Shari Van Elsen - Centrummaten - Niet werkzoekende werklozen-verbetering

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

Title produced by software: Central Tendency

Date of computation: Sat, 31 May 2008 10:54:50 -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/31/t1212252980831wks8dcwlmy3m.htm/, Retrieved Sat, 31 May 2008 16:56:20 +0000

User-defined keywords:

Dataseries X:

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492.865 480.961 461.935 456.608 441.977 439.148 488.180 520.564 501.492 485.025 464.196 460.170 467.037 460.070 447.988 442.867 436.087 431.328 484.015 509.673 512.927 502.831 470.984 471.067 476.049 474.605 470.439 461.251 454.724 455.626 516.847 525.192 522.975 518.585 509.239 512.238 519.164 517.009 509.933 509.127 500.857 506.971 569.323 579.714 577.992 565.464 547.344 554.788 562.325 560.854 555.332 543.599 536.662 542.722 593.530 610.763 612.613 611.324 594.167 595.454 590.865 589.379 584.428 573.100 567.456 569.028 620.735 628.884 628.232 612.117 595.404 597.141 593.408 590.072 579.799 574.205 572.775 572.942 619.567 625.809 619.916 587.625 565.742 557.274 560.576 548.854 531.673 525.919 511.038 498.662 555.362 564.591 541.657 527.070 509.846 514.258 516.922

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 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 533.269350515464 5.46272067254695 97.6197361134396 Geometric Mean 530.552923318592 Harmonic Mean 527.813362243658 Quadratic Mean 535.948660456603 Winsorized Mean ( 1 / 32 ) 533.31169072165 5.452173000726 97.8163551763003 Winsorized Mean ( 2 / 32 ) 533.324845360825 5.43165086168023 98.1883517446564 Winsorized Mean ( 3 / 32 ) 533.255412371134 5.38884272172209 98.9554603665856 Winsorized Mean ( 4 / 32 ) 533.258340206186 5.37670074435109 99.1794718659843 Winsorized Mean ( 5 / 32 ) 533.504319587629 5.32849462658193 100.122897173654 Winsorized Mean ( 6 / 32 ) 533.490835051546 5.19034617568721 102.785212583804 Winsorized Mean ( 7 / 32 ) 533.520134020618 5.17442398604273 103.107154624305 Winsorized Mean ( 8 / 32 ) 533.535721649484 5.15145693317035 103.569869373077 Winsorized Mean ( 9 / 32 ) 533.804886597938 5.09406386086101 104.789594551277 Winsorized Mean ( 10 / 32 ) 532.410865979381 4.88478587130606 108.993695938002 Winsorized Mean ( 11 / 32 ) 532.342144329897 4.83976656498669 109.993351369698 Winsorized Mean ( 12 / 32 ) 532.420577319588 4.82601531858376 110.323018509571 Winsorized Mean ( 13 / 32 ) 532.55781443299 4.75783527923307 111.932797832975 Winsorized Mean ( 14 / 32 ) 532.875917525773 4.68473048864263 113.747401012213 Winsorized Mean ( 15 / 32 ) 533.383134020619 4.60621855842685 115.796314754718 Winsorized Mean ( 16 / 32 ) 533.053567010309 4.5371034290578 117.487638389810 Winsorized Mean ( 17 / 32 ) 532.929134020619 4.5166480081728 117.992177618511 Winsorized Mean ( 18 / 32 ) 533.457072164948 4.40716433145237 121.043154292626 Winsorized Mean ( 19 / 32 ) 533.396350515464 4.32279180441647 123.391635463570 Winsorized Mean ( 20 / 32 ) 533.749958762887 4.09930208776156 130.205080605402 Winsorized Mean ( 21 / 32 ) 533.408979381443 3.8842263966988 137.326953916689 Winsorized Mean ( 22 / 32 ) 533.618773195876 3.8516005623735 138.544681504315 Winsorized Mean ( 23 / 32 ) 533.958556701031 3.7035227464767 144.175854518244 Winsorized Mean ( 24 / 32 ) 534.180742268041 3.44151280127128 155.216840126446 Winsorized Mean ( 25 / 32 ) 535.390020618557 3.22471534759576 166.027063758581 Winsorized Mean ( 26 / 32 ) 535.936020618557 3.15051547025294 170.110582118655 Winsorized Mean ( 27 / 32 ) 536.066288659794 3.12438958502073 171.574726541741 Winsorized Mean ( 28 / 32 ) 535.456350515464 2.95950976747797 180.927380743794 Winsorized Mean ( 29 / 32 ) 536.605886597938 2.80981748621069 190.975353107936 Winsorized Mean ( 30 / 32 ) 536.786505154639 2.67910270920826 200.360554789358 Winsorized Mean ( 31 / 32 ) 536.274525773196 2.61037514029822 205.439638730213 Winsorized Mean ( 32 / 32 ) 536.325989690722 2.58418255379264 207.541835194109 Trimmed Mean ( 1 / 32 ) 533.335947368421 5.37869093865044 99.1572026449691 Trimmed Mean ( 2 / 32 ) 533.361247311828 5.29500286717648 100.729170633337 Trimmed Mean ( 3 / 32 ) 533.380648351648 5.21178209323767 102.341317961799 Trimmed Mean ( 4 / 32 ) 533.426146067416 5.13451208221465 103.890328336190 Trimmed Mean ( 5 / 32 ) 533.47291954023 5.04980607169487 105.642258725627 Trimmed Mean ( 6 / 32 ) 533.465752941176 4.96592286570149 107.425299862329 Trimmed Mean ( 7 / 32 ) 533.465752941176 4.90297623498723 108.804474542301 Trimmed Mean ( 8 / 32 ) 533.450728395062 4.8331029556211 110.374377143081 Trimmed Mean ( 9 / 32 ) 533.437683544304 4.75625461051108 112.154989004465 Trimmed Mean ( 10 / 32 ) 533.386285714286 4.67746958935594 114.033084667843 Trimmed Mean ( 11 / 32 ) 533.51244 4.62285349323405 115.407602854134 Trimmed Mean ( 12 / 32 ) 533.653808219178 4.5653521622704 116.892145282783 Trimmed Mean ( 13 / 32 ) 533.794211267606 4.49882151570243 118.652009066037 Trimmed Mean ( 14 / 32 ) 533.794211267606 4.43047492959438 120.482390657941 Trimmed Mean ( 15 / 32 ) 534.036701492537 4.36030414148466 122.476938342815 Trimmed Mean ( 16 / 32 ) 534.101723076923 4.28835312568036 124.547048114697 Trimmed Mean ( 17 / 32 ) 534.202587301587 4.21198787243015 126.829089608317 Trimmed Mean ( 18 / 32 ) 534.321704918033 4.12202431264881 129.626043999405 Trimmed Mean ( 19 / 32 ) 534.400677966102 4.03048039336623 132.589822008729 Trimmed Mean ( 20 / 32 ) 534.490631578947 3.93204344921136 135.932025798481 Trimmed Mean ( 21 / 32 ) 534.555945454546 3.84865211548219 138.894327004552 Trimmed Mean ( 22 / 32 ) 534.655905660377 3.78054348379274 141.423027655272 Trimmed Mean ( 23 / 32 ) 534.745568627451 3.69929968043819 144.553189744311 Trimmed Mean ( 24 / 32 ) 534.813306122449 3.62210800557978 147.652501057004 Trimmed Mean ( 25 / 32 ) 534.813306122449 3.56944780358152 149.830824136391 Trimmed Mean ( 26 / 32 ) 534.822666666667 3.53719754705172 151.199546972559 Trimmed Mean ( 27 / 32 ) 534.726069767442 3.50337176038566 152.631837652473 Trimmed Mean ( 28 / 32 ) 534.726069767442 3.45823129097776 154.624148813441 Trimmed Mean ( 29 / 32 ) 534.533333333333 3.42632403347468 156.007817156528 Trimmed Mean ( 30 / 32 ) 534.345972972973 3.40545479085574 156.908843543537 Trimmed Mean ( 31 / 32 ) 534.345972972973 3.39467172120397 157.407259628469 Trimmed Mean ( 32 / 32 ) 533.916272727273 3.38402730118091 157.775403449303 Median 527.07 Midrange 530.106 Midmean - Weighted Average at Xnp 533.992645833333 Midmean - Weighted Average at X(n+1)p 534.813306122449 Midmean - Empirical Distribution Function 534.813306122449 Midmean - Empirical Distribution Function - Averaging 534.813306122449 Midmean - Empirical Distribution Function - Interpolation 534.813306122449 Midmean - Closest Observation 533.88064 Midmean - True Basic - Statistics Graphics Toolkit 534.813306122449 Midmean - MS Excel (old versions) 534.813306122449 Number of observations 97

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212252980831wks8dcwlmy3m/1z7lo1212252884.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212252980831wks8dcwlmy3m/1z7lo1212252884.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212252980831wks8dcwlmy3m/2mgat1212252884.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/31/t1212252980831wks8dcwlmy3m/2mgat1212252884.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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