589588278 Trimmed Mean ( 4 / 32 ) 0.7025 0.00668802091985749 105.038547040754 Trimmed Mean ( 5 / 32 ) 0.702441860465116 0.00662031869350723 106.103934415427 Trimmed Mean ( 6 / 32 ) 0.702261904761905 0.00656262298024526 107.009332529973 Trimmed Mean ( 7 / 32 ) 0.702073170731707 0.00649447407125099 108.103160168052 Trimmed Mean ( 8 / 32 ) 0.70175 0.00643559868075588 109.041914328564 Trimmed Mean ( 9 / 32 ) 0.701410256410256 0.00636529352589555 110.192916250720 Trimmed Mean ( 10 / 32 ) 0.701184210526316 0.0063105789910448 111.112500377755 Trimmed Mean ( 11 / 32 ) 0.700945945945946 0.00624434262699856 112.252960450197 Trimmed Mean ( 12 / 32 ) 0.700555555555556 0.00618851253199993 113.202575244549 Trimmed Mean ( 13 / 32 ) 0.700142857142857 0.0061198954548739 114.404381954803 Trimmed Mean ( 14 / 32 ) 0.699705882352941 0.00603607310989759 115.920710305116 Trimmed Mean ( 15 / 32 ) 0.699545454545455 0.00600478371143073 116.498026933726 Trimmed Mean ( 16 / 32 ) 0.699375 0.00596315988328762 117.282617553165 Trimmed Mean ( 17 / 32 ) 0.699193548387097 0.00590914101145159 118.324058781488 Trimmed Mean ( 18 / 32 ) 0.699 0.00584014936733371 119.688719591623 Trimmed Mean ( 19 / 32 ) 0.698793103448276 0.0057529160190933 121.467635044395 Trimmed Mean ( 20 / 32 ) 0.698571428571429 0.00564322701401648 123.789354359897 Trimmed Mean ( 21 / 32 ) 0.698333333333333 0.0055055400596769 126.841931175470 Trimmed Mean ( 22 / 32 ) 0.69826923076923 0.00538643311270908 129.634809559167 Trimmed Mean ( 23 / 32 ) 0.6982 0.00523481282436368 133.376306551108 Trimmed Mean ( 24 / 32 ) 0.698333333333333 0.00509948312404186 136.941983402395 Trimmed Mean ( 25 / 32 ) 0.698260869565217 0.0049860127819188 140.043938936013 Trimmed Mean ( 26 / 32 ) 0.698181818181818 0.00483635727796876 144.361092047991 Trimmed Mean ( 27 / 32 ) 0.697857142857143 0.00470420913020811 148.347389229754 Trimmed Mean ( 28 / 32 ) 0.6975 0.00452556838759169 154.124286777418 Trimmed Mean ( 29 / 32 ) 0.697368421052632 0.00437704165775574 159.324145297305 Trimmed Mean ( 30 / 32 ) 0.697222222222222 0.00417116159663657 167.153011473933 Trimmed Mean ( 31 / 32 ) 0.697352941176471 0.00398993438375926 174.778047482434 Trimmed Mean ( 32 / 32 ) 0.6975 0.00372978421930554 187.008137465355 Median 0.7 Midrange 0.705 Midmean - Weighted Average at Xnp 0.685 Midmean - Weighted Average at X(n+1)p 0.699591836734694 Midmean - Empirical Distribution Function 0.685 Midmean - Empirical Distribution Function - Averaging 0.699591836734694 Midmean - Empirical Distribution Function - Interpolation 0.699591836734694 Midmean - Closest Observation 0.685 Midmean - True Basic - Statistics Graphics Toolkit 0.699591836734694 Midmean - MS Excel (old versions) 0.685 Number of observations 96

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211777716gniksztmy0sjhb9/160pw1211777658.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211777716gniksztmy0sjhb9/160pw1211777658.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211777716gniksztmy0sjhb9/2d08n1211777658.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211777716gniksztmy0sjhb9/2d08n1211777658.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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As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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