Elke Van Buggenhout- stap1 opgave 5

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

Title produced by software: Central Tendency

Date of computation: Wed, 16 Apr 2008 08:49:20 -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/Apr/16/t1208357476zvfwyl5r33tv90l.htm/, Retrieved Wed, 16 Apr 2008 16:51:17 +0200

User-defined keywords:

Dataseries X:

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10.893 10.756 10.940 10.997 10.827 10.166 10.186 10.457 10.368 10.244 10.511 10.812 10.738 10.171 9.721 9.897 9.828 9.924 10.371 10.846 10.413 10.709 10.662 10.570 10.297 10.635 10.872 10.296 10.383 10.431 10.574 10.653 10.805 10.872 10.625 10.407 10.463 10.556 10.646 10.702 11.353 11.346 11.451 11.964 12.574 13.031 13.812 14.544 14.931 14.886 16.005 17.064 15.168 16.050 15.839 15.137 14.954 15.648 15.305 15.579 16.348 15.928 16.171 15.937 15.713 15.594 15.683 16.438 17.032 17.696 17.745 19.394

Text written by user:

Output produced by software:

Summary of compuational 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 12.5908888888889 0.315365733079492 39.9247209452373 Geometric Mean 12.3311327981450 Harmonic Mean 12.0957307709021 Quadratic Mean 12.8682487833427 Winsorized Mean ( 1 / 24 ) 12.5694722222222 0.308988821690469 40.6793752390620 Winsorized Mean ( 2 / 24 ) 12.5700277777778 0.308432229395661 40.7545858693411 Winsorized Mean ( 3 / 24 ) 12.5448194444444 0.302438834415738 41.4788645402598 Winsorized Mean ( 4 / 24 ) 12.5564861111111 0.300491425223168 41.786503897027 Winsorized Mean ( 5 / 24 ) 12.5155833333333 0.292220568444567 42.8292347795754 Winsorized Mean ( 6 / 24 ) 12.5093333333333 0.290673091709796 43.0357459637939 Winsorized Mean ( 7 / 24 ) 12.4977638888889 0.286891376943840 43.5627031457812 Winsorized Mean ( 8 / 24 ) 12.4900972222222 0.283857450999889 44.0013012807161 Winsorized Mean ( 9 / 24 ) 12.4845972222222 0.282854023370126 44.1379517019832 Winsorized Mean ( 10 / 24 ) 12.4850138888889 0.280144723869355 44.566300290957 Winsorized Mean ( 11 / 24 ) 12.4840972222222 0.279857485360973 44.6087665159988 Winsorized Mean ( 12 / 24 ) 12.4712638888889 0.277089832069686 45.0080170597977 Winsorized Mean ( 13 / 24 ) 12.4528472222222 0.272768644523057 45.6535143326181 Winsorized Mean ( 14 / 24 ) 12.4481805555556 0.271665326854029 45.8217495022625 Winsorized Mean ( 15 / 24 ) 12.4446388888889 0.270050005733851 46.0827203283002 Winsorized Mean ( 16 / 24 ) 12.4384166666667 0.267445598544360 46.5082122658435 Winsorized Mean ( 17 / 24 ) 12.4362916666667 0.266709700487103 46.6285689795075 Winsorized Mean ( 18 / 24 ) 12.3797916666667 0.254225176777653 48.6961670106108 Winsorized Mean ( 19 / 24 ) 12.3555138888889 0.247174641896488 49.9869800319692 Winsorized Mean ( 20 / 24 ) 12.3507916666667 0.245397985601044 50.3296375331539 Winsorized Mean ( 21 / 24 ) 12.2985833333333 0.236794789221935 51.9377279109236 Winsorized Mean ( 22 / 24 ) 12.3071388888889 0.234097191425853 52.5727746408568 Winsorized Mean ( 23 / 24 ) 12.2959583333333 0.231506911544599 53.1127051512006 Winsorized Mean ( 24 / 24 ) 12.185625 0.213271696859518 57.1366251567205 Trimmed Mean ( 1 / 24 ) 12.5347 0.306478415541040 40.8991281747262 Trimmed Mean ( 2 / 24 ) 12.4978823529412 0.303300376390209 41.2062869874652 Trimmed Mean ( 3 / 24 ) 12.4585303030303 0.299659601924416 41.5756085338882 Trimmed Mean ( 4 / 24 ) 12.426171875 0.297777442122548 41.729728707543 Trimmed Mean ( 5 / 24 ) 12.3883387096774 0.2958877025032 41.8683798105582 Trimmed Mean ( 6 / 24 ) 12.3578 0.295799227412536 41.7776615175712 Trimmed Mean ( 7 / 24 ) 12.3264482758621 0.295686168849899 41.6876052194359 Trimmed Mean ( 8 / 24 ) 12.2949821428571 0.296008067952385 41.5359697048355 Trimmed Mean ( 9 / 24 ) 12.2624629629630 0.296567126627448 41.3480182460251 Trimmed Mean ( 10 / 24 ) 12.2282884615385 0.296909952446264 41.1851753731683 Trimmed Mean ( 11 / 24 ) 12.19132 0.297269815515007 41.0109582733082 Trimmed Mean ( 12 / 24 ) 12.1513958333333 0.297113805206543 40.8981192404914 Trimmed Mean ( 13 / 24 ) 12.1096739130435 0.296799610424546 40.8008416713272 Trimmed Mean ( 14 / 24 ) 12.0664772727273 0.29654561501568 40.6901220646586 Trimmed Mean ( 15 / 24 ) 12.0197380952381 0.295608767838744 40.6609661246412 Trimmed Mean ( 16 / 24 ) 11.96875 0.293829511333986 40.7336551922979 Trimmed Mean ( 17 / 24 ) 11.9131315789474 0.291094032338261 40.9253720636359 Trimmed Mean ( 18 / 24 ) 11.8515833333333 0.286551190404476 41.3593931213633 Trimmed Mean ( 19 / 24 ) 11.7894411764706 0.282600053082262 41.7177599504513 Trimmed Mean ( 20 / 24 ) 11.72240625 0.277746939892607 42.2053479852291 Trimmed Mean ( 21 / 24 ) 11.647 0.269883205901342 43.1557049320722 Trimmed Mean ( 22 / 24 ) 11.5672142857143 0.259991663262471 44.4907122811732 Trimmed Mean ( 23 / 24 ) 11.4740769230769 0.24392294447271 47.0397606419541 Trimmed Mean ( 24 / 24 ) 11.366875 0.217249266709625 52.3218106655014 Median 10.872 Midrange 14.5575 Midmean - Weighted Average at Xnp 11.8140540540541 Midmean - Weighted Average at X(n+1)p 11.8515833333333 Midmean - Empirical Distribution Function 11.8140540540541 Midmean - Empirical Distribution Function - Averaging 11.8515833333333 Midmean - Empirical Distribution Function - Interpolation 11.8515833333333 Midmean - Closest Observation 11.8140540540541 Midmean - True Basic - Statistics Graphics Toolkit 11.8515833333333 Midmean - MS Excel (old versions) 11.9131315789474 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/16/t1208357476zvfwyl5r33tv90l/1b3f11208357354.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/16/t1208357476zvfwyl5r33tv90l/1b3f11208357354.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/16/t1208357476zvfwyl5r33tv90l/2kp1w1208357354.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/16/t1208357476zvfwyl5r33tv90l/2kp1w1208357354.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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