Question

Consider the following stem and leaf display.

3 | 1 1 1 4 5

4 | 4 6 7

5 | 0 0 4 5 6 6 8 9

6 | 1 3 3 6

Find the 3^rd quartile.

Answer 1

The given values are arranged here in ascending order as:

31, 31, 31, 34, 35, 44, 46, 47, 50, 50, 54, 55, 56, 56, 58, 59, 61, 63, 63, 66.

There are a total of 20 numbers here.

The third quartile value is computed as the median of the second half of values that is the last 10 values. Therefore, the third quarile value would be given as the 0.75*(n + 1) = 0.75*21 = 15.75^th value

Therefore the third quartile value here is computed as:
= a₁₅ + (a₁₆ - a₁₅)*0.75 = 58 + 0.75*(59 - 58) = 58.75

Therefore 58.75 is the required third quartile value here.