Define the measures of dispersion and which type of variables can they be applied to?

Question

What will be an ideal response?

Answer 1

The variation ratio is a very simple measure of dispersion that you can use whenever you have data measured at the nominal or ordinal level. The measure of dispersion for this type of data, the variation ratio, is based on the mode. The variation ratio (VR) simply measures the extent to which the observations are not concentrated in the modal category of the variable. More specifically, it is the proportion of cases not in the modal category of the variable.
The range is the difference between the highest score in the distribution and the lowest score:
Range = highest value – lowest value. The range can be used with interval/ratio level variables:
the interquartile range (IQR). In calculating the interquartile range, we still take the difference between two scores, but rather than taking the difference between the highest and lowest scores, in the IQR we take the difference between the score at the 75th percentile (the third quartile or Q3) and the score at the 25th percentile (the first quartile or Q1). Note that since we are taking the range of scores between the 75th and 25th percentiles, this range covers the dispersion at the middle 50 percent of our distribution. In other words, one-half of all our scores can be found between the 75th and 25th percentiles and the IQR measures the dispersion within those two boundaries.
The variance is the average squared difference of each score in a set of scores from the mean of those scores.
The variance is the standard deviation squared while the standard deviation is the square root of the variance. The standard deviation standardizes the scores so that they are easier to interpret and are comparable across groups. The variance and standard deviation are the two most frequently used measures of dispersion for interval/ratio-level data.