Gemiddelde Zomertemperatuur Nederland

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sat, 02 Apr 2011 17:08:43 +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/02/t1301764076rpv2l3jm2edmyth.htm/, Retrieved Sat, 02 Apr 2011 19:07:58 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

17 16,7 15,4 15,1 16,1 17 16,1 14,3 16,1 14,8 15,9 17,6 15,9 14,8 16,5 15,6 14,6 17,1 15,2 14,8 15,4 16,6 15,1 15,4 15,2 16,6 16,1 15,7 15,8 15,7 16,9 15,9 17,1 17 16,6 17,1 16,6 16,6 16,5 17 15,9 17 16,1 16,1 16,8 16,7 15,7 18,7 16,1 16,3 17,2 16,1 16,5 16,5 15,1 16,7 14,4 16,2 15,9 17,3 15,6 15,6 14,7 15,8 15,8 14,8 16,1 16,3 16,1 17,4 16,7 16,1 15,4 16,9 15,5 17,6 18,4 15,9 15,2 15,5 15,9 15,8 17,6 18,2 15,9 15,7 16,4 15,6 15,8 17 16,8 16,6 17,7 15,7 18 18,2 16,4 18 16,3

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 'Gwilym Jenkins' @ www.wessa.org Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 16.240404040404 0.091697377122683 177.108708558543 Geometric Mean 16.2152491639835 Harmonic Mean 16.1902943061582 Quadratic Mean 16.265753824362 Winsorized Mean ( 1 / 33 ) 16.2383838383838 0.0907004178729259 179.033175581774 Winsorized Mean ( 2 / 33 ) 16.2383838383838 0.0889563283084952 182.54332375399 Winsorized Mean ( 3 / 33 ) 16.2414141414141 0.08840194766916 183.722356459802 Winsorized Mean ( 4 / 33 ) 16.2373737373737 0.0859374902690152 188.944006702371 Winsorized Mean ( 5 / 33 ) 16.2373737373737 0.0859374902690152 188.944006702371 Winsorized Mean ( 6 / 33 ) 16.2191919191919 0.0823620172878676 196.925627288892 Winsorized Mean ( 7 / 33 ) 16.2121212121212 0.0810957824253227 199.91324736339 Winsorized Mean ( 8 / 33 ) 16.2363636363636 0.0771109782008371 210.558392789101 Winsorized Mean ( 9 / 33 ) 16.2363636363636 0.0771109782008371 210.558392789101 Winsorized Mean ( 10 / 33 ) 16.2161616161616 0.0736271601448949 220.247006461324 Winsorized Mean ( 11 / 33 ) 16.2161616161616 0.0701576260847677 231.138972640957 Winsorized Mean ( 12 / 33 ) 16.2040404040404 0.0682997140690005 237.249022560623 Winsorized Mean ( 13 / 33 ) 16.1909090909091 0.066404725181802 243.821641405515 Winsorized Mean ( 14 / 33 ) 16.2191919191919 0.0623473484003917 260.142449283217 Winsorized Mean ( 15 / 33 ) 16.2191919191919 0.0623473484003917 260.142449283217 Winsorized Mean ( 16 / 33 ) 16.2030303030303 0.06008745336641 269.657464166856 Winsorized Mean ( 17 / 33 ) 16.2030303030303 0.06008745336641 269.657464166856 Winsorized Mean ( 18 / 33 ) 16.2212121212121 0.0576863177000333 281.196872463967 Winsorized Mean ( 19 / 33 ) 16.2212121212121 0.0576863177000333 281.196872463967 Winsorized Mean ( 20 / 33 ) 16.2414141414141 0.0551979646173439 294.239366505751 Winsorized Mean ( 21 / 33 ) 16.2414141414141 0.0551979646173439 294.239366505751 Winsorized Mean ( 22 / 33 ) 16.2191919191919 0.0521576659213342 310.96468050649 Winsorized Mean ( 23 / 33 ) 16.2191919191919 0.0521576659213342 310.96468050649 Winsorized Mean ( 24 / 33 ) 16.2191919191919 0.0461164839520324 351.700531550978 Winsorized Mean ( 25 / 33 ) 16.2191919191919 0.0461164839520324 351.700531550978 Winsorized Mean ( 26 / 33 ) 16.1929292929293 0.0428391622996507 377.99360266812 Winsorized Mean ( 27 / 33 ) 16.1929292929293 0.0428391622996507 377.99360266812 Winsorized Mean ( 28 / 33 ) 16.1929292929293 0.0428391622996507 377.99360266812 Winsorized Mean ( 29 / 33 ) 16.2222222222222 0.0395176951290797 410.505272871667 Winsorized Mean ( 30 / 33 ) 16.1919191919192 0.0358849247529427 451.217866650016 Winsorized Mean ( 31 / 33 ) 16.1919191919192 0.0358849247529427 451.217866650016 Winsorized Mean ( 32 / 33 ) 16.1919191919192 0.0358849247529427 451.217866650016 Winsorized Mean ( 33 / 33 ) 16.1919191919192 0.0358849247529427 451.217866650016 Trimmed Mean ( 1 / 33 ) 16.2350515463918 0.0877853867946923 184.940251893648 Trimmed Mean ( 2 / 33 ) 16.2315789473684 0.0844621101914636 192.175863361379 Trimmed Mean ( 3 / 33 ) 16.2279569892473 0.081740727284238 198.529637897858 Trimmed Mean ( 4 / 33 ) 16.2230769230769 0.0788667741582088 205.702301079704 Trimmed Mean ( 5 / 33 ) 16.2191011235955 0.0764354695968987 212.193386252887 Trimmed Mean ( 6 / 33 ) 16.2149425287356 0.0736371087071922 220.20069518498 Trimmed Mean ( 7 / 33 ) 16.2141176470588 0.071364314481726 227.202037388178 Trimmed Mean ( 8 / 33 ) 16.2144578313253 0.0690418138118053 234.849824130096 Trimmed Mean ( 9 / 33 ) 16.2111111111111 0.0672199264989075 241.165260889933 Trimmed Mean ( 10 / 33 ) 16.2075949367089 0.0651010288162426 248.960657479888 Trimmed Mean ( 11 / 33 ) 16.2064935064935 0.0633248755041282 255.926180311827 Trimmed Mean ( 12 / 33 ) 16.2053333333333 0.0618889832381034 261.845202254933 Trimmed Mean ( 13 / 33 ) 16.2054794520548 0.0605307075471633 267.723278129998 Trimmed Mean ( 14 / 33 ) 16.2070422535211 0.0592482735797506 273.5445486307 Trimmed Mean ( 15 / 33 ) 16.2057971014493 0.0583914845204083 277.536994213347 Trimmed Mean ( 16 / 33 ) 16.2044776119403 0.0573590670880283 282.509434595083 Trimmed Mean ( 17 / 33 ) 16.2046153846154 0.0564762871116468 286.927774706238 Trimmed Mean ( 18 / 33 ) 16.2047619047619 0.0554009992603049 292.499451654705 Trimmed Mean ( 19 / 33 ) 16.2032786885246 0.0544704869764053 297.468952233588 Trimmed Mean ( 20 / 33 ) 16.2016949152542 0.0533227617664948 303.842006274973 Trimmed Mean ( 21 / 33 ) 16.1982456140351 0.0522963425494433 309.739550117114 Trimmed Mean ( 22 / 33 ) 16.1945454545455 0.0510112011082495 317.470381067473 Trimmed Mean ( 23 / 33 ) 16.1924528301887 0.0499527393917637 324.155452280531 Trimmed Mean ( 24 / 33 ) 16.1901960784314 0.0486084719446154 333.073545222292 Trimmed Mean ( 25 / 33 ) 16.1877551020408 0.0479718466420515 337.442817718233 Trimmed Mean ( 26 / 33 ) 16.1851063829787 0.0471165543011801 343.512097245476 Trimmed Mean ( 27 / 33 ) 16.1851063829787 0.0465968694005821 347.343214065289 Trimmed Mean ( 28 / 33 ) 16.1837209302326 0.0458620195208507 352.878505990666 Trimmed Mean ( 29 / 33 ) 16.1829268292683 0.0448442343446287 360.869731990566 Trimmed Mean ( 30 / 33 ) 16.1794871794872 0.0441105663894668 366.793911386971 Trimmed Mean ( 31 / 33 ) 16.1783783783784 0.0438628655927201 368.839977957653 Trimmed Mean ( 32 / 33 ) 16.1771428571429 0.0434026902093288 372.722123424179 Trimmed Mean ( 33 / 33 ) 16.1757575757576 0.0426468725607199 379.295282502294 Median 16.1 Midrange 16.5 Midmean - Weighted Average at Xnp 16.1901960784314 Midmean - Weighted Average at X(n+1)p 16.1901960784314 Midmean - Empirical Distribution Function 16.1901960784314 Midmean - Empirical Distribution Function - Averaging 16.1901960784314 Midmean - Empirical Distribution Function - Interpolation 16.1901960784314 Midmean - Closest Observation 16.1901960784314 Midmean - True Basic - Statistics Graphics Toolkit 16.1901960784314 Midmean - MS Excel (old versions) 16.1901960784314 Number of observations 99

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Apr/02/t1301764076rpv2l3jm2edmyth/1ko9t1301764122.png (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/02/t1301764076rpv2l3jm2edmyth/1ko9t1301764122.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/02/t1301764076rpv2l3jm2edmyth/26h0h1301764122.png (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/02/t1301764076rpv2l3jm2edmyth/26h0h1301764122.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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