Earlier this year, this column explored two ways to describe data dispersion: trimmed means and weighted averages. Those two are siblings in a large family. Others members of the family include the inter-quartile range, the mode and the range. Those three I explain here and in a later column I will turn to standard deviations. The family of mathematical descriptors makes a difference to general counsel who want to master business-speak and who want to extract the most regarding their department's data.
Start with inter-quartile calculations. When you order a set of numbers from largest to smallest, the middle number in that ranking is the median. Midway between the median and the lowest number stands the first quartile figure; midway between the median and the highest figure stands the third quartile figure. The difference between the first quartile and the third quartile becomes the inter-quartile difference. Average the first and third quartile figures and you have the inter-quartile mean. Inter-quartiles avoid the unusual and misleading data points at either end of a ranked list.