Discuss how calculating the range, variance, and standard deviation of a data set can help to spot differences in two data sets with the same mean

What will be an ideal response?

If you had two data sets consisting of test scores, each with a mean of 85%,you could conclude that each set of test scores were similar. However, if the range, variance, and standard deviation were also calculated to describe how the data is dispersed, you could reveal two completely different sets of test scores. Perhaps one data set had a majority of scores below 75% with a few scores above 95% and the other set could have most of the scores around the 82%-87% range.