Uitvoer per gewest - Waals Gewest - Central Tendency

*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: Sun, 07 Dec 2008 11:05:37 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/07/t1228673166rzqmu663ciw2k0k.htm/, Retrieved Sun, 07 Dec 2008 18:06:06 +0000

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/2008/Dec/07/t1228673166rzqmu663ciw2k0k.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

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Dataseries X:

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2283 2249.5 2468.9 2469.2 2417.7 2411.1 2361 1924.1 2486.9 2674.9 2296.2 2101.5 2322 2273.8 2501.3 2435.2 2273.3 2454.7 2328.8 1897 2608.1 2712.3 2322 2282.6 2241.1 2417.2 2829 2600.6 2321 2768.5 2457.3 2142.7 2764.4 2788.9 2679.5 2536.5 2682.7 2699.6 3097.8 3015.2 2878 3010.9 2612.3 2419.3 3096.5 3013 3397.4 3423.1 3298.7 3065.7 3918.3 3154.4 3334.7 3461.6 3018.5 2832 3301.3 3342.8 3464.4 3016.6 3201.3 3135.3 3549.8 3247.2 3441.8 3535.6 3384.7 2996.6 3402.8 3889.4 3766.3 3200.7

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 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 2811.22361111111 57.2314766451724 49.1202355050233 Geometric Mean 2770.32235615996 Harmonic Mean 2730.10637172916 Quadratic Mean 2852.28584961547 Winsorized Mean ( 1 / 24 ) 2811.19861111111 57.0397973693117 49.2848632141807 Winsorized Mean ( 2 / 24 ) 2812.70694444444 55.1792890232757 50.9739613219371 Winsorized Mean ( 3 / 24 ) 2805.40277777778 52.875311368511 53.0569504967206 Winsorized Mean ( 4 / 24 ) 2810.08055555556 51.8134375504441 54.2345902608708 Winsorized Mean ( 5 / 24 ) 2805.71944444444 50.7837762991974 55.2483420672438 Winsorized Mean ( 6 / 24 ) 2807.46944444444 50.4402449672751 55.6593142294588 Winsorized Mean ( 7 / 24 ) 2805.59305555556 50.0849676456175 56.0166690214693 Winsorized Mean ( 8 / 24 ) 2804.49305555556 49.5708750800965 56.5754195588451 Winsorized Mean ( 9 / 24 ) 2802.00555555556 49.1218679445664 57.0419178423263 Winsorized Mean ( 10 / 24 ) 2803.08888888889 48.7221030310657 57.5321817923502 Winsorized Mean ( 11 / 24 ) 2804.9375 47.8422754821288 58.6288480581942 Winsorized Mean ( 12 / 24 ) 2798.12083333333 46.6479707241583 59.9837632783505 Winsorized Mean ( 13 / 24 ) 2796.65833333333 46.4083036586577 60.262024526975 Winsorized Mean ( 14 / 24 ) 2791.48611111111 45.1710767949661 61.7980865008335 Winsorized Mean ( 15 / 24 ) 2797.65277777778 44.1332240281073 63.391080968751 Winsorized Mean ( 16 / 24 ) 2797.34166666667 40.8096750352989 68.5460412082935 Winsorized Mean ( 17 / 24 ) 2787.94444444444 38.9655227048116 71.549006683803 Winsorized Mean ( 18 / 24 ) 2787.91944444444 38.9263675134102 71.6203340443723 Winsorized Mean ( 19 / 24 ) 2776.12361111111 37.0784202839779 74.8716798032173 Winsorized Mean ( 20 / 24 ) 2775.23472222222 35.7251544906274 77.6829313068558 Winsorized Mean ( 21 / 24 ) 2769.98472222222 33.4338805521922 82.8496326622366 Winsorized Mean ( 22 / 24 ) 2770.38194444444 33.2736352349189 83.2605732702473 Winsorized Mean ( 23 / 24 ) 2764.24861111111 31.4390561054101 87.9240331466388 Winsorized Mean ( 24 / 24 ) 2748.61527777778 29.3427808129386 93.6726241217663 Trimmed Mean ( 1 / 24 ) 2808.46857142857 55.1341387609006 50.9388309048957 Trimmed Mean ( 2 / 24 ) 2805.57794117647 52.8615235814649 53.0741028841667 Trimmed Mean ( 3 / 24 ) 2801.68939393939 51.3484951481576 54.5622493094604 Trimmed Mean ( 4 / 24 ) 2800.296875 50.5849830067914 55.3582646182572 Trimmed Mean ( 5 / 24 ) 2797.45645161290 50.0221338434452 55.9243726060973 Trimmed Mean ( 6 / 24 ) 2795.47333333333 49.6259082864788 56.3309253141669 Trimmed Mean ( 7 / 24 ) 2792.99137931034 49.1959547299735 56.7727853771819 Trimmed Mean ( 8 / 24 ) 2790.67678571429 48.7190047980606 57.2810712632902 Trimmed Mean ( 9 / 24 ) 2788.37407407407 48.2108986539658 57.8370068163977 Trimmed Mean ( 10 / 24 ) 2786.27692307692 47.6402796904552 58.4857381438748 Trimmed Mean ( 11 / 24 ) 2783.856 46.9695055358869 59.2694338217591 Trimmed Mean ( 12 / 24 ) 2780.98125 46.267528464518 60.1065443150416 Trimmed Mean ( 13 / 24 ) 2778.74565217391 45.5924475382358 60.9474990313591 Trimmed Mean ( 14 / 24 ) 2776.49090909091 44.7268194793893 62.07664531949 Trimmed Mean ( 15 / 24 ) 2774.65476190476 43.8356308759226 63.2967909087122 Trimmed Mean ( 16 / 24 ) 2771.895 42.8390874040914 64.7048097419383 Trimmed Mean ( 17 / 24 ) 2768.88157894737 42.2218908076724 65.5792889892136 Trimmed Mean ( 18 / 24 ) 2766.63888888889 41.7438592153019 66.2765479976209 Trimmed Mean ( 19 / 24 ) 2764.13529411765 40.9907625962699 67.4331268569563 Trimmed Mean ( 20 / 24 ) 2762.715625 40.335660728426 68.4931292833146 Trimmed Mean ( 21 / 24 ) 2761.21333333333 39.6507235612063 69.6384097271522 Trimmed Mean ( 22 / 24 ) 2760.13928571429 39.1801426797349 70.4474026109637 Trimmed Mean ( 23 / 24 ) 2758.85 38.34318322727 71.9515117888773 Trimmed Mean ( 24 / 24 ) 2758.14583333333 37.5275256365856 73.4966077977818 Median 2738.35 Midrange 2907.65 Midmean - Weighted Average at Xnp 2757.19459459459 Midmean - Weighted Average at X(n+1)p 2766.63888888889 Midmean - Empirical Distribution Function 2757.19459459459 Midmean - Empirical Distribution Function - Averaging 2766.63888888889 Midmean - Empirical Distribution Function - Interpolation 2766.63888888889 Midmean - Closest Observation 2757.19459459459 Midmean - True Basic - Statistics Graphics Toolkit 2766.63888888889 Midmean - MS Excel (old versions) 2768.88157894737 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t1228673166rzqmu663ciw2k0k/10c6g1228673131.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t1228673166rzqmu663ciw2k0k/10c6g1228673131.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t1228673166rzqmu663ciw2k0k/2t7bu1228673131.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t1228673166rzqmu663ciw2k0k/2t7bu1228673131.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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