Median

The median is the value that divides an arranged series into two equal halves: half the values are below it, half above. It depends on position, so it is a positional average, and it is not strongly affected by extreme values.

Ungrouped data: arrange the values in order; the median is the ((N + 1) ÷ 2)th item. For 9 values, it is the 5th.

Grouped data:

M = l + (i ÷ f) × (N/2 − c)

• l: the lower limit of the median class (the class containing the N/2th item);
• i: the class interval;
• f: the frequency of the median class;
• c: the cumulative frequency of the class just before the median class.

Example: N = 40, so N/2 = 20. The cumulative frequencies show that the 20th item lies in the class 50-60, which has f = 10; the cumulative frequency before it is c = 14. So M = 50 + (10 ÷ 10) × (20 − 14) = 56.