Question

Mr. Evans displays the test scores of his first period class in the box plot below.

The test scores from Mr. Evan's 3rd period class result in a 1st Quartile of 78 and an IQR that is one-third the IQR of his first period class. What value represents the value of the 3rd quartile of the scores from 3rd period?

Answer 1

I think it is the last one, have a nice day!

Answer 2

Answer: Third option is correct.

Explanation:

Since we have given that

1st Quartile of 3rd class period = 78

For 1st class period,

1st Quartile = 70

3rd Quartile = 85

IQR = Q₃-Q₁

`IQR=85-70\\\\IQR=15`

According to question,

IQR of 3rd class period is one - third of the IQR of 1st class period.

So, it becomes

`IQR_3=(1)/(3)* IQR_(1)\\\\IQR_3=(1)/(3)* 15\\\\IQR_3=5`

Now, we need to find the value of 3rd quartile of the scores from 3rd period.

`IQR_3=Q_3-Q_1\\\\5=Q_3-78\\\\5+78=Q_3\\\\Q_3=83`

Hence, Third option is correct.