Question

Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarised as follows. Find the mean heart beats per minute for these women, choosing a suitable method.

Number of heart beats per minute	$65-68$	$68-71$	$71-74$	$74-77$	$77-8$0	$80-83$	$83-86$
Number of women	$2$	$4$	$3$	$8$	$7$	$4$	$2$

Answer 1

Class interval	Mid value $\left(x_i\right)$	$\left(f_i\right)$	$u_i=\frac{x_i-75.5}{3}$	$f_i{u}_i$
$65-68$	$66.5$	$2$	$-3$	$-6$
$68-71$	$69.5$	$4$	$-2$	$-8$
$71-74$	$72.5$	$3$	$-1$	$-3$
$74-77$	$75.5$	$8$	$0$	$0$
$77-80$	$78.5$	$7$	$1$	$7$
$80-83$	$81.5$	$4$	$2$	$8$
$83-86$	$84.5$	$2$	$3$	$6$
Total		$30$		$4$

Lets take assumed mean, $A$ as $75.5$

Class interval $=3$

$\therefore u_i=\frac{x_i-A}{h}=\frac{x_i-75.5}{3}$

$\overline{x}=A+h\frac{\sum f_i{u}_i}{\sum f_i}=75.5+3\times \frac{4}{30}=75.5+0.4=75.9$

Hence, the mean heart beats per minute for these women is $75.9$