Question

Find the mean for the given frequency distribution table.

Class - Interval	Frequency
$0-4$	$3$
$5-9$	$5$
$10-14$	$7$
$15-19$	$4$
$20-24$	$6$
	$N=24$

Answer 1

To find the mean, first we have to find the mid-point of each class interval. Mid-point of each class interval. Mid-point of $0-4=(0+4)/2=2$; mid-point of $5-9=(5+9)/2=7$ and the like. Denote the mid-point of the class interval by x. Write down the frequencies f corresponding to each class interval.

Class interval	Mid-point of CI	(x) Frequency (f)	$fx$
$0-4$	$2$	$3$	$6$
$5-9$	$7$	$5$	$35$
$10-14$	$12$	$7$	$84$
$15-19$	$17$	$4$	$68$
$20-24$	$22$	$6$	$132$
		$N=25$	$\sum fx=325$

Multiply f and x to get $fx$. Add all $fx$ and find out $\sum fx$. Now the mean is calculated using the formula.
$\overline{X}=\frac{\text{sum of all scores}}{\text{total number of scores}}=\frac{\sum fx}{N}$
Thus we get
$\overline{X}=\frac{\sum fx}{N}=\frac{325}{25}=13$.
Therefore mean is $13$.