Michiel van Schaik - Centrummaten - Gemiddelde consumptieprijs hotelkamer

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

Title produced by software: Central Tendency

Date of computation: Sat, 19 Apr 2008 04:47:12 -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/19/t1208602083sf89rg9z30fnqw4.htm/, Retrieved Sat, 19 Apr 2008 12:48:03 +0200

User-defined keywords:

Dataseries X:

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65,05 65,84 66,6 67,55 68,07 69,06 69,06 69,11 69,29 69,38 69,28 69,75 69,9 70,21 70,48 71,55 72,18 72,64 72,77 72,74 73,13 73,44 73,34 73,34 73,81 74,26 74,72 75,11 75,26 75,89 75,91 76,43 76,56 76,76 76,76 76,56 76,82 77,09 77,51 77,76 77,86 77,89 77,94 77,99 78,17 78,91 78,87 78,88 79,08 79,41 79,51 79,73 80,38 80,56 80,46 80,45 80,58 80,68 80,52 81,49 81,66 81,95 82,3 82,4 83,14 83,17 83,11 83,21 83,33 83,88 83,8 83,73

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 76.1945833333333 0.598511192048271 127.306864676288 Geometric Mean 76.024561131931 Harmonic Mean 75.8515426765101 Quadratic Mean 76.3612980525985 Winsorized Mean ( 1 / 24 ) 76.2044444444444 0.595527109952959 127.961335715622 Winsorized Mean ( 2 / 24 ) 76.2236111111111 0.590165831233111 129.156259270123 Winsorized Mean ( 3 / 24 ) 76.2465277777778 0.578495605751095 131.80139489354 Winsorized Mean ( 4 / 24 ) 76.26875 0.571371895200662 133.483551852362 Winsorized Mean ( 5 / 24 ) 76.3347222222222 0.557623295005082 136.892993721732 Winsorized Mean ( 6 / 24 ) 76.3322222222222 0.557192381365897 136.994375327067 Winsorized Mean ( 7 / 24 ) 76.3341666666667 0.555799264815952 137.341251597272 Winsorized Mean ( 8 / 24 ) 76.2741666666667 0.539254098171137 141.443833111975 Winsorized Mean ( 9 / 24 ) 76.2629166666667 0.537036055094843 142.007069996815 Winsorized Mean ( 10 / 24 ) 76.2268055555556 0.527183878175363 144.592444327744 Winsorized Mean ( 11 / 24 ) 76.2390277777778 0.510246118760909 149.416183630986 Winsorized Mean ( 12 / 24 ) 76.2356944444444 0.501572793394057 151.993280832819 Winsorized Mean ( 13 / 24 ) 76.1454166666667 0.470890340455973 161.705199968497 Winsorized Mean ( 14 / 24 ) 76.1784722222222 0.459007513538961 165.963453702280 Winsorized Mean ( 15 / 24 ) 76.3972222222222 0.420803139911711 181.550979487109 Winsorized Mean ( 16 / 24 ) 76.5283333333333 0.397394389076498 192.575273926683 Winsorized Mean ( 17 / 24 ) 76.6227777777778 0.378966772476073 202.188643814717 Winsorized Mean ( 18 / 24 ) 76.6452777777778 0.374925656283381 204.427935227369 Winsorized Mean ( 19 / 24 ) 76.6347222222222 0.371131479145971 206.489415553136 Winsorized Mean ( 20 / 24 ) 76.5541666666667 0.331469303936683 230.954015220938 Winsorized Mean ( 21 / 24 ) 76.55125 0.314011972194586 243.784494791692 Winsorized Mean ( 22 / 24 ) 76.5206944444444 0.309978628067678 246.857968633042 Winsorized Mean ( 23 / 24 ) 76.4472222222222 0.291725562277829 262.051846349401 Winsorized Mean ( 24 / 24 ) 76.5138888888889 0.266775986655778 286.809505788146 Trimmed Mean ( 1 / 24 ) 76.244 0.58408146287954 130.536585811361 Trimmed Mean ( 2 / 24 ) 76.2858823529412 0.570396494851288 133.741849821202 Trimmed Mean ( 3 / 24 ) 76.3198484848485 0.557424375479538 136.915161665100 Trimmed Mean ( 4 / 24 ) 76.34734375 0.547110068172583 139.546588870151 Trimmed Mean ( 5 / 24 ) 76.3701612903226 0.537158017432475 142.174479039444 Trimmed Mean ( 6 / 24 ) 76.3786666666667 0.529249787056936 144.314969102576 Trimmed Mean ( 7 / 24 ) 76.388275862069 0.519518899898887 147.036567633894 Trimmed Mean ( 8 / 24 ) 76.3982142857143 0.507773540071053 150.457257530638 Trimmed Mean ( 9 / 24 ) 76.4188888888889 0.497167073525962 153.708668490288 Trimmed Mean ( 10 / 24 ) 76.4428846153846 0.484284184838458 157.847162902674 Trimmed Mean ( 11 / 24 ) 76.474 0.470221658543357 162.633937868578 Trimmed Mean ( 12 / 24 ) 76.5060416666667 0.456221544297057 167.694933794822 Trimmed Mean ( 13 / 24 ) 76.5413043478261 0.440148592464926 173.898782497925 Trimmed Mean ( 14 / 24 ) 76.5911363636364 0.426214992041232 179.70070925198 Trimmed Mean ( 15 / 24 ) 76.6416666666667 0.410613392984046 186.651648426978 Trimmed Mean ( 16 / 24 ) 76.671 0.399536718892757 191.899758831878 Trimmed Mean ( 17 / 24 ) 76.6878947368421 0.390159386385177 196.555298713571 Trimmed Mean ( 18 / 24 ) 76.6955555555556 0.381528971719086 201.021576972208 Trimmed Mean ( 19 / 24 ) 76.7014705882353 0.370079273762551 207.256866369253 Trimmed Mean ( 20 / 24 ) 76.709375 0.354518055838236 216.376496871578 Trimmed Mean ( 21 / 24 ) 76.728 0.343630180789501 223.286557146159 Trimmed Mean ( 22 / 24 ) 76.7496428571429 0.332339583032914 230.937410935915 Trimmed Mean ( 23 / 24 ) 76.7784615384615 0.315680311662919 243.215869668949 Trimmed Mean ( 24 / 24 ) 76.8216666666667 0.295767036866210 259.737080509809 Median 76.79 Midrange 74.465 Midmean - Weighted Average at Xnp 76.585945945946 Midmean - Weighted Average at X(n+1)p 76.6955555555556 Midmean - Empirical Distribution Function 76.585945945946 Midmean - Empirical Distribution Function - Averaging 76.6955555555556 Midmean - Empirical Distribution Function - Interpolation 76.6955555555556 Midmean - Closest Observation 76.585945945946 Midmean - True Basic - Statistics Graphics Toolkit 76.6955555555556 Midmean - MS Excel (old versions) 76.6878947368421 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/19/t1208602083sf89rg9z30fnqw4/15kg71208602027.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/19/t1208602083sf89rg9z30fnqw4/15kg71208602027.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/19/t1208602083sf89rg9z30fnqw4/2heav1208602027.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/19/t1208602083sf89rg9z30fnqw4/2heav1208602027.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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