# Question #c1800

Aug 11, 2016

mean = $32.6$

#### Explanation:

This is finding a mean from grouped data. We do not know the actual scores, but we assume they are uniformly spread across each interval.

We need the midpoint of each interval, as this will be used to represent the whole interval.

We do not know the width of the last interval, so an assumption is required.

Let the midpoint of each interval be $x$.
The number of students in each interval is $f$

Mean= $\frac{\Sigma f x}{\Sigma f}$

= $\frac{4 \times 5 + 6 \times 15 + 10 \times 25 + 15 \times 35 + 8 \times 45 + 7 \times 55}{50}$

=$\frac{1630}{50} = 32.6$