centrummaten eigen reeks

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

Title produced by software: Central Tendency

Date of computation: Sun, 20 Apr 2008 11:37:28 -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/20/t1208713141nvcqvmbor8wkr8a.htm/, Retrieved Sun, 20 Apr 2008 19:39:01 +0200

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Dataseries X:

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430,00 433,87 434,55 434,55 434,55 434,55 434,71 434,71 434,71 434,71 434,73 436,34 437,55 439,58 439,65 439,76 439,76 439,76 440,06 440,13 441,18 441,14 441,14 441,19 449,06 456,46 456,79 456,87 457,25 455,93 456,00 456,22 456,22 456,58 457,61 457,61 460,43 460,43 462,18 462,37 462,59 463,19 463,48 464,30 461,41 463,35 463,35 463,35 464,27 472,28 472,36 472,56 472,56 472,56 474,15 474,59 474,97 474,99 474,99 474,99 478,34 485,70 485,75 485,85 485,84 485,85 485,84 486,00 488,79 489,71 489,71 489,71

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 458.725972222222 2.14490617108878 213.867617337017 Geometric Mean 458.370605853554 Harmonic Mean 458.01610150729 Quadratic Mean 459.081868284405 Winsorized Mean ( 1 / 24 ) 458.779722222222 2.13541986405094 214.842865305142 Winsorized Mean ( 2 / 24 ) 458.798611111111 2.13235547668162 215.160472129673 Winsorized Mean ( 3 / 24 ) 458.760277777778 2.12462641447953 215.925150252902 Winsorized Mean ( 4 / 24 ) 458.605277777778 2.09491626976283 218.913416443941 Winsorized Mean ( 5 / 24 ) 458.594861111111 2.09300174358094 219.108685655702 Winsorized Mean ( 6 / 24 ) 458.608194444444 2.09084980520318 219.340573054638 Winsorized Mean ( 7 / 24 ) 458.607222222222 2.09067141672248 219.358823464078 Winsorized Mean ( 8 / 24 ) 458.607222222222 2.09067141672248 219.358823464078 Winsorized Mean ( 9 / 24 ) 458.595972222222 2.08860942855756 219.569999997050 Winsorized Mean ( 10 / 24 ) 458.591805555556 2.08689097481925 219.748808677116 Winsorized Mean ( 11 / 24 ) 457.713333333333 1.85537400951398 246.69599282208 Winsorized Mean ( 12 / 24 ) 457.356666666667 1.73913057488347 262.980062148186 Winsorized Mean ( 13 / 24 ) 457.723194444444 1.68186331046421 272.152434503199 Winsorized Mean ( 14 / 24 ) 457.736805555556 1.67979721820914 272.495275378272 Winsorized Mean ( 15 / 24 ) 457.755555555556 1.67572361788580 273.168886963049 Winsorized Mean ( 16 / 24 ) 457.671111111111 1.6635663130036 275.11443789985 Winsorized Mean ( 17 / 24 ) 457.567222222222 1.64876694598842 277.520860868494 Winsorized Mean ( 18 / 24 ) 457.244722222222 1.5820508640102 289.020241146478 Winsorized Mean ( 19 / 24 ) 457.263194444444 1.57922651014967 289.548833878876 Winsorized Mean ( 20 / 24 ) 457.54375 1.53669632019370 297.745067771312 Winsorized Mean ( 21 / 24 ) 457.485416666667 1.52868485440795 299.267318144425 Winsorized Mean ( 22 / 24 ) 457.473194444445 1.52349594660143 300.278576693927 Winsorized Mean ( 23 / 24 ) 454.927222222222 1.20480326549095 377.594612541861 Winsorized Mean ( 24 / 24 ) 457.540555555556 0.792699570525592 577.192889422392 Trimmed Mean ( 1 / 24 ) 458.693714285714 2.12122849256215 216.239653528166 Trimmed Mean ( 2 / 24 ) 458.602647058824 2.10325676242259 218.044061596451 Trimmed Mean ( 3 / 24 ) 458.495757575758 2.08263862424308 220.151375393989 Trimmed Mean ( 4 / 24 ) 458.3965625 2.06032567229797 222.487429372625 Trimmed Mean ( 5 / 24 ) 458.335967741935 2.04295293971519 224.349743369925 Trimmed Mean ( 6 / 24 ) 458.273833333333 2.02119726072465 226.733848416671 Trimmed Mean ( 7 / 24 ) 458.204655172414 1.99407524148271 229.783032074413 Trimmed Mean ( 8 / 24 ) 458.130714285714 1.95980301251591 233.763654489737 Trimmed Mean ( 9 / 24 ) 458.051296296296 1.91659372837785 238.992379821662 Trimmed Mean ( 10 / 24 ) 457.9675 1.86261499133819 245.873410302026 Trimmed Mean ( 11 / 24 ) 457.8776 1.79468584164585 255.129666359932 Trimmed Mean ( 12 / 24 ) 457.9 1.76256836797131 259.791341045701 Trimmed Mean ( 13 / 24 ) 457.970869565217 1.74485780952699 262.468876870469 Trimmed Mean ( 14 / 24 ) 458.002045454545 1.73178483311213 264.468216084031 Trimmed Mean ( 15 / 24 ) 458.034523809524 1.71229489229687 267.497453779774 Trimmed Mean ( 16 / 24 ) 458.068 1.68477553857617 271.886663541614 Trimmed Mean ( 17 / 24 ) 458.115 1.64826037653272 277.938489890590 Trimmed Mean ( 18 / 24 ) 458.179444444444 1.59999776509985 286.362552772598 Trimmed Mean ( 19 / 24 ) 458.289411764706 1.54840645709046 295.974877698363 Trimmed Mean ( 20 / 24 ) 458.4109375 1.47430227889379 310.934157847168 Trimmed Mean ( 21 / 24 ) 458.515 1.38022676381102 332.202658303749 Trimmed Mean ( 22 / 24 ) 458.641071428571 1.24049447591861 369.724396466127 Trimmed Mean ( 23 / 24 ) 458.788076923077 1.01669268017290 451.25541461069 Trimmed Mean ( 24 / 24 ) 459.291666666667 0.768163551300043 597.908695211273 Median 459.02 Midrange 459.855 Midmean - Weighted Average at Xnp 456.762564102564 Midmean - Weighted Average at X(n+1)p 458.179444444445 Midmean - Empirical Distribution Function 456.762564102564 Midmean - Empirical Distribution Function - Averaging 458.179444444445 Midmean - Empirical Distribution Function - Interpolation 458.179444444445 Midmean - Closest Observation 456.762564102564 Midmean - True Basic - Statistics Graphics Toolkit 458.179444444445 Midmean - MS Excel (old versions) 457.19725 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208713141nvcqvmbor8wkr8a/1uo9d1208713042.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208713141nvcqvmbor8wkr8a/1uo9d1208713042.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208713141nvcqvmbor8wkr8a/2fk231208713042.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208713141nvcqvmbor8wkr8a/2fk231208713042.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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