R version 2.8.0 (2008-10-20)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(1687,1508,1507,1385,1632,1511,1559,1630,1579,1653,2152,2148,1752,1765,1717,1558,1575,1520,1805,1800,1719,2008,2242,2478,2030,1655,1693,1623,1805,1746,1795,1926,1619,1992,2233,2192,2080,1768,1835,1569,1976,1853,1965,1689,1778,1976,2397,2654,2097,1963,1677,1941,2003,1813,2012,1912,2084,2080,2118,2150,1608,1503,1548,1382,1731,1798,1779,1887,2004,2077,2092,2051,1577,1356,1652,1382,1519,1421,1442,1543,1656,1561,1905,2199,1473,1655,1407,1395,1530,1309,1526,1327,1627,1748,1958,2274,1648,1401,1411,1403,1394,1520,1528,1643,1515,1685,2000,2215,1956,1462,1563,1459,1446,1622,1657,1638,1643,1683,2050,2262,1813,1445,1762,1461,1556,1431,1427,1554,1645,1653,2016,2207,1665,1361,1506,1360,1453,1522,1460,1552,1548,1827,1737,1941,1474,1458,1542,1404,1522,1385,1641,1510,1681,1938,1868,1726,1456,1445,1456,1365,1487,1558,1488,1684,1594,1850,1998,2079,1494,1057,1218,1168,1236,1076,1174,1139,1427,1487,1483,1513,1357,1165,1282,1110,1297,1185,1222,1284,1444,1575,1737,1763)
> par20 = ''
> par19 = ''
> par18 = ''
> par17 = ''
> par16 = ''
> par15 = ''
> par14 = ''
> par13 = ''
> par12 = ''
> par11 = ''
> par10 = ''
> par9 = ''
> par8 = ''
> par7 = ''
> par6 = ''
> par5 = ''
> par4 = ''
> par3 = 'Pearson Chi-Squared'
> par2 = '6'
> par1 = '5'
> ylimmax = ''
> ylimmin = ''
> ylab = ''
> xlab = ''
> main = ''
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: Wessa, P., (2007), Central Tendency (v1.0.2) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_centraltendency.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: Write here your technical program description (don't use hard returns!)
> 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))
[1] 1670.307
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 20.90087
> (armose <- arm / armse)
[1] 79.91568
> (geo <- geomean(x))
[1] 1646.007
> (har <- harmean(x))
[1] 1622.258
> (qua <- quamean(x))
[1] 1695.1
> (win <- winmean(x))
          [,1]      [,2]
 [1,] 1669.490 20.678970
 [2,] 1669.000 20.462043
 [3,] 1667.531 20.067075
 [4,] 1667.823 19.954726
 [5,] 1667.380 19.864390
 [6,] 1667.286 19.797484
 [7,] 1667.031 19.648563
 [8,] 1668.073 19.428304
 [9,] 1667.885 19.351450
[10,] 1668.250 19.212305
[11,] 1668.594 18.593820
[12,] 1668.594 18.563244
[13,] 1669.339 18.450612
[14,] 1668.026 18.067624
[15,] 1667.792 17.712558
[16,] 1669.792 17.423981
[17,] 1669.172 17.326302
[18,] 1669.078 17.252962
[19,] 1669.177 17.243691
[20,] 1669.490 17.191887
[21,] 1671.130 16.995537
[22,] 1668.151 16.629674
[23,] 1668.391 16.582972
[24,] 1665.891 16.286014
[25,] 1665.240 15.969468
[26,] 1664.833 15.895314
[27,] 1665.115 15.756588
[28,] 1664.823 15.664732
[29,] 1664.823 15.634413
[30,] 1664.823 15.540576
[31,] 1665.146 15.448267
[32,] 1665.812 15.193569
[33,] 1664.094 14.800521
[34,] 1664.094 14.800521
[35,] 1662.818 14.519583
[36,] 1664.505 14.308493
[37,] 1663.927 14.172186
[38,] 1663.729 14.113156
[39,] 1660.682 13.785758
[40,] 1660.891 13.768713
[41,] 1661.745 13.579247
[42,] 1659.776 13.248511
[43,] 1656.641 12.921333
[44,] 1655.495 12.718696
[45,] 1651.510 12.270869
[46,] 1647.198 11.799287
[47,] 1643.771 11.422867
[48,] 1643.271 11.330139
[49,] 1642.250 10.733758
[50,] 1640.427 10.517530
[51,] 1639.099  9.978135
[52,] 1640.182  9.889842
[53,] 1637.974  9.689154
[54,] 1638.255  9.666238
[55,] 1638.542  9.397989
[56,] 1640.583  9.136244
[57,] 1640.583  8.985977
[58,] 1636.052  8.532637
[59,] 1636.052  8.481385
[60,] 1633.552  8.160171
[61,] 1632.917  8.052952
[62,] 1632.917  7.946436
[63,] 1633.245  7.866568
[64,] 1631.245  7.477930
> (tri <- trimean(x))
          [,1]      [,2]
 [1,] 1668.358 20.215706
 [2,] 1667.202 19.718156
 [3,] 1666.274 19.306197
 [4,] 1665.837 19.017683
 [5,] 1665.313 18.742518
 [6,] 1664.872 18.470377
 [7,] 1664.438 18.193199
 [8,] 1664.034 17.924120
 [9,] 1663.477 17.672552
[10,] 1662.930 17.414565
[11,] 1662.329 17.157412
[12,] 1661.679 16.963020
[13,] 1661.012 16.757809
[14,] 1660.262 16.550066
[15,] 1659.605 16.369610
[16,] 1658.950 16.212804
[17,] 1658.127 16.071995
[18,] 1657.327 15.929264
[19,] 1656.513 15.781579
[20,] 1655.671 15.622236
[21,] 1654.787 15.453936
[22,] 1653.777 15.288023
[23,] 1652.918 15.140867
[24,] 1652.021 14.984395
[25,] 1651.239 14.839921
[26,] 1650.471 14.708551
[27,] 1649.703 14.570901
[28,] 1648.897 14.431184
[29,] 1648.082 14.285402
[30,] 1647.242 14.127710
[31,] 1646.377 13.961991
[32,] 1645.469 13.786971
[33,] 1644.500 13.614562
[34,] 1643.581 13.457148
[35,] 1642.631 13.282896
[36,] 1641.708 13.113720
[37,] 1640.678 12.942136
[38,] 1639.638 12.762943
[39,] 1638.570 12.568366
[40,] 1637.598 12.381520
[41,] 1636.582 12.173937
[42,] 1635.491 11.957476
[43,] 1634.443 11.745895
[44,] 1633.490 11.540218
[45,] 1632.549 11.327973
[46,] 1631.740 11.133049
[47,] 1631.082 10.959143
[48,] 1630.542 10.798665
[49,] 1630.000 10.625044
[50,] 1629.478 10.483982
[51,] 1629.011 10.343604
[52,] 1628.580 10.233707
[53,] 1628.081 10.113761
[54,] 1627.655  9.995029
[55,] 1627.195  9.858490
[56,] 1626.700  9.726585
[57,] 1626.090  9.597619
[58,] 1625.447  9.461416
[59,] 1624.973  9.353698
[60,] 1624.472  9.230062
[61,] 1624.057  9.120720
[62,] 1623.647  9.001238
[63,] 1623.212  8.869200
[64,] 1622.734  8.718431
> (midr <- midrange(x))
[1] 1855.5
> midm <- array(NA,dim=8)
> for (j in 1:8) midm[j] <- midmean(x,j)
> midm
[1] 1628.794 1630.542 1628.794 1630.542 1630.542 1628.794 1630.542 1631.082
> postscript(file="/var/www/html/freestat/rcomp/tmp/1prhd1290722729.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> 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()
null device 
          1 
> postscript(file="/var/www/html/freestat/rcomp/tmp/2prhd1290722729.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> 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()
null device 
          1 
> 
> #Note: the /var/www/html/freestat/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/freestat/rcomp/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="/var/www/html/freestat/rcomp/tmp/39u8c1290722729.tab") 
> 
> try(system("convert tmp/1prhd1290722729.ps tmp/1prhd1290722729.png",intern=TRUE))
character(0)
> try(system("convert tmp/2prhd1290722729.ps tmp/2prhd1290722729.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.362   0.509   1.495