Question

A university reports that the middle 50% of the SAT I math scores of its students were between 565 and 670, with half the scores above 595 and half below. a. What SAT I math scores would be considered outliers for that university? Outliers would lie below or above b. What can you say about the shape of this distribution? The distribution is probably Open Show Work Click if you would like to Show Work for this question:

Answer 1

Since middle 50% were between 565 and 670 so we have

$Q_{1}=565, Q_{3}=670$

And since half of the scores are less than 595 and half are greater than 595 so we have

$Q_{2}=595$

The lower fence is

$LF=Q_{2}-1.5(Q_{3}-Q_{1})=595-1.5\cdot (670-565)=437.5$

The upper fence is

$UF=Q_{2}+1.5(Q_{3}-Q_{1})=595+1.5\cdot (670-565)=752.5$

(a)

Outliers would lie below 437.5 or above 752.5.

(b)

The middle of both quartiles is

$\frac{Q_{1}+Q_{3}}{2}=\frac{565+670}{2}=617.5$

For a symmetrical distribution, median should be near 617.5. But it is given that median is 595. That is actual median is less than 617.5. So distribution is likely to be right skewed.