Question

Lesson 33: Measures of Variability Rosario recorded the weights of 2 litters of puppies 4 weeks after their births. The interquartile for litter A was 3, and the interquartile range for litter B was 5. Which of the following statements must be true? range A. The weights of litter A vary less than the weights of litter B. B. The weights of litter A vary more than the weights of litter B. C. The median weight of the puppies in litter A is less than that of litter B. D. The least weight of litter A is greater than the least weight of litter B. Use the two data sets to answer the questions below. Data set A: 15, 23, 11, 6, 20

Answer 1

8) The interquartile range for A is less than that of B. This means data in A vary less than in B.

Answer is A

9) The interquartile range is given as

`\begin{gathered} Q_3-Q_{1\text{ }}\text{where} \\ Q_3term=\text{ third quartile} \\ Q_1term=\text{ First quartile} \\ Q_{3\text{ }}term=\text{ }(3)/(4)(n+1)\text{ where} \\ n\text{ is frequency =5} \\ Q_3term=\text{ }(3)/(4)(5+1)=4(1)/(2) \\ Q_1term=\text{ }(1)/(4)(5+1)=1(1)/(2) \end{gathered}`
`\begin{gathered} To\text{ get the interquartile range, we arrange the data in ascending order to be} \\ A\colon\text{ 6,11,15,20,23} \\ TheQ_1in\text{ the dataset lies halfway between the 1st and 2nd t}erm\text{ (1}(1)/(2)\text{) } \\ \text{Thus it is given as the midpoint = }(6+11)/(2)=(17)/(2)=8.5 \\ \text{The Q}_3\text{ lie between the 4th and 5th term, thus, }(20+23)/(2)=(43)/(2)=21.5 \end{gathered}`

Thus, the interquartile range = 21.5 - 8.5 = 13

`\begin{gathered} To\text{ get the interquartile range, we arrange the data in ascending order to be} \\ B\colon\text{ 9,10,14,15,18} \\ TheQ_1in\text{ the dataset lies halfway between the 1st and 2nd t}erm\text{ (1}(1)/(2)\text{) } \\ \text{Thus it is given as the midpoint = }(9+10)/(2)=(19)/(2)=9.5 \\ \text{The Q}_3\text{ lie between the 4th and 5th term, thus, }(15+18)/(2)=(33)/(2)=16.5 \end{gathered}`

Thus, the interquartile range = 16.5 - 9.5 = 7