CVWS1WGQ1B

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

Title produced by software: Central Tendency

Date of computation: Sun, 06 Jan 2008 06:44:31 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Jan/06/t1199627125cvuauulzp6mtzic.htm/, Retrieved Sun, 06 Jan 2008 14:45:27 +0100

User-defined keywords:

Investigating associations Werkgelegenheidsgraad BE Q1 Maandelijkse opsplitsing

Dataseries X:

» Textbox « » Textfile « » CSV «

59.9 59.9 59.9 60.9 60.9 60.9 61.1 61.1 61.1 60.2 60.2 60.2 60.1 60.1 60.1 59.7 59.7 59.7 60.5 60.5 60.5 59.5 59.5 59.5 59.5 59.5 59.5 59.7 59.7 59.7 60.4 60.4 60.4 60 60 60 59 59 59 59.3 59.3 59.3 59.7 59.7 59.7 60.4 60.4 60.4 59.9 59.9 59.9 60.5 60.5 60.5 60.4 60.4 60.4 60.6 60.6 60.6 60.9 60.9 60.9 61 61 61 61.2 61.2 61.2 61.2 61.2 61.2 60.3 60.3 60.3 60.4 60.4 60.4 61.2 61.2 61.2 62.1 62.1 62.1 61.7 61.7 61.7 61.6 61.6 61.

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 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 60.4233333333333 0.0774927003126606 779.729356307661 Geometric Mean 60.4189181701649 Harmonic Mean 60.4145104352478 Quadratic Mean 60.4277557639423 Winsorized Mean ( 1 / 30 ) 60.4233333333333 0.0774927003126606 779.729356307662 Winsorized Mean ( 2 / 30 ) 60.4233333333333 0.0774927003126606 779.729356307661 Winsorized Mean ( 3 / 30 ) 60.42 0.0726388635262284 831.786141287626 Winsorized Mean ( 4 / 30 ) 60.42 0.0726388635262284 831.786141287626 Winsorized Mean ( 5 / 30 ) 60.42 0.0726388635262284 831.786141287626 Winsorized Mean ( 6 / 30 ) 60.4266666666667 0.06918104854765 873.456935609272 Winsorized Mean ( 7 / 30 ) 60.4266666666667 0.06918104854765 873.456935609271 Winsorized Mean ( 8 / 30 ) 60.3911111111111 0.0631990384660426 955.57009373742 Winsorized Mean ( 9 / 30 ) 60.3911111111111 0.0631990384660426 955.57009373742 Winsorized Mean ( 10 / 30 ) 60.3911111111111 0.0631990384660426 955.57009373742 Winsorized Mean ( 11 / 30 ) 60.3911111111111 0.0631990384660426 955.57009373742 Winsorized Mean ( 12 / 30 ) 60.4177777777778 0.059262588337617 1019.49272673647 Winsorized Mean ( 13 / 30 ) 60.4177777777778 0.059262588337617 1019.49272673647 Winsorized Mean ( 14 / 30 ) 60.4177777777778 0.059262588337617 1019.49272673647 Winsorized Mean ( 15 / 30 ) 60.4177777777778 0.059262588337617 1019.49272673647 Winsorized Mean ( 16 / 30 ) 60.4177777777778 0.059262588337617 1019.49272673647 Winsorized Mean ( 17 / 30 ) 60.3988888888889 0.0565441381723962 1068.17241965454 Winsorized Mean ( 18 / 30 ) 60.3988888888889 0.0565441381723962 1068.17241965454 Winsorized Mean ( 19 / 30 ) 60.3988888888889 0.0565441381723962 1068.17241965454 Winsorized Mean ( 20 / 30 ) 60.3766666666667 0.053540095467991 1127.69068002060 Winsorized Mean ( 21 / 30 ) 60.4233333333333 0.047300405279189 1277.43796224761 Winsorized Mean ( 22 / 30 ) 60.4233333333333 0.047300405279189 1277.43796224761 Winsorized Mean ( 23 / 30 ) 60.4233333333333 0.047300405279189 1277.43796224761 Winsorized Mean ( 24 / 30 ) 60.3966666666667 0.0437462322258449 1380.61413734701 Winsorized Mean ( 25 / 30 ) 60.3966666666667 0.0437462322258449 1380.61413734701 Winsorized Mean ( 26 / 30 ) 60.3966666666667 0.0437462322258449 1380.61413734701 Winsorized Mean ( 27 / 30 ) 60.4266666666667 0.0400311988191881 1509.48930956578 Winsorized Mean ( 28 / 30 ) 60.4266666666667 0.0400311988191881 1509.48930956578 Winsorized Mean ( 29 / 30 ) 60.4266666666667 0.0400311988191881 1509.48930956578 Winsorized Mean ( 30 / 30 ) 60.36 0.0233199533601399 2588.34136877699 Trimmed Mean ( 1 / 30 ) 60.4204545454545 0.0751723740307693 803.758765430549 Trimmed Mean ( 2 / 30 ) 60.4174418604651 0.0725006129596263 833.33698011781 Trimmed Mean ( 3 / 30 ) 60.4142857142857 0.0694033017484219 870.481435210097 Trimmed Mean ( 4 / 30 ) 60.4121951219512 0.067972536475052 888.773587905232 Trimmed Mean ( 5 / 30 ) 60.41 0.0663134100648608 910.977130280486 Trimmed Mean ( 6 / 30 ) 60.4076923076923 0.0643823398421277 938.264941221744 Trimmed Mean ( 7 / 30 ) 60.403947368421 0.0630355174032357 958.252582937004 Trimmed Mean ( 8 / 30 ) 60.4 0.0614522507223688 982.876937622307 Trimmed Mean ( 9 / 30 ) 60.4013888888889 0.0608846190517097 992.063181631958 Trimmed Mean ( 10 / 30 ) 60.4028571428571 0.0601919437932042 1003.50401293531 Trimmed Mean ( 11 / 30 ) 60.4044117647059 0.0593509607231382 1017.74951961573 Trimmed Mean ( 12 / 30 ) 60.4060606060606 0.0583326521923118 1035.54455927896 Trimmed Mean ( 13 / 30 ) 60.4060606060606 0.0577964102449484 1045.15246448788 Trimmed Mean ( 14 / 30 ) 60.4032258064516 0.0571196403644561 1057.48610147130 Trimmed Mean ( 15 / 30 ) 60.4016666666667 0.0562727250600802 1073.37376326059 Trimmed Mean ( 16 / 30 ) 60.4 0.0552177672029758 1093.85082120352 Trimmed Mean ( 17 / 30 ) 60.3982142857143 0.0539053446154238 1120.44946037564 Trimmed Mean ( 18 / 30 ) 60.3981481481481 0.0527702680792586 1144.54882164769 Trimmed Mean ( 19 / 30 ) 60.3980769230769 0.0513388166217537 1176.46024777058 Trimmed Mean ( 20 / 30 ) 60.398 0.0495275639602508 1219.48255013054 Trimmed Mean ( 21 / 30 ) 60.4 0.0478250357297639 1262.93685050841 Trimmed Mean ( 22 / 30 ) 60.3978260869565 0.0468824339480839 1288.28264662707 Trimmed Mean ( 23 / 30 ) 60.3954545454545 0.0456286306968093 1323.63065959106 Trimmed Mean ( 24 / 30 ) 60.3928571428571 0.0439608178860284 1373.78829710198 Trimmed Mean ( 25 / 30 ) 60.3925 0.0425753479893031 1418.48517633193 Trimmed Mean ( 26 / 30 ) 60.3925 0.0406878235998683 1484.28927027189 Trimmed Mean ( 27 / 30 ) 60.3916666666667 0.0380840757456029 1585.74589206459 Trimmed Mean ( 28 / 30 ) 60.3882352941176 0.0355162351172627 1700.29945726894 Trimmed Mean ( 29 / 30 ) 60.384375 0.0317847393769095 1899.79141511751 Trimmed Mean ( 30 / 30 ) 60.38 0.0259973473447872 2322.5446503913 Median 60.4 Midrange 60.55 Midmean - Weighted Average at Xnp 60.4122448979592 Midmean - Weighted Average at X(n+1)p 60.4122448979592 Midmean - Empirical Distribution Function 60.4122448979592 Midmean - Empirical Distribution Function - Averaging 60.4122448979592 Midmean - Empirical Distribution Function - Interpolation 60.4122448979592 Midmean - Closest Observation 60.4122448979592 Midmean - True Basic - Statistics Graphics Toolkit 60.4122448979592 Midmean - MS Excel (old versions) 60.4122448979592 Number of observations 90

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/06/t1199627125cvuauulzp6mtzic/109yf1199627068.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/06/t1199627125cvuauulzp6mtzic/109yf1199627068.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/06/t1199627125cvuauulzp6mtzic/2zta91199627068.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/06/t1199627125cvuauulzp6mtzic/2zta91199627068.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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