Opdracht 5 IKO - Aantal bouwvergunningen - Centrummaten - Nathan Jacobs - Centrummaten - Nathan Jacobs

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Mon, 04 Apr 2011 11:32:31 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Apr/04/t1301916580xvzka6ozravfbs3.htm/, Retrieved Mon, 04 Apr 2011 13:29:42 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

1394 1570 1657 1746 1754 1787 1819 1828 1832 1846 1851 1852 1853 1855 1878 1898 1947 1954 2040 2057 2058 2063 2069 2069 2072 2072 2074 2085 2093 2113 2137 2139 2150 2154 2155 2160 2164 2172 2187 2194 2201 2214 2218 2226 2251 2260 2260 2266 2267 2276 2277 2280 2282 2289 2295 2299 2311 2318 2333 2351 2355 2360 2368 2379 2408 2411 2442 2450 2456 2467 2479 2498 2521 2533 2539 2540 2546 2548 2565 2570 2628 2669 2678 2695 2725 2798 2799 2825 2842 2844 2920 2930 2947 2981 3016 3249 3336 3440 3595

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 'Herman Ole Andreas Wold' @ www.yougetit.org Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 2319.43434343434 40.1384615547674 57.7858306868479 Geometric Mean 2286.63032169831 Harmonic Mean 2254.633205605 Quadratic Mean 2353.22397805842 Winsorized Mean ( 1 / 33 ) 2319.64646464646 39.2738046046518 59.0634517841369 Winsorized Mean ( 2 / 33 ) 2319.30303030303 38.3574403360989 60.4655318493787 Winsorized Mean ( 3 / 33 ) 2319.36363636364 37.214620025324 62.3239908075199 Winsorized Mean ( 4 / 33 ) 2310.27272727273 34.9872074220792 66.031927024127 Winsorized Mean ( 5 / 33 ) 2310.17171717172 34.3644749533231 67.2255787498455 Winsorized Mean ( 6 / 33 ) 2310.0505050505 33.6652319224319 68.6182857843692 Winsorized Mean ( 7 / 33 ) 2309.48484848485 33.3408042451457 69.2690203722696 Winsorized Mean ( 8 / 33 ) 2309 33.1405059622812 69.6730461094344 Winsorized Mean ( 9 / 33 ) 2303.36363636364 31.7012162355211 72.6585257565836 Winsorized Mean ( 10 / 33 ) 2303.66666666667 31.5919764935223 72.9193587219533 Winsorized Mean ( 11 / 33 ) 2301.88888888889 31.2501358937928 73.6601241259278 Winsorized Mean ( 12 / 33 ) 2298.85858585859 30.7010911962303 74.8787256832374 Winsorized Mean ( 13 / 33 ) 2298.9898989899 30.6403906377721 75.0313508129955 Winsorized Mean ( 14 / 33 ) 2291.91919191919 28.4986796656541 80.4219430095689 Winsorized Mean ( 15 / 33 ) 2290.40404040404 27.3566951432247 83.7237110847176 Winsorized Mean ( 16 / 33 ) 2295.57575757576 25.8156375680429 88.921908340449 Winsorized Mean ( 17 / 33 ) 2295.23232323232 25.4177337520773 90.3004314082383 Winsorized Mean ( 18 / 33 ) 2303.41414141414 22.2815051807357 103.377851843045 Winsorized Mean ( 19 / 33 ) 2295.54545454545 20.2906944313025 113.132917274833 Winsorized Mean ( 20 / 33 ) 2294.73737373737 20.127544177144 114.009804352743 Winsorized Mean ( 21 / 33 ) 2292.19191919192 19.5119945074132 117.47604368795 Winsorized Mean ( 22 / 33 ) 2293.08080808081 19.2936207232278 118.851761469538 Winsorized Mean ( 23 / 33 ) 2291.68686868687 19.1079652637653 119.933589843426 Winsorized Mean ( 24 / 33 ) 2292.17171717172 18.989549146547 120.70701097127 Winsorized Mean ( 25 / 33 ) 2290.65656565657 18.7893593576345 121.912435759861 Winsorized Mean ( 26 / 33 ) 2288.0303030303 18.3149030571858 124.927240722281 Winsorized Mean ( 27 / 33 ) 2284.75757575758 17.1524870193238 133.202699595901 Winsorized Mean ( 28 / 33 ) 2281.64646464646 16.2088151366044 140.765777474618 Winsorized Mean ( 29 / 33 ) 2283.9898989899 15.0858499419262 151.399484137933 Winsorized Mean ( 30 / 33 ) 2287.92929292929 13.8474271032182 165.224144230921 Winsorized Mean ( 31 / 33 ) 2286.67676767677 13.5458392327705 168.810269218667 Winsorized Mean ( 32 / 33 ) 2287.64646464646 12.8357149733387 178.225090647321 Winsorized Mean ( 33 / 33 ) 2278.64646464646 11.4435986444084 199.119746807956 Trimmed Mean ( 1 / 33 ) 2315.82474226804 37.5730874541822 61.6351995318999 Trimmed Mean ( 2 / 33 ) 2311.84210526316 35.6110672549852 64.919203030612 Trimmed Mean ( 3 / 33 ) 2307.87096774194 33.921950765843 68.0347360820357 Trimmed Mean ( 4 / 33 ) 2303.7032967033 32.4843814993188 70.9172590142007 Trimmed Mean ( 5 / 33 ) 2301.87640449438 31.623861981667 72.789224979189 Trimmed Mean ( 6 / 33 ) 2299.98850574713 30.8177789107773 74.6318711807877 Trimmed Mean ( 7 / 33 ) 2298.03529411765 30.0690682383469 76.4252246162713 Trimmed Mean ( 8 / 33 ) 2296.0843373494 29.2802142188462 78.4176072001388 Trimmed Mean ( 9 / 33 ) 2294.11111111111 28.4095760676867 80.7513320735697 Trimmed Mean ( 10 / 33 ) 2292.82278481013 27.6961345914184 82.7849379934973 Trimmed Mean ( 11 / 33 ) 2291.42857142857 26.8847596917153 85.2315065376867 Trimmed Mean ( 12 / 33 ) 2290.17333333333 26.0001896966977 88.0829470880442 Trimmed Mean ( 13 / 33 ) 2289.19178082192 25.0636909964928 91.3349825906427 Trimmed Mean ( 14 / 33 ) 2288.14084507042 23.9645638439602 95.480178982982 Trimmed Mean ( 15 / 33 ) 2287.75362318841 23.060767104612 99.205443288609 Trimmed Mean ( 16 / 33 ) 2287.49253731343 22.1903219981567 103.085143942636 Trimmed Mean ( 17 / 33 ) 2286.72307692308 21.4216428535343 106.74825887809 Trimmed Mean ( 18 / 33 ) 2285.93650793651 20.5660410520591 111.151023288833 Trimmed Mean ( 19 / 33 ) 2284.3606557377 20.0712260780697 113.812711134456 Trimmed Mean ( 20 / 33 ) 2283.37288135593 19.7966414437357 115.341427375221 Trimmed Mean ( 21 / 33 ) 2282.38596491228 19.4773783440977 117.181374443236 Trimmed Mean ( 22 / 33 ) 2281.54545454545 19.176862780854 118.973863484247 Trimmed Mean ( 23 / 33 ) 2280.56603773585 18.8287390624963 121.121548828427 Trimmed Mean ( 24 / 33 ) 2279.62745098039 18.4172757940465 123.776582186889 Trimmed Mean ( 25 / 33 ) 2278.57142857143 17.9107765986667 127.217902362818 Trimmed Mean ( 26 / 33 ) 2277.55319148936 17.2999015710182 131.651222530933 Trimmed Mean ( 27 / 33 ) 2277.55319148936 16.6108459152507 137.112414569947 Trimmed Mean ( 28 / 33 ) 2275.97674418605 15.9695338531298 142.51992356934 Trimmed Mean ( 29 / 33 ) 2275.48780487805 15.3390193485326 148.346367728895 Trimmed Mean ( 30 / 33 ) 2274.74358974359 14.7577705668415 154.138701333018 Trimmed Mean ( 31 / 33 ) 2273.56756756757 14.2607917379016 159.42786412938 Trimmed Mean ( 32 / 33 ) 2272.37142857143 13.6462563410208 166.519767164322 Trimmed Mean ( 33 / 33 ) 2270.93939393939 12.975278022503 175.020480486115 Median 2276 Midrange 2494.5 Midmean - Weighted Average at Xnp 2274.44 Midmean - Weighted Average at X(n+1)p 2279.62745098039 Midmean - Empirical Distribution Function 2279.62745098039 Midmean - Empirical Distribution Function - Averaging 2279.62745098039 Midmean - Empirical Distribution Function - Interpolation 2274.44 Midmean - Closest Observation 2274.44 Midmean - True Basic - Statistics Graphics Toolkit 2279.62745098039 Midmean - MS Excel (old versions) 2279.62745098039 Number of observations 99

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Apr/04/t1301916580xvzka6ozravfbs3/14ocb1301916750.png (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/04/t1301916580xvzka6ozravfbs3/14ocb1301916750.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/04/t1301916580xvzka6ozravfbs3/2nqrt1301916750.png (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/04/t1301916580xvzka6ozravfbs3/2nqrt1301916750.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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