a group of 8 friends participated in a charity run, and the number of kilometers each person completed is…

a group of 8 friends participated in a charity run, and the number of kilometers each person completed is recorded below in kilometers: 7, 5, 12, 9, 10, 8, 15, 6. the event organizers want to analyze the running distances and determine how spread out the data is. find the first quartile ($q_1$) and third quartile ($q_3$) for the running distances. use the keypad to enter your answer in the box. the first quartile of the data set is . the third quartile of the data set is .

a group of 8 friends participated in a charity run, and the number of kilometers each person completed is recorded below in kilometers: 7, 5, 12, 9, 10, 8, 15, 6. the event organizers want to analyze the running distances and determine how spread out the data is. find the first quartile ($q_1$) and third quartile ($q_3$) for the running distances. use the keypad to enter your answer in the box. the first quartile of the data set is . the third quartile of the data set is .

Answer

Answer:

The first quartile of the data set is 6.5. The third quartile of the data set is 11.5.

Explanation:

Step1: Arrange data in ascending order

5, 6, 7, 8, 9, 10, 12, 15

Step2: Calculate position of quartiles

For $Q_1$: $n = 8$, position $= \frac{n + 1}{4}=\frac{8+1}{4}=2.25$. So $Q_1$ is between 2nd and 3rd values. $Q_1=6+(7 - 6)\times0.25 = 6.5$. For $Q_3$: position $= \frac{3(n + 1)}{4}=\frac{3\times(8 + 1)}{4}=6.75$. So $Q_3$ is between 6th and 7th values. $Q_3=10+(12 - 10)\times0.75=11.5$.