Question

Consider the following random sample of test scores (in percentages) from a biology final exam.

95      65      70      75      74      86      82

95      45      80      72      70      78      72      80

1. Find the five-number summary for this data set.

2. Make a box-and-whisker plot.

3. Find the interquartile range.

Answer 1

Solution:

Let's sort the data from shortest to largest scores

45, 65, 70, 70, 72, 72, 74, 75, 78, 80, 80, 82, 86, 95, 95

Total no. Of score = 15

Five number of summary can be calculated as

Minimum = 45

Quartile 1 = (n+1)/4 = (15+1)/4 =4 th value i.e. 70

Median = (n+1)/2 = (15+1)/2 = 8th value i.e. 75

Quartile 3 = 3*(n+1)/4 = 3*(15+1)/4 = 12th value i.e. 82

Maximum value = 95

So five number summary is 45, 70, 75, 82, 95

Solution(b)

Solution(c)

Interquartile range can be calculated as

Interquartile range = Quartile 3 - Quartile 1 = 82 -70 = 12