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Data:
156.3 177.2 192.2 176.0 176.2 167.0 175.4 173.9 170.9 161.7 175.6 180.5 173.6 162.1 170.7 171.1 165.7 180.1 165.5 171.2 171.1 165.3 173.6 185.5 156.8 166.0 181.7 156.4 170.0 176.0 175.0 163.4 171.5 163.2 191.6 164.6 189.1 188.2 191.6 163.2 154.6 170.8 197.3 161.2 156.6 166.0 168.7 172.0 169.9 175.8 175.2 164.1 169.7 177.3 160.5 175.5 186.3 175.6 177.3 183.7 161.2 159.9 195.7 174.5 149.4 180.4 171.4 189.0 171.8 166.9 171.0 167.6 174.1 172.7 174.2 179.2 192.1 182.1 162.1 168.8 182.8 172.6 184.8 186.2 172.0 180.2 177.1 165.1 178.2 163.3 187.1 168.3 166.1 168.0 162.9 166.0 167.0 178.2 163.5 167.4 180.4 180.3 163.7 180.4 157.9 176.8 198.1 165.7 182.7 178.6 167.3 167.0 166.0 163.1 187.8 171.8 156.7 184.4 153.2 185.3 177.3 168.1 171.1 167.9 184.3 158.6 188.6 151.6 171.8 168.9 170.5 186.0 183.3 163.5 173.4 165.5 178.5 167.4 182.5 186.0 168.8 165.0 182.5 163.9 158.7 174.3 171.7 150.7 176.1 167.7 184.1 165.2 181.3 166.4 173.9 159.0 166.8 171.5 182.1 150.1 170.7 169.0 172.4 173.2 175.4 156.6 172.6 168.3 162.3 170.7 170.1 183.2 173.3 160.2 184.6 167.4 166.8 164.9 174.0 180.8 151.6 160.5 162.2 153.3 162.0 173.3 177.5 179.7 159.4 165.4 173.3 175.5 179.7 167.3 159.2 166.5 167.8 172.2 173.9 168.2 188.0 169.6 169.0 161.0 152.9 175.0 175.6 175.2 180.3 186.3 177.8 178.9 178.2 169.2 177.7 152.7 173.6 168.0 152.0 180.7 172.1 172.9 169.7 178.4 162.7 150.7 178.2 155.3 162.2 187.4 169.4 160.7 161.8 168.6 173.1 154.6 158.2 177.4 185.9 153.0 166.7 169.8 178.9 189.3 177.8 172.7 167.8 162.9 172.4 173.7 159.8 172.5 182.0 176.7 155.5 160.6 160.5 171.0 167.1 169.8 176.6 168.3 157.1 169.7 190.5 176.1 151.7 172.3 181.1 178.5 165.6 158.6 163.4 184.1 179.8 184.2 179.1 172.7 175.5 164.1 153.0 170.0 158.0 163.0 180.2 175.1 182.2 161.4 151.5 177.8 179.4 182.7 160.2 170.8 180.6 167.7 177.5 171.2 177.7 178.0 172.7 165.1 171.1 173.5 173.1 166.9 169.5 157.2 168.8 171.2 159.4 169.6 158.2 164.8 168.9 172.0 153.1 179.3 169.3 161.5 166.2 176.2 171.6 180.3 173.2 169.4 172.8 174.6 167.2 175.5 181.9 160.2 166.5 176.2 183.3 156.1 157.2 165.0 177.7 162.0 177.9 160.4 160.8 159.7 168.8 161.0 166.9 183.8 175.4 173.6 183.6 189.6 179.6 165.8 182.1 173.9 178.7 160.5 178.6 180.2 174.7 155.8 186.1 160.8 173.4 177.4 175.3 166.4 163.8 163.3 170.2 154.9 181.3 191.2 159.4 169.7 176.5 159.1 159.4 160.3 167.2 167.5 159.9 185.2 172.3 177.6 162.9 177.1 177.5 175.1 180.7 159.6 175.8 170.9 176.0 158.2 160.1 172.0 173.5 183.4 166.4 174.5 161.4 162.5 159.6 192.4 143.3 175.5 163.2 184.6 175.7 175.4 168.9 187.8 175.4 152.6 155.7 171.0 174.1 163.5 182.5 182.0 168.0 160.7 177.2 171.6 164.3 189.4 177.2 181.8 172.7 170.0 150.3 173.9 174.0 182.6 166.2 176.3 164.8 185.7 171.8 170.3 185.5 182.2 171.9 168.2 172.3 165.0 147.9 176.5 179.1 168.4 162.6 176.2 180.9 171.8 159.4 160.2 173.9 155.6 164.7 182.2 191.4 157.2 158.6 153.9 171.3 167.2 176.2 160.8 176.8 169.9 173.5 161.7 185.5 145.9 163.3 167.2 179.4 172.4 173.8 167.1 177.9 151.3 177.0 161.1 193.4 172.1 162.4 184.4 180.2 164.9 162.7 175.6 187.5 158.3 162.0 156.9 167.6 180.7 173.1 165.7 186.2 158.6 157.8 155.0 180.0 162.9 179.7 157.7 167.2 172.3 168.1 178.4 189.6 149.9 175.2 190.1 177.5 173.8 158.0 176.1 166.5 170.8 163.5 162.7 166.4 192.1 174.5 172.7 189.8 165.3 166.0 170.1 153.5 178.7 177.4 162.3 178.7 180.4 167.5 184.8 181.6 179.6 165.8 164.6 182.5 157.6 178.0 164.7 172.5 172.1 149.2 164.9 163.2 165.1 187.0 176.4 163.1 176.4 161.1 173.1 162.3 173.0 173.8 165.4 180.1 173.7 157.8 178.1 180.7 162.4 161.4 170.8 149.9 179.3 175.1 174.4 169.3 163.9 168.8 166.0 175.6 176.9 172.2 165.3 176.4 159.0 164.2 174.6 178.7 171.5 171.9 162.2 181.4 172.5 176.8 178.7 173.2 169.8 183.9 160.6 162.1 171.8 177.2 172.8 157.3 157.5 161.7 168.6 160.6 164.1 176.8 172.6 180.5 155.5 177.8 166.4 157.5 170.0 173.9 163.0 167.0 170.4 168.0 144.0 167.5 172.1 175.0 163.6 176.3 169.7 164.9 172.8 162.0 168.5 176.6 185.7 187.8 167.5 161.5 178.8 177.6 171.4 175.7 174.3 182.9 161.5 188.0 176.1 168.9 171.0 150.3 151.0 160.2 178.2 189.5 154.7 166.8 170.2 167.9 197.2 173.0 183.4 163.6 164.0 177.5 165.3 156.2 172.6 169.1 168.9 161.9 162.4 160.0 180.4 156.2 180.8 196.7 152.2 167.3 184.7 184.2 176.5 155.8 156.7 186.1 162.3 192.6 169.8 173.4 169.4 170.9 165.7 172.1 174.0 176.3 171.4 174.8 155.7 145.4 170.3 156.5 177.9 162.0 182.3 164.3 168.0 155.8 167.3 158.2 157.8 175.1 168.2 165.5 171.0 169.0 169.5 170.6 163.5 174.6 183.0 157.3 155.5 171.9 153.8 164.7 173.0 163.7 182.6 183.0 168.9 172.9 162.7 162.8 178.1 152.1 179.8 181.7 168.8 170.5 178.9 175.8 178.5 168.0 179.8 179.5 166.8 175.2 169.8 159.5 166.1 168.3 177.4 175.9 170.4 175.1 154.5 166.7 166.1 160.9 175.2 172.4 167.2 166.6 185.9 181.7 174.5 149.0 176.3 193.6 160.5 156.0 166.7 165.1 178.1 178.9 168.4 175.6 176.9 182.8 170.2 175.2 181.4 160.3 182.8 166.7 161.0 164.0 181.8 161.3 183.5 160.8 168.3 158.4 165.1 159.0 169.6 183.5 161.8 185.0 169.9 151.1 167.5 164.3 167.3 165.9 170.3 184.6 165.6 176.8 178.1 172.2 162.2 160.8 183.1 167.6 173.2 167.7 195.5 201.3 174.6 161.7 163.1 185.0 168.0 169.0 160.5 147.9 152.3 168.8 145.9 150.2 189.9 159.8 177.1 162.4 164.8 157.4 165.6 158.0 152.1 185.3 167.7 178.6 165.3 157.6 194.9 168.3 176.6 158.0 157.4 169.9 177.3 179.5 171.5 178.4 167.4 159.7 166.3 183.6 160.4 169.8 183.3 168.8 157.9 181.8 170.0 173.8 171.9 175.5 168.9 176.3 182.4 186.5 172.3 165.5 182.2 179.2 182.8 177.9 172.8 160.2 167.1 160.7 176.8 156.0 165.7 175.3 175.9 162.3 162.2 174.4 161.3 184.1 166.2 172.9 165.0 178.4 172.1 156.2 188.8 180.1 165.3 177.9 189.3 174.1 178.7 172.1 186.0 173.1 174.9 168.5 150.9 175.6 164.6 165.5 178.3 164.1 175.4 143.9 179.5 177.5 159.5 161.9 172.5 165.0 182.0 171.5 178.3 175.3 170.7 160.8 166.6 174.0 192.0 176.4 169.0 150.2 160.5 165.7 164.9 159.3 163.9 179.5 177.0 171.3 177.8 162.9 153.3 169.0 164.0 175.9 159.3 168.1 161.8 169.5 178.7 180.3 170.0 157.8 174.6 163.5 165.6 146.7 168.0 155.3 158.3 161.7 168.7 179.5 171.9 175.1 180.8 177.1 173.6 172.9 185.4 164.7 159.9 181.7 172.6 173.7 173.5 171.9 161.2 168.2 155.3 178.1 176.9 176.0 179.9 184.8 168.4 160.7 156.2 190.0 187.3 152.1 149.6
Sample Range:
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R Code
num <- 50 res <- array(NA,dim=c(num,3)) 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 <- hyperlink('http://www.xycoon.com/difference.htm','Interquartile Difference','') mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_1.htm','(Weighted Average at Xnp)',''),sep=' ') res[18,] <- c('', mylink2, qarr[1,1]) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ') res[19,] <- c('', mylink2, qarr[2,1]) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_3.htm','(Empirical Distribution Function)',''),sep=' ') res[20,] <- c('', mylink2, qarr[3,1]) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ') res[21,] <- c('', mylink2, qarr[4,1]) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ') res[22,] <- c('', mylink2, qarr[5,1]) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_6.htm','(Closest Observation)',''),sep=' ') res[23,] <- c('', mylink2, qarr[6,1]) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ') res[24,] <- c('', mylink2, qarr[7,1]) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_8.htm','(MS Excel (old versions))',''),sep=' ') res[25,] <- c('', mylink2, qarr[8,1]) mylink1 <- hyperlink('http://www.xycoon.com/deviation.htm','Semi Interquartile Difference','') mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_1.htm','(Weighted Average at Xnp)',''),sep=' ') res[26,] <- c('', mylink2, qarr[1,2]) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ') res[27,] <- c('', mylink2, qarr[2,2]) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_3.htm','(Empirical Distribution Function)',''),sep=' ') res[28,] <- c('', mylink2, qarr[3,2]) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ') res[29,] <- c('', mylink2, qarr[4,2]) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ') res[30,] <- c('', mylink2, qarr[5,2]) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_6.htm','(Closest Observation)',''),sep=' ') res[31,] <- c('', mylink2, qarr[6,2]) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ') res[32,] <- c('', mylink2, qarr[7,2]) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_8.htm','(MS Excel (old versions))',''),sep=' ') res[33,] <- c('', mylink2, qarr[8,2]) mylink1 <- hyperlink('http://www.xycoon.com/variation1.htm','Coefficient of Quartile Variation','') mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_1.htm','(Weighted Average at Xnp)',''),sep=' ') res[34,] <- c('', mylink2, qarr[1,3]) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ') res[35,] <- c('', mylink2, qarr[2,3]) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_3.htm','(Empirical Distribution Function)',''),sep=' ') res[36,] <- c('', mylink2, qarr[3,3]) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ') res[37,] <- c('', mylink2, qarr[4,3]) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ') res[38,] <- c('', mylink2, qarr[5,3]) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_6.htm','(Closest Observation)',''),sep=' ') res[39,] <- c('', mylink2, qarr[6,3]) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ') res[40,] <- c('', mylink2, qarr[7,3]) mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_8.htm','(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) 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,hyperlink(res[i,2],res[i,1],''),header=TRUE) } else { a<-table.element(a,res[i,2],header=TRUE) } a<-table.element(a,res[i,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable.tab')
Compute
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Raw Input
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Raw Output
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Computing time
0 seconds
R Server
Big Analytics Cloud Computing Center
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