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

\[4,5,6,6,7,8,9,9,10,10,12,12,14,15\]

Step2: Find the median (Q2)

Since \(n = 14\) (even), \(Q2=\frac{9 + 9}{2}=9\)

Step3: Find the lower - half data set

The lower - half data set is \[4,5,6,6,7,8,9\], and its median (Q1) is \(6\)

Step4: Find the upper - half data set

The upper - half data set is \[9,10,10,12,12,14,15\], and its median (Q3) is \(12\)

Step5: Calculate the inter - quartile range

\(Q3 - Q1=12 - 6 = 6\)

Answer:

6