datareeks - centrummaten- gemiddelde gokuitgaven 2005 - Frederik Verbraken

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Fri, 20 May 2011 09:18:24 +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/20/t1305882927rkvdaot2a344cd4.htm/, Retrieved Fri, 20 May 2011 11:15:29 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

5.81 5.76 5.99 6.12 6.03 6.25 5.80 5.67 5.89 5.91 5.86 6.07 6.27 6.68 6.77 6.71 6.62 6.50 5.89 6.05 6.43 6.47 6.62 6.77 6.70 6.95 6.73 7.07 7.28 7.32 6.76 6.93 6.99 7.16 7.28 7.08 7.34 7.87 6.28 6.30 6.36 6.28 5.89 6.04 5.96 6.10 6.26 6.02 6.25 6.41 6.22 6.57 6.18 6.26 6.10 6.02 6.06 6.35 6.21 6.48 6.74 6.53 6.80 6.75 6.56 6.66 6.18 6.40 6.43 6.54 6.44 6.64 6.82 6.97 7.00 6.91 6.74 6.98 6.37 6.56 6.63 6.87 6.68 6.75 6.84 7.15 7.09 6.97 7.15

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 2 seconds R Server 'Gwilym Jenkins' @ www.wessa.org Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 6.5185393258427 0.0467409653158419 139.460947838691 Geometric Mean 6.5039065475851 Harmonic Mean 6.48938650079612 Quadratic Mean 6.53326948107604 Winsorized Mean ( 1 / 29 ) 6.51359550561798 0.0449324902726231 144.964044193799 Winsorized Mean ( 2 / 29 ) 6.51404494382022 0.0446721455709969 145.818940652124 Winsorized Mean ( 3 / 29 ) 6.51303370786517 0.044340417654239 146.887062694199 Winsorized Mean ( 4 / 29 ) 6.5152808988764 0.0439475410093343 148.25131848657 Winsorized Mean ( 5 / 29 ) 6.51022471910112 0.0424098447505931 153.507393327821 Winsorized Mean ( 6 / 29 ) 6.50955056179775 0.0422931516563444 153.915002946375 Winsorized Mean ( 7 / 29 ) 6.50955056179775 0.0422931516563444 153.915002946375 Winsorized Mean ( 8 / 29 ) 6.50595505617977 0.041095419217002 158.313388210629 Winsorized Mean ( 9 / 29 ) 6.51 0.0401214321233452 162.257418428792 Winsorized Mean ( 10 / 29 ) 6.51224719101124 0.0394240820227275 165.184497821839 Winsorized Mean ( 11 / 29 ) 6.50730337078652 0.0375292749349573 173.392728265186 Winsorized Mean ( 12 / 29 ) 6.50595505617977 0.0373293594937357 174.285204579295 Winsorized Mean ( 13 / 29 ) 6.50595505617977 0.0369000247407964 176.313026939162 Winsorized Mean ( 14 / 29 ) 6.50595505617977 0.0364418180906059 178.529925153677 Winsorized Mean ( 15 / 29 ) 6.5076404494382 0.0361983041521432 179.777495157958 Winsorized Mean ( 16 / 29 ) 6.50584269662921 0.0354234593978199 183.659157158141 Winsorized Mean ( 17 / 29 ) 6.50393258426966 0.0346113759283701 187.913147334271 Winsorized Mean ( 18 / 29 ) 6.50595505617977 0.0331946156815107 195.994287706231 Winsorized Mean ( 19 / 29 ) 6.49741573033708 0.0320393527535974 202.794849830652 Winsorized Mean ( 20 / 29 ) 6.49516853932584 0.0305303447399051 212.744683843555 Winsorized Mean ( 21 / 29 ) 6.50460674157303 0.0280021049204133 232.289921063442 Winsorized Mean ( 22 / 29 ) 6.49966292134831 0.0273774777509383 237.40912075531 Winsorized Mean ( 23 / 29 ) 6.49966292134831 0.0254080335223324 255.811332885539 Winsorized Mean ( 24 / 29 ) 6.5023595505618 0.0250607140553903 259.464256931785 Winsorized Mean ( 25 / 29 ) 6.50797752808989 0.0236581565248707 275.083881588506 Winsorized Mean ( 26 / 29 ) 6.50505617977528 0.0233068768952526 279.104583982262 Winsorized Mean ( 27 / 29 ) 6.50808988764045 0.0229317482264993 283.802605163782 Winsorized Mean ( 28 / 29 ) 6.50494382022472 0.0225568873380539 288.379496813408 Winsorized Mean ( 29 / 29 ) 6.50820224719101 0.0221567921216816 293.733958031875 Trimmed Mean ( 1 / 29 ) 6.51275862068966 0.0441155591859315 147.629515319996 Trimmed Mean ( 2 / 29 ) 6.51188235294118 0.0431762377969438 150.820976657723 Trimmed Mean ( 3 / 29 ) 6.51072289156626 0.0422521234671409 154.09220548713 Trimmed Mean ( 4 / 29 ) 6.50987654320988 0.0413273195397967 157.519931505384 Trimmed Mean ( 5 / 29 ) 6.50835443037975 0.0403889843214649 161.141819724366 Trimmed Mean ( 6 / 29 ) 6.50792207792208 0.0397464355746079 163.735992519533 Trimmed Mean ( 7 / 29 ) 6.5076 0.039021287791421 166.77050831292 Trimmed Mean ( 8 / 29 ) 6.5072602739726 0.0381673297952265 170.492940137155 Trimmed Mean ( 9 / 29 ) 6.5074647887324 0.0374228748463417 173.890028904835 Trimmed Mean ( 10 / 29 ) 6.50710144927536 0.0367383443302687 177.120160635932 Trimmed Mean ( 11 / 29 ) 6.50641791044776 0.0360553255287489 180.456501641064 Trimmed Mean ( 12 / 29 ) 6.50630769230769 0.035586817750863 182.829151453136 Trimmed Mean ( 13 / 29 ) 6.5063492063492 0.035047551333075 185.643474618698 Trimmed Mean ( 14 / 29 ) 6.50639344262295 0.0344615353698638 188.80161237136 Trimmed Mean ( 15 / 29 ) 6.5064406779661 0.0338204102105046 192.382074536317 Trimmed Mean ( 16 / 29 ) 6.50631578947368 0.0330703582558783 196.741617950787 Trimmed Mean ( 17 / 29 ) 6.50636363636364 0.0322807169888994 201.555734917568 Trimmed Mean ( 18 / 29 ) 6.5066037735849 0.0314443588986584 206.924357865109 Trimmed Mean ( 19 / 29 ) 6.50666666666667 0.0306589930723295 212.227017740484 Trimmed Mean ( 20 / 29 ) 6.50755102040816 0.0298772013566395 217.809926128239 Trimmed Mean ( 21 / 29 ) 6.50872340425532 0.0291628764008299 223.185234364265 Trimmed Mean ( 22 / 29 ) 6.50911111111111 0.0287251380814823 226.599819734451 Trimmed Mean ( 23 / 29 ) 6.51 0.0282450909110921 230.482529530236 Trimmed Mean ( 24 / 29 ) 6.5109756097561 0.0279716862028434 232.770222093162 Trimmed Mean ( 25 / 29 ) 6.51179487179487 0.0276298841588808 235.67941270944 Trimmed Mean ( 26 / 29 ) 6.51216216216216 0.0274166362308085 237.525935251106 Trimmed Mean ( 27 / 29 ) 6.51285714285714 0.0271304704155676 240.056919142841 Trimmed Mean ( 28 / 29 ) 6.51333333333333 0.026751758178792 243.473093985161 Trimmed Mean ( 29 / 29 ) 6.5141935483871 0.0262362065902631 248.290221605614 Median 6.53 Midrange 6.77 Midmean - Weighted Average at Xnp 6.49533333333333 Midmean - Weighted Average at X(n+1)p 6.50195652173913 Midmean - Empirical Distribution Function 6.50195652173913 Midmean - Empirical Distribution Function - Averaging 6.50195652173913 Midmean - Empirical Distribution Function - Interpolation 6.50195652173913 Midmean - Closest Observation 6.50195652173913 Midmean - True Basic - Statistics Graphics Toolkit 6.50195652173913 Midmean - MS Excel (old versions) 6.50195652173913 Number of observations 89

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/20/t1305882927rkvdaot2a344cd4/1fn7p1305883102.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t1305882927rkvdaot2a344cd4/1fn7p1305883102.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t1305882927rkvdaot2a344cd4/249pd1305883102.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t1305882927rkvdaot2a344cd4/249pd1305883102.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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