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Data:
19.0142 19.3591 18.1271 19.1170 17.4516 16.3009 16.3009 19.9219 20.7805 19.1823 18.1073 16.1320 16.3489 15.3737 16.8836 19.4425 16.7027 15.5555 18.4142 16.1190 16.1499 14.0406 17.3857 18.4703 19.0302 23.2022 15.7916 17.3628 14.4647 17.7904 14.0870 18.3571 15.0053 13.5792 15.9513 13.8922 14.1961 14.7569 14.6411 15.5663 12.6109 12.8912 13.4162 15.2774 16.9474 14.9464 16.0203 14.3762 15.4509 15.5105 14.2117 16.5118 13.4452 14.3703 12.6933 13.8435 14.6380 21.4254 13.4509 13.5555 15.2513 12.5049 16.3285 14.3594 14.8086 21.2790 16.3805 15.4997 15.5883 15.1415 13.5313 12.5784 14.1387 18.5715 12.5949 21.2790 16.4421 22.0127 17.6014 12.5813 0.0000 13.0320 16.5304 13.3991 22.8003 21.2790 13.2589 21.4254 21.4254 15.9111 15.4818 16.5334 13.9953 11.5974 13.1350 12.0713 21.1069 14.6537 18.5810 13.4088 11.3471 13.4846 14.8980 18.6050 14.8623 18.7632 11.7920 13.2176 15.4060 18.5810 14.1420 13.6971 14.4587 12.8128 12.5163 13.8396 17.7936 13.4640 16.6465 22.2304 11.4139 22.2574 15.2371 11.7328 18.5810 13.2270 13.3560 24.1526 11.6651 13.0219 14.4006 15.9796 25.8791 15.1965 13.5205 14.0285 15.5245 14.2474 12.5423 12.5819 13.3072 11.7095 13.5564 14.0288 14.1011 13.1571 14.0367 13.0532 13.1672 11.9818 13.5205 13.9726 13.4707 13.0249 13.3665 13.2552 14.0069 14.8897 12.2838 18.5810 12.7860 16.4457 12.7860 13.7298 13.3245 29.7497 14.0235 16.7371 14.3667 12.8917 12.1446 11.1726 14.8909 12.3693 13.7120 13.8045 11.7371 15.8137 13.5313 15.1433 12.5443 14.2891 12.0129 15.8484 13.9389 13.2643 11.9157 14.5107 18.5810 14.6748 11.2541 14.2909 18.7425 14.6990 17.8537 13.7975 15.3113 15.0697 12.2954 11.7013 13.4984 13.1221 11.3435 11.6380 15.8386 22.0766 22.1418 15.3185 12.2616 19.1513 13.9080 16.1295 11.5769 13.6835 14.2917 11.4913 12.6730 15.3104 14.7270 16.5976 16.8635 12.3499 14.9389 12.9998 15.5382 22.1418 15.0847 13.2700 13.9652 15.7070 22.1987 15.2892 15.6484 13.9702 13.5977 15.9219 12.9451 14.9353 15.6629 13.2376 16.9984 21.9562 25.4723 11.6127 16.8093 16.6241 21.1429 14.2748 15.5355 13.0042 15.8324 20.4061 12.8521 22.7055 18.2286 13.9672 15.3631 12.9055 16.4566 22.1365 15.8765 13.9538 17.8447 19.8724 14.2128 12.8624 16.2064 21.8178 25.4723 16.1634 13.1344 14.0921 17.1003 13.3178 14.9895 13.7042 17.1530 14.5892 18.9282 17.6722 19.4932 16.6923 13.7842 18.7042 14.8740 19.4582 18.5405 17.4832 20.9196 17.4120 19.2811 18.7677 19.9852 24.4309 19.7337 18.4062 18.6397 18.1697 18.6135 20.2632 18.3774 23.5084 19.8833 17.9163 26.7899 22.9468 22.7283 22.3903 23.0452 21.2729 19.4397 21.2074 22.0338 19.8808 19.1850 20.5497 24.0326 20.4090 20.5497 25.2660 24.7581 23.5327 21.4355 20.2494 21.2122 21.1859 20.4476 20.9151 21.0413 20.8246 25.1920 32.1813 17.8607 24.7216
Sample Range:
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R Code
num <- 50 res <- array(NA,dim=c(num,3)) x <- as.numeric(na.omit(x)) 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] } } } } iqd <- 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) } iqdiff <- qvalue3 - qvalue1 return(c(iqdiff,iqdiff/2,iqdiff/(qvalue3 + qvalue1))) } range <- max(x) - min(x) lx <- length(x) biasf <- (lx-1)/lx varx <- var(x) bvarx <- varx*biasf sdx <- sqrt(varx) mx <- mean(x) bsdx <- sqrt(bvarx) x2 <- x*x mse0 <- sum(x2)/lx xmm <- x-mx xmm2 <- xmm*xmm msem <- sum(xmm2)/lx axmm <- abs(x - mx) medx <- median(x) axmmed <- abs(x - medx) xmmed <- x - medx xmmed2 <- xmmed*xmmed msemed <- sum(xmmed2)/lx qarr <- array(NA,dim=c(8,3)) for (j in 1:8) { qarr[j,] <- iqd(x,j) } sdpo <- 0 adpo <- 0 for (i in 1:(lx-1)) { for (j in (i+1):lx) { ldi <- x[i]-x[j] aldi <- abs(ldi) sdpo = sdpo + ldi * ldi adpo = adpo + aldi } } denom <- (lx*(lx-1)/2) sdpo = sdpo / denom adpo = adpo / denom gmd <- 0 for (i in 1:lx) { for (j in 1:lx) { ldi <- abs(x[i]-x[j]) gmd = gmd + ldi } } gmd <- gmd / (lx*(lx-1)) sumx <- sum(x) pk <- x / sumx ck <- cumsum(pk) dk <- array(NA,dim=lx) for (i in 1:lx) { if (ck[i] <= 0.5) dk[i] <- ck[i] else dk[i] <- 1 - ck[i] } bigd <- sum(dk) * 2 / (lx-1) iod <- 1 - sum(pk*pk) res[1,] <- c('Absolute range','http://www.xycoon.com/absolute.htm', range) res[2,] <- c('Relative range (unbiased)','http://www.xycoon.com/relative.htm', range/sd(x)) res[3,] <- c('Relative range (biased)','http://www.xycoon.com/relative.htm', range/sqrt(varx*biasf)) res[4,] <- c('Variance (unbiased)','http://www.xycoon.com/unbiased.htm', varx) res[5,] <- c('Variance (biased)','http://www.xycoon.com/biased.htm', bvarx) res[6,] <- c('Standard Deviation (unbiased)','http://www.xycoon.com/unbiased1.htm', sdx) res[7,] <- c('Standard Deviation (biased)','http://www.xycoon.com/biased1.htm', bsdx) res[8,] <- c('Coefficient of Variation (unbiased)','http://www.xycoon.com/variation.htm', sdx/mx) res[9,] <- c('Coefficient of Variation (biased)','http://www.xycoon.com/variation.htm', bsdx/mx) res[10,] <- c('Mean Squared Error (MSE versus 0)','http://www.xycoon.com/mse.htm', mse0) res[11,] <- c('Mean Squared Error (MSE versus Mean)','http://www.xycoon.com/mse.htm', msem) res[12,] <- c('Mean Absolute Deviation from Mean (MAD Mean)', 'http://www.xycoon.com/mean2.htm', sum(axmm)/lx) res[13,] <- c('Mean Absolute Deviation from Median (MAD Median)', 'http://www.xycoon.com/median1.htm', sum(axmmed)/lx) res[14,] <- c('Median Absolute Deviation from Mean', 'http://www.xycoon.com/mean3.htm', median(axmm)) res[15,] <- c('Median Absolute Deviation from Median', 'http://www.xycoon.com/median2.htm', median(axmmed)) res[16,] <- c('Mean Squared Deviation from Mean', 'http://www.xycoon.com/mean1.htm', msem) res[17,] <- c('Mean Squared Deviation from Median', 'http://www.xycoon.com/median.htm', msemed) load(file='createtable') mylink1 <- 'Interquartile Difference' mylink2 <- paste(mylink1,'(Weighted Average at Xnp)',sep=' ') res[18,] <- c('', mylink2, qarr[1,1]) mylink2 <- paste(mylink1,'(Weighted Average at X(n+1)p)',sep=' ') res[19,] <- c('', mylink2, qarr[2,1]) mylink2 <- paste(mylink1,'(Empirical Distribution Function)',sep=' ') res[20,] <- c('', mylink2, qarr[3,1]) mylink2 <- paste(mylink1,'(Empirical Distribution Function - Averaging)',sep=' ') res[21,] <- c('', mylink2, qarr[4,1]) mylink2 <- paste(mylink1,'(Empirical Distribution Function - Interpolation)',sep=' ') res[22,] <- c('', mylink2, qarr[5,1]) mylink2 <- paste(mylink1,'(Closest Observation)',sep=' ') res[23,] <- c('', mylink2, qarr[6,1]) mylink2 <- paste(mylink1,'(True Basic - Statistics Graphics Toolkit)',sep=' ') res[24,] <- c('', mylink2, qarr[7,1]) mylink2 <- paste(mylink1,'(MS Excel (old versions))',sep=' ') res[25,] <- c('', mylink2, qarr[8,1]) mylink1 <- 'Semi Interquartile Difference' mylink2 <- paste(mylink1,'(Weighted Average at Xnp)',sep=' ') res[26,] <- c('', mylink2, qarr[1,2]) mylink2 <- paste(mylink1,'(Weighted Average at X(n+1)p)',sep=' ') res[27,] <- c('', mylink2, qarr[2,2]) mylink2 <- paste(mylink1,'(Empirical Distribution Function)',sep=' ') res[28,] <- c('', mylink2, qarr[3,2]) mylink2 <- paste(mylink1,'(Empirical Distribution Function - Averaging)',sep=' ') res[29,] <- c('', mylink2, qarr[4,2]) mylink2 <- paste(mylink1,'(Empirical Distribution Function - Interpolation)',sep=' ') res[30,] <- c('', mylink2, qarr[5,2]) mylink2 <- paste(mylink1,'(Closest Observation)',sep=' ') res[31,] <- c('', mylink2, qarr[6,2]) mylink2 <- paste(mylink1,'(True Basic - Statistics Graphics Toolkit)',sep=' ') res[32,] <- c('', mylink2, qarr[7,2]) mylink2 <- paste(mylink1,'(MS Excel (old versions))',sep=' ') res[33,] <- c('', mylink2, qarr[8,2]) mylink1 <- 'Coefficient of Quartile Variation' mylink2 <- paste(mylink1,'(Weighted Average at Xnp)',sep=' ') res[34,] <- c('', mylink2, qarr[1,3]) mylink2 <- paste(mylink1,'(Weighted Average at X(n+1)p)',sep=' ') res[35,] <- c('', mylink2, qarr[2,3]) mylink2 <- paste(mylink1,'(Empirical Distribution Function)',sep=' ') res[36,] <- c('', mylink2, qarr[3,3]) mylink2 <- paste(mylink1,'(Empirical Distribution Function - Averaging)',sep=' ') res[37,] <- c('', mylink2, qarr[4,3]) mylink2 <- paste(mylink1,'(Empirical Distribution Function - Interpolation)',sep=' ') res[38,] <- c('', mylink2, qarr[5,3]) mylink2 <- paste(mylink1,'(Closest Observation)',sep=' ') res[39,] <- c('', mylink2, qarr[6,3]) mylink2 <- paste(mylink1,'(True Basic - Statistics Graphics Toolkit)',sep=' ') res[40,] <- c('', mylink2, qarr[7,3]) mylink2 <- paste(mylink1,'(MS Excel (old versions))',sep=' ') res[41,] <- c('', mylink2, qarr[8,3]) res[42,] <- c('Number of all Pairs of Observations', 'http://www.xycoon.com/pair_numbers.htm', lx*(lx-1)/2) res[43,] <- c('Squared Differences between all Pairs of Observations', 'http://www.xycoon.com/squared_differences.htm', sdpo) res[44,] <- c('Mean Absolute Differences between all Pairs of Observations', 'http://www.xycoon.com/mean_abs_differences.htm', adpo) res[45,] <- c('Gini Mean Difference', 'http://www.xycoon.com/gini_mean_difference.htm', gmd) res[46,] <- c('Leik Measure of Dispersion', 'http://www.xycoon.com/leiks_d.htm', bigd) res[47,] <- c('Index of Diversity', 'http://www.xycoon.com/diversity.htm', iod) res[48,] <- c('Index of Qualitative Variation', 'http://www.xycoon.com/qualitative_variation.htm', iod*lx/(lx-1)) res[49,] <- c('Coefficient of Dispersion', 'http://www.xycoon.com/dispersion.htm', sum(axmm)/lx/medx) res[50,] <- c('Observations', '', lx) print(res) a<-table.start() a<-table.row.start(a) a<-table.element(a,'Variability - Ungrouped Data',2,TRUE) a<-table.row.end(a) for (i in 1:num) { a<-table.row.start(a) if (res[i,1] != '') { a<-table.element(a,res[i,1],header=TRUE) } else { a<-table.element(a,res[i,2],header=TRUE) } a<-table.element(a,signif(as.numeric(res[i,3],6))) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable.tab')
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