Mean, median and mode

The median is the middle value: half of the values are below it. For a grouped table we work it out in three steps. The ages of 40 visitors at a school fair give the cumulative table: less than 10 → 0, less than 20 → 5, less than 30 → 14, less than 40 → 26, less than 50 → 36, less than 60 → 40. Step 1: the rank of the median is total ÷ 2 = 40 ÷ 2 = 20. Step 2: find where the cumulative frequency first reaches 20: it is 14 below 30 and 26 below 40, so the median is in the class 30–. Step 3: use proportion. The 20th value is 20 − 14 = 6 values into the class, and the class holds 26 − 14 = 12 values, so it is 6/12 of the way along the class: median = 30 + 6/12 × 10 = 35. On the curve: draw a horizontal line at height 20 to the curve and go down to the axis, reading 35. Be careful: the rank 20 is a count, not an age; the median is the age 35.