central tendency part 3

*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: Mon, 26 Oct 2009 13:26:04 -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/Oct/26/t1256585456zfbpvyhualoujgs.htm/, Retrieved Mon, 26 Oct 2009 20:30:58 +0100

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/Oct/26/t1256585456zfbpvyhualoujgs.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?

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User-defined keywords:

Dataseries X:

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203.5327635 233.3949787 265.3749378 238.2887181 233.8883315 200.1135257 193.075291 200.3316602 189.6318264 182.4144612 165.0136023 165.1644974 174.5445478 190.5782252 188.5721003 171.1662469 177.7862583 176.8870021 164.7797008 157.3494377 157.6769892 148.3253595 151.4509619 179.5390722 199.2856905 204.9991588 198.04192 227.3417515 216.5149126 198.1351744 188.54102 198.1050532 191.7526316 181.680574 185.3262878 177.5496333 170.1294823 142.5548596 147.9798013 135.9440529 131.9967053 118.6290495 115.4275422 103.2848045 90.8634411 83.36926589 99.34306884 109.5846973 121.2429684 155.2730714 196.2456621 185.3875028 174.7443763 152.3898484 156.4934404 145.2000346 124.4642236 132.2930956 128.6486894 140.8415436

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 168.9747588455 4.93414599483262 34.24599900823 Geometric Mean 164.387405105761 Harmonic Mean 159.39585929651 Quadratic Mean 173.172951502525 Winsorized Mean ( 1 / 20 ) 168.648224770667 4.76754063802861 35.3742605622347 Winsorized Mean ( 2 / 20 ) 168.784199475333 4.65715936435047 36.2418775632501 Winsorized Mean ( 3 / 20 ) 168.956618618333 4.60256815593086 36.7092051424847 Winsorized Mean ( 4 / 20 ) 168.973062991667 4.41060241210203 38.31065401135 Winsorized Mean ( 5 / 20 ) 168.557730158333 4.1108261576399 41.0033710243552 Winsorized Mean ( 6 / 20 ) 167.726305508333 3.83153199568355 43.77525900796 Winsorized Mean ( 7 / 20 ) 167.860183261667 3.73823425714985 44.9036019988883 Winsorized Mean ( 8 / 20 ) 167.862870181667 3.58136366429053 46.8712160832514 Winsorized Mean ( 9 / 20 ) 168.457819876667 3.45042025620955 48.8224063644135 Winsorized Mean ( 10 / 20 ) 168.877849993333 3.32188979101242 50.8378846433264 Winsorized Mean ( 11 / 20 ) 168.721260263333 3.27926350133541 51.4509615328641 Winsorized Mean ( 12 / 20 ) 169.445427483333 3.14359390641593 53.9018182779598 Winsorized Mean ( 13 / 20 ) 170.492871608333 2.95522267189963 57.6920559081727 Winsorized Mean ( 14 / 20 ) 170.473518498333 2.82213949946953 60.4057731839184 Winsorized Mean ( 15 / 20 ) 170.342219473333 2.59193704966792 65.720044973761 Winsorized Mean ( 16 / 20 ) 170.73078142 2.41967759505850 70.5593099546272 Winsorized Mean ( 17 / 20 ) 170.495941096667 2.35552007525524 72.3814425899945 Winsorized Mean ( 18 / 20 ) 171.149702176667 2.16736489955624 78.9667223141379 Winsorized Mean ( 19 / 20 ) 171.111436303333 2.07350593036964 82.5227619545943 Winsorized Mean ( 20 / 20 ) 172.062150536667 1.92743869801226 89.2698432972793 Trimmed Mean ( 1 / 20 ) 168.788643569655 4.58702292222481 36.7969915196737 Trimmed Mean ( 2 / 20 ) 168.939092282857 4.36399641250616 38.7120144734121 Trimmed Mean ( 3 / 20 ) 169.025143842593 4.16276719933185 40.6040347079035 Trimmed Mean ( 4 / 20 ) 169.051499698077 3.93811657510259 42.9269922497592 Trimmed Mean ( 5 / 20 ) 169.07503071 3.73593446594609 45.2564230585836 Trimmed Mean ( 6 / 20 ) 169.204355847917 3.58939516756755 47.1400745665412 Trimmed Mean ( 7 / 20 ) 169.525671139130 3.49062779459668 48.5659546404655 Trimmed Mean ( 8 / 20 ) 169.850116829545 3.38894680718335 50.1188500420024 Trimmed Mean ( 9 / 20 ) 170.204982302381 3.29847502549082 51.6011129346216 Trimmed Mean ( 10 / 20 ) 170.49617604 3.21359433766486 53.0546665587823 Trimmed Mean ( 11 / 20 ) 170.751701205263 3.13254921848332 54.5088646006767 Trimmed Mean ( 12 / 20 ) 171.059343772222 3.02955828736905 56.4634601966265 Trimmed Mean ( 13 / 20 ) 171.296684402941 2.92479903385543 58.5669929523809 Trimmed Mean ( 14 / 20 ) 171.412618940625 2.83178226664106 60.5317085850486 Trimmed Mean ( 15 / 20 ) 171.546776146667 2.73438064344459 62.7369772229529 Trimmed Mean ( 16 / 20 ) 171.718855671429 2.65931321636487 64.5726327439377 Trimmed Mean ( 17 / 20 ) 171.861366380769 2.5961417661543 66.1987602608273 Trimmed Mean ( 18 / 20 ) 172.062164216667 2.50930758212674 68.5695788918938 Trimmed Mean ( 19 / 20 ) 172.200416040909 2.43611071336111 70.6866133367656 Trimmed Mean ( 20 / 20 ) 172.37236021 2.33999529166288 73.663550018302 Median 174.64446205 Midrange 174.372101845 Midmean - Weighted Average at Xnp 170.611553032258 Midmean - Weighted Average at X(n+1)p 171.546776146667 Midmean - Empirical Distribution Function 170.611553032258 Midmean - Empirical Distribution Function - Averaging 171.546776146667 Midmean - Empirical Distribution Function - Interpolation 171.546776146667 Midmean - Closest Observation 170.611553032258 Midmean - True Basic - Statistics Graphics Toolkit 171.546776146667 Midmean - MS Excel (old versions) 171.412618940625 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/26/t1256585456zfbpvyhualoujgs/18nk41256585162.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/26/t1256585456zfbpvyhualoujgs/18nk41256585162.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/26/t1256585456zfbpvyhualoujgs/2jegm1256585162.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/26/t1256585456zfbpvyhualoujgs/2jegm1256585162.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')

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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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