inflation in consumer prices (%)

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Thu, 19 May 2011 16:19:16 +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/May/19/t1305821779rxd44dwlahp15qj.htm/, Retrieved Thu, 19 May 2011 18:16:20 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

0.440 0.548 0.163 0.381 0.164 0.109 0.328 0.435 0.325 0.108 0.054 0.270 0.431 0.215 0.214 0.160 0.427 0.372 0.106 0.053 0.317 0.527 0.472 0.000 0.052 0.418 0.364 0.311 0.052 0.052 0.620 0.616 1.377 0.151 0.502 0.000 0.606 0.050 0.150 0.501 0.299 0.248 0.545 0.444 0.491 0.444 0.050 0.545 0.138 0.423 0.495 0.370 0.388 0.169 0.241 0.014 0.376 0.331 0.789 0.289 0.359 0.236 0.367 0.309 0.551 0.901 0.870 0.160 0.032 0.877 1.812 0.784 0.270 0.462 0.146 0.108 0.132 0.680 0.117 0.345 0.204 0.227 0.236 0.092 0.138 0.046 0.023 0.009 0.142 0.207 0.346 0.207 0.165 0.247 0.123 0.433

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 0.33221875 0.0288548439300781 11.5134481685308 Geometric Mean 0 Harmonic Mean 0 Quadratic Mean 0.435277485729889 Winsorized Mean ( 1 / 32 ) 0.3276875 0.0266827828733068 12.2808592175674 Winsorized Mean ( 2 / 32 ) 0.317958333333333 0.023244773590401 13.6787021003566 Winsorized Mean ( 3 / 32 ) 0.317364583333333 0.0230280536376889 13.7816503438188 Winsorized Mean ( 4 / 32 ) 0.317447916666667 0.022902333012391 13.8609423107644 Winsorized Mean ( 5 / 32 ) 0.313697916666667 0.0218180932470454 14.3778795477074 Winsorized Mean ( 6 / 32 ) 0.314260416666667 0.0216299583342648 14.5289423035473 Winsorized Mean ( 7 / 32 ) 0.30696875 0.019974201854402 15.3682611319135 Winsorized Mean ( 8 / 32 ) 0.30196875 0.019041980705643 15.8580535642762 Winsorized Mean ( 9 / 32 ) 0.30178125 0.0189502245226076 15.9249432448664 Winsorized Mean ( 10 / 32 ) 0.300739583333333 0.0187701485006117 16.0222271722322 Winsorized Mean ( 11 / 32 ) 0.2944375 0.0177496034827221 16.5883987372796 Winsorized Mean ( 12 / 32 ) 0.2941875 0.0176747683705262 16.6444896947321 Winsorized Mean ( 13 / 32 ) 0.293916666666667 0.0175941057880056 16.7054052196866 Winsorized Mean ( 14 / 32 ) 0.299458333333333 0.0168361421792385 17.7866360443672 Winsorized Mean ( 15 / 32 ) 0.298833333333333 0.0161311556091481 18.5252278617821 Winsorized Mean ( 16 / 32 ) 0.295 0.0154853212894856 19.0502989563608 Winsorized Mean ( 17 / 32 ) 0.294822916666667 0.0154604333334426 19.0695118505465 Winsorized Mean ( 18 / 32 ) 0.293885416666667 0.0152796653497361 19.2337600294199 Winsorized Mean ( 19 / 32 ) 0.294677083333333 0.0149704203581572 19.6839551785042 Winsorized Mean ( 20 / 32 ) 0.29196875 0.0142783378830609 20.4483709792565 Winsorized Mean ( 21 / 32 ) 0.29175 0.0137474718568957 21.2220838156259 Winsorized Mean ( 22 / 32 ) 0.289 0.0130526850769985 22.1410382840905 Winsorized Mean ( 23 / 32 ) 0.289 0.0130526850769985 22.1410382840905 Winsorized Mean ( 24 / 32 ) 0.289 0.0128068221266033 22.5660977518901 Winsorized Mean ( 25 / 32 ) 0.288739583333333 0.0125205203915558 23.0613085002495 Winsorized Mean ( 26 / 32 ) 0.28928125 0.0123245289501547 23.4719924120401 Winsorized Mean ( 27 / 32 ) 0.289 0.0122221667329947 23.6455618969607 Winsorized Mean ( 28 / 32 ) 0.290458333333333 0.0117704182119006 24.6769764764741 Winsorized Mean ( 29 / 32 ) 0.28925 0.0116234600941976 24.885016824241 Winsorized Mean ( 30 / 32 ) 0.288625 0.0113252769030088 25.4850280899817 Winsorized Mean ( 31 / 32 ) 0.279260416666667 0.0101568536707684 27.4947760122196 Winsorized Mean ( 32 / 32 ) 0.277260416666667 0.00985619456109926 28.1305746297833 Trimmed Mean ( 1 / 32 ) 0.320010638297872 0.0245741562333821 13.0222431752576 Trimmed Mean ( 2 / 32 ) 0.312 0.0220043810518586 14.1789945949717 Trimmed Mean ( 3 / 32 ) 0.308822222222222 0.0212412077883782 14.5388259132416 Trimmed Mean ( 4 / 32 ) 0.305715909090909 0.0204553311340457 14.945537038121 Trimmed Mean ( 5 / 32 ) 0.302441860465116 0.0195858669602109 15.4418418689116 Trimmed Mean ( 6 / 32 ) 0.299869047619048 0.0189123637928902 15.855714859492 Trimmed Mean ( 7 / 32 ) 0.297060975609756 0.0181757980544868 16.3437651936513 Trimmed Mean ( 8 / 32 ) 0.2953625 0.0177283317890362 16.660479029542 Trimmed Mean ( 9 / 32 ) 0.294346153846154 0.0174109391333778 16.9058171757016 Trimmed Mean ( 10 / 32 ) 0.293302631578947 0.0170571178715251 17.1953218467571 Trimmed Mean ( 11 / 32 ) 0.292337837837838 0.0166764213009646 17.530010339864 Trimmed Mean ( 12 / 32 ) 0.292083333333333 0.0164161900266833 17.7923947553345 Trimmed Mean ( 13 / 32 ) 0.291842857142857 0.0161192583879966 18.1052285482427 Trimmed Mean ( 14 / 32 ) 0.291617647058824 0.0157788718245105 18.4815270890174 Trimmed Mean ( 15 / 32 ) 0.29080303030303 0.0154966455456899 18.7655469982607 Trimmed Mean ( 16 / 32 ) 0.29 0.0152707379162874 18.9905688637806 Trimmed Mean ( 17 / 32 ) 0.289516129032258 0.0150984910683564 19.1751697385859 Trimmed Mean ( 18 / 32 ) 0.289016666666667 0.0148863204877761 19.4149163256288 Trimmed Mean ( 19 / 32 ) 0.288568965517241 0.0146508696220729 19.6963711343444 Trimmed Mean ( 20 / 32 ) 0.288017857142857 0.0144059306661552 19.9930059235615 Trimmed Mean ( 21 / 32 ) 0.287666666666667 0.0142124737292226 20.2404361230366 Trimmed Mean ( 22 / 32 ) 0.287307692307692 0.0140495390084901 20.4496170396817 Trimmed Mean ( 23 / 32 ) 0.28716 0.0139478726342195 20.5880859060533 Trimmed Mean ( 24 / 32 ) 0.287 0.0138023985478524 20.7934873786597 Trimmed Mean ( 25 / 32 ) 0.286826086956522 0.0136439650387479 21.0221945117827 Trimmed Mean ( 26 / 32 ) 0.286659090909091 0.0134753295519884 21.2728816614947 Trimmed Mean ( 27 / 32 ) 0.286428571428571 0.0132750822293668 21.5764065698171 Trimmed Mean ( 28 / 32 ) 0.2862 0.0130143017977167 21.9911912639227 Trimmed Mean ( 29 / 32 ) 0.285815789473684 0.0127472338372824 22.4217891600721 Trimmed Mean ( 30 / 32 ) 0.2855 0.0124023487278924 23.019833280282 Trimmed Mean ( 31 / 32 ) 0.285205882352941 0.0119880198228193 23.7909084709762 Trimmed Mean ( 32 / 32 ) 0.28578125 0.0117078632226346 24.4093430684691 Median 0.294 Midrange 0.906 Midmean - Weighted Average at Xnp 0.28104 Midmean - Weighted Average at X(n+1)p 0.287 Midmean - Empirical Distribution Function 0.28104 Midmean - Empirical Distribution Function - Averaging 0.287 Midmean - Empirical Distribution Function - Interpolation 0.287 Midmean - Closest Observation 0.28104 Midmean - True Basic - Statistics Graphics Toolkit 0.287 Midmean - MS Excel (old versions) 0.287307692307692 Number of observations 96

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/19/t1305821779rxd44dwlahp15qj/1xbt71305821955.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305821779rxd44dwlahp15qj/1xbt71305821955.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305821779rxd44dwlahp15qj/2fr4l1305821955.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305821779rxd44dwlahp15qj/2fr4l1305821955.ps (open in new window)

Parameters (Session):

par1 = Studio 100 PRIJS 2005 ; par2 = Studio 100 PRIJS 2005 ; par3 = Studio 100 PRIJS 2005 ; par4 = 12 ;

Parameters (R input):

par1 = Studio 100 PRIJS 2005 ; par2 = Studio 100 PRIJS 2005 ; par3 = Studio 100 PRIJS 2005 ; par4 = 12 ;

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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