Question

6) If a school has 354 students with an IQ between 100 and 130, about how many students does the whole school have?

Answer 1

`IQR= Q_3 -Q_1 = 130-100=30`

We know that below the third quartile we have 75% of the values and below the first quartile we have 25% of the values. Then between the third and the first quartile we will have 75-25%=50% of the values.

And then we can apply the following proportion rule:

`(354)/(50) =(x)/(100)`

And solving for x we got:

`x = 100 ((354)/(50))=708`

So then the total of students is approximately 708

Explanation:

We know that 354 students are between 100 and 130 so then the interquartile range is:

`IQR= Q_3 -Q_1 = 130-100=30`

We know that below the third quartile we have 75% of the values and below the first quartile we have 25% of the values. Then between the third and the first quartile we will have 75-25%=50% of the values.

And then we can apply the following proportion rule:

`(354)/(50) =(x)/(100)`

And solving for x we got:

`x = 100 ((354)/(50))=708`

So then the total of students is approximately 708