centrummaten roomijs - Volckaerts Sophie - 2mar03a

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

Title produced by software: Central Tendency

Date of computation: Sat, 19 Apr 2008 05:44:40 -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/19/t1208605532x5mn018pyk93hrg.htm/, Retrieved Sat, 19 Apr 2008 13:45:34 +0200

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

2,6900 2,7200 2,6800 2,7200 2,7000 2,7200 2,7200 2,7100 2,6800 2,6500 2,6600 2,6900 2,6700 2,6700 2,6500 2,6600 2,7600 2,7900 2,7900 2,7800 2,8100 2,8100 2,7900 2,7900 2,7900 2,8000 2,8000 2,8000 2,7700 2,7800 2,7500 2,7400 2,7400 2,7200 2,7100 2,7100 2,7000 2,6900 2,7000 2,7100 2,7600 2,7600 2,7500 2,7400 2,7100 2,7300 2,7300 2,7300 2,7200 2,7200 2,7500 2,8200 2,8500 2,8300 2,8500 2,8500 2,7900 2,8100 2,8000 2,7900 2,7900 2,8000 2,8000 2,8600 2,8600 2,8500 2,8100 2,7900 2,7800 2,7700 2,7800 2,8500 2,8200

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 11 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 2.75712328767123 0.0065876581137532 418.528593934637 Geometric Mean 2.75655619168462 Harmonic Mean 2.75598869082038 Quadratic Mean 2.75768987100753 Winsorized Mean ( 1 / 24 ) 2.75712328767123 0.0065876581137532 418.528593934637 Winsorized Mean ( 2 / 24 ) 2.75712328767123 0.00647110264240011 426.066999711293 Winsorized Mean ( 3 / 24 ) 2.75712328767123 0.00647110264240011 426.066999711293 Winsorized Mean ( 4 / 24 ) 2.75767123287671 0.0063615107022595 433.493137392229 Winsorized Mean ( 5 / 24 ) 2.75767123287671 0.0063615107022595 433.493137392229 Winsorized Mean ( 6 / 24 ) 2.75849315068493 0.00621063319809953 444.156507508612 Winsorized Mean ( 7 / 24 ) 2.75657534246575 0.0058462647862868 471.510518807097 Winsorized Mean ( 8 / 24 ) 2.75657534246575 0.00546964495271486 503.977016112815 Winsorized Mean ( 9 / 24 ) 2.75657534246575 0.00546964495271486 503.977016112815 Winsorized Mean ( 10 / 24 ) 2.75520547945205 0.00526001830619176 523.80150012193 Winsorized Mean ( 11 / 24 ) 2.75671232876712 0.00501161054737492 550.065154246889 Winsorized Mean ( 12 / 24 ) 2.75671232876712 0.00501161054737492 550.065154246889 Winsorized Mean ( 13 / 24 ) 2.75671232876712 0.00501161054737492 550.065154246889 Winsorized Mean ( 14 / 24 ) 2.75671232876712 0.00444848235078966 619.697261084507 Winsorized Mean ( 15 / 24 ) 2.75671232876712 0.00444848235078966 619.697261084507 Winsorized Mean ( 16 / 24 ) 2.75671232876712 0.00444848235078966 619.697261084507 Winsorized Mean ( 17 / 24 ) 2.75671232876712 0.00444848235078966 619.697261084507 Winsorized Mean ( 18 / 24 ) 2.75671232876712 0.00444848235078966 619.697261084507 Winsorized Mean ( 19 / 24 ) 2.75931506849315 0.00408401479321209 675.637873075122 Winsorized Mean ( 20 / 24 ) 2.75657534246575 0.00372279159343909 740.459215424211 Winsorized Mean ( 21 / 24 ) 2.75657534246575 0.00372279159343909 740.45921542421 Winsorized Mean ( 22 / 24 ) 2.75657534246575 0.00372279159343909 740.459215424211 Winsorized Mean ( 23 / 24 ) 2.75657534246575 0.00372279159343909 740.459215424211 Winsorized Mean ( 24 / 24 ) 2.75657534246575 0.00372279159343909 740.45921542421 Trimmed Mean ( 1 / 24 ) 2.75718309859155 0.00643863807846775 428.224581812136 Trimmed Mean ( 2 / 24 ) 2.75724637681159 0.00626184830214189 440.324684305825 Trimmed Mean ( 3 / 24 ) 2.75731343283582 0.00612541210292627 450.143335093908 Trimmed Mean ( 4 / 24 ) 2.75738461538462 0.00596172456285206 462.514593942511 Trimmed Mean ( 5 / 24 ) 2.75730158730159 0.00580537010258388 474.957072258727 Trimmed Mean ( 6 / 24 ) 2.7572131147541 0.0056158010272002 490.974146234794 Trimmed Mean ( 7 / 24 ) 2.75694915254237 0.00542874913767196 507.842429743337 Trimmed Mean ( 8 / 24 ) 2.75701754385965 0.0052979219473246 520.396029098148 Trimmed Mean ( 9 / 24 ) 2.75709090909091 0.00522666516744416 527.504789528946 Trimmed Mean ( 10 / 24 ) 2.75716981132075 0.00513516405823375 536.919518062893 Trimmed Mean ( 11 / 24 ) 2.75745098039216 0.00506307770660588 544.619525944558 Trimmed Mean ( 12 / 24 ) 2.75755102040816 0.00502147270390497 549.15184907084 Trimmed Mean ( 13 / 24 ) 2.75765957446808 0.00496251225093216 555.698290508015 Trimmed Mean ( 14 / 24 ) 2.75777777777778 0.00488130725255306 564.967053925029 Trimmed Mean ( 15 / 24 ) 2.75790697674419 0.00488582984577086 564.470532908838 Trimmed Mean ( 16 / 24 ) 2.75804878048780 0.00487926814028199 565.258702984175 Trimmed Mean ( 17 / 24 ) 2.75820512820513 0.00485792471188212 567.774366996418 Trimmed Mean ( 18 / 24 ) 2.75837837837838 0.00481666142201019 572.674335333954 Trimmed Mean ( 19 / 24 ) 2.75857142857143 0.0047481594336335 580.977001115662 Trimmed Mean ( 20 / 24 ) 2.75848484848485 0.00472984584205695 583.208193374273 Trimmed Mean ( 21 / 24 ) 2.75870967741935 0.00476866870094023 578.507304748477 Trimmed Mean ( 22 / 24 ) 2.75896551724138 0.00479492824178769 575.392451798769 Trimmed Mean ( 23 / 24 ) 2.75925925925926 0.00480164756642088 574.648434957086 Trimmed Mean ( 24 / 24 ) 2.7596 0.0047777260979117 577.596945376629 Median 2.76 Midrange 2.755 Midmean - Weighted Average at Xnp 2.75777777777778 Midmean - Weighted Average at X(n+1)p 2.75777777777778 Midmean - Empirical Distribution Function 2.75777777777778 Midmean - Empirical Distribution Function - Averaging 2.75777777777778 Midmean - Empirical Distribution Function - Interpolation 2.75777777777778 Midmean - Closest Observation 2.75777777777778 Midmean - True Basic - Statistics Graphics Toolkit 2.75777777777778 Midmean - MS Excel (old versions) 2.75777777777778 Number of observations 73

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/19/t1208605532x5mn018pyk93hrg/1f2gc1208605468.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/19/t1208605532x5mn018pyk93hrg/1f2gc1208605468.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/19/t1208605532x5mn018pyk93hrg/2aazy1208605468.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/19/t1208605532x5mn018pyk93hrg/2aazy1208605468.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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