Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. 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 .

Explanation:

Step1: Sort the data set

Sorted data: $4, 5, 6, 6, 7, 8, 9, 9, 10, 10, 12, 12, 14, 15$

Step2: Find median (split data)

Median position: $\frac{14}{2}=7$, so median is average of 7th & 8th values: $\frac{9+9}{2}=9$. Lower half: $4,5,6,6,7,8,9$; Upper half: $9,10,10,12,12,14,15$

Step3: Calculate first quartile ($Q_1$)

$Q_1$ is median of lower half: 4th value = $6$

Step4: Calculate third quartile ($Q_3$)

$Q_3$ is median of upper half: 4th value = $12$

Step5: Compute difference of $Q_3-Q_1$

$12-6=6$

Answer:

6