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

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

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

Answer

Explanation:

Step1: Sort the data set

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

Step2: Find the median

Since there are 14 data - points, the median is the average of the 7th and 8th ordered values. Median $=\frac{9 + 9}{2}=9$.

Step3: Find the first quartile ($Q_1$)

The lower half of the data set is {4, 5, 6, 6, 7, 8, 9}. Since there are 7 data - points, the first quartile is the 4th value. So, $Q_1 = 6$.

Step4: Find the third quartile ($Q_3$)

The upper half of the data set is {9, 10, 10, 12, 12, 14, 15}. Since there are 7 data - points, the third quartile is the 4th value. So, $Q_3 = 12$.

Step5: Calculate the inter - quartile range

Inter - quartile range (IQR)=$Q_3 - Q_1$. So, $IQR=12 - 6 = 6$.

Answer:

6