Question

Calculate the five-number summary of the given data. Use the approximation method 16, 5, 7, 24, 5, 22, 13, 8, 7,21, 10, 24, 18, 11

Answer 1

Answers

5-Point Summary consists of

1. Sample Minimum = 5
2. Lower Quartile or First Quartile, Q1 = 7
3. Median = 12
4. Upper Quartile or Third Quartile, Q3 = 21
5. Sample Maximum = 24

Explanations

The ordered (in ascending order of magnitude) set of the given observations is:

i	xi
1	5
2	5
3	7
4	7
5	8
6	10
7	11
8	13
9	16
10	18
11	21
12	22
13	24
14	24

First and the last answers are trivially clear.

Median = average of the two middle observations = average of the 7^th and 8^th observations = (11 + 13)/2 = 12.

Q1 = median of the lower half of the ordered set = mid-value of first 7 values = 4^th observation = 7.

Q3 = median of the upper half of the ordered set = mid-value of last 7 values = 11^h observation = 21.

DONE