Center and Spread in Action

You already know how to calculate medianThe middle value of a data set when the values are ordered from least to greatest., modeThe value or values that occur most often in a data set., rangeThe difference between the greatest and least values in a data set., and interquartile rangeThe distance between the first quartile and the third quartile, showing the spread of the middle half of a data set. on a clean data set. But what happens when a data set has an even number of values, like 4, 6, 7, 9? There's no single middle value, so the median is the average of the two middle values: (6 + 7) ÷ 2 = 6.5. And what if every value in a data set is different, like 2, 5, 8, 11, 14? Then there's no mode at all, and that's a perfectly valid answer, not a mistake.

Range and interquartile range still work the same way in these cases: range is greatest minus least, and interquartile range is the third quartile minus the first quartile. Practicing these edge cases now means you won't freeze up on them later, when a real data set doesn't cooperate with a clean, odd-numbered, single-mode example.

Adapted from Studio Aletheia's The Center for Quantitative Studies curriculum library, drawing on mathematical resources and the SC CCR Mathematics Standards.