Question

This data set represents the number of cups of coffee sold in a café between 8 a.m. and 10 a.m. every day for 14 days.

{10, 9, 6, 12, 4, 6, 7, 8, 15, 14, 12, 9, 10, 5}.

The difference of the values of the first and third quartiles of the data set is
.

Answer 1

6

Explanation:

The difference between the third quartile and first quartile is known as interquartile range.

The upper quartile is the median of upper half of the data.

The lower quartile is the median of lower half of the data.

Let's arrange in least to greatest:

4,5,6,6,7,8,9,9,10,10,12,12,14,15

The upper half of the data is 9,10,10,12,12,14,15

The median is the 4th number here, so 12. Thus, third quartile = 12

The lower half of the data is 4,5,6,6,7,8,9

The median is the 4th number here, so 6. Thus, first quartile = 6

Interquartile range (difference in third quartile and first quartile) = 12 - 6 = 6