# ::Free Statistics and Forecasting Software::

v1.1.23-r7
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### :: Variability - Free Statistics Software (Calculator) ::

All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

This free online software (calculator) computes the following statistics: absolute range, relative range, variance, standard error, coefficient of variation, mean squared error, mean absolute deviation, median absolute deviation, mean squared deviation, interquartile difference, semi interquartile difference, coefficient of quartile variation, number of pairs of observations, squared differences between observations, mean absolute differences between observations, Gini mean difference, Leik measure of dispersion, index of diversity, index of qualitative variation, and coefficient of dispersion.

Enter (or paste) your data delimited by hard returns.

 Send output to: Browser Blue - Charts White Browser Black/White CSV MS Excel MS Word Data (click to load default data) 41086 39690 43129 37863 35953 29133 24693 22205 21725 27192 21790 13253 37702 30364 32609 30212 29965 28352 25814 22414 20506 28806 22228 13971 36845 35338 35022 34777 26887 23970 22780 17351 21382 24561 17409 11514 31514 27071 29462 26105 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698 Sample Range:(leave blank to include all observations) From: To:

Click here to edit the underlying code of this R Module.

 Source code of R module 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")
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 Cite this software as: Wessa P., (2012), Variability (v1.0.5) in Free Statistics Software (v1.1.23-r7), Office for Research Development and Education, URL http://www.wessa.net/rwasp_variability.wasp/ The R code is based on : Borghers, E, and P. Wessa, Statistics - Econometrics - Forecasting, Office for Research Development and Education, http://www.xycoon.com/
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 To cite Wessa.net in publications use:Wessa, P. (2013), Free Statistics Software, Office for Research Development and Education, version 1.1.23-r7, URL http://www.wessa.net/ © All rights reserved. Academic license for non-commercial use only. The free use of the scientific content, services, and applications in this website is granted for non commercial use only. In any case, the source (url) should always be clearly displayed. Under no circumstances are you allowed to reproduce, copy or redistribute the design, layout, or any content of this website (for commercial use) including any materials contained herein without the express written permission. Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. We make no warranties or representations as to the accuracy or completeness of such information (or software), and it assumes no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site. Software Version : 1.1.23-r7Algorithms & Software : Patrick Wessa, PhDServer : www.wessa.net
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