Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. the 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 there are 14 data - points, the median is the average of the 7th and 8th ordered values. So, $Q2=\frac{9 + 9}{2}=9$.

Step3: Find the lower half and Q1

The lower half of the data set is $4,5,6,6,7,8,9$. Since there are 7 data - points, the median of the lower half (Q1) is the 4th value. So, $Q1 = 6$.

Step4: Find the upper half and Q3

The upper half of the data set is $9,10,10,12,12,14,15$. Since there are 7 data - points, the median of the upper half (Q3) is the 4th value. So, $Q3 = 12$.

Step5: Calculate the inter - quartile range (IQR)

$IQR=Q3 - Q1=12−6 = 6$

Answer:

$6$