Question

A student takes ten exams during a semester and receives the following grades: 90, 85, 97, 76, 89, 58, 82, 102, 70, and 67. Find the five-number summary used in a boxplot.

Answer 1

Quartile 1: 70 Median: 83.5 Quartile 3: 90 Minimum: 58 Maximum: 102

Answer 2

58, 70, 83.5, 90, 102

Explanation:

What is five number of summary : The distribution of the ordered observation is divided into five summaries that is minimum, first quartile, median, third quartile and maximum.

Formula of five number summary :

Minimum : First element of set

First quartile : (n+1)/4

Median : (n+1)/2

Third quartile : 3(n+1)/4

Maximum : Last element of set

The five number summary of grades (90, 85, 97, 76, 89, 58, 82, 102, 70, 67)

Minimum : 58

First quartile : 70

Median : 83.5

Third quartile : 90

Maximum : 102