Question

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

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

Answer 1

To find the class mark $\left(x_i\right)$ for each interval, using the following relation:
$\left(x_i\right)=\frac{\text{Upper class limit}+\text{Lower class limit}}{2}$
Class size, $h$, of this data $=3$
Considering $75.5$ as assumed mean $\left(a\right),d_i,u_i,f_i{u}_i$ are calculated as follows:
From the table:
$\sum f_i=30$
$\sum f_i{u}_i=4$
Mean, $\overline{x}=a+\left(\frac{\sum f_i{u}_i}{\sum f_i}\right)\times h$
$=75.5+4/30\times 3$
$=75.5+0.4=75.9$
$\therefore$ mean heart beats per minute for these women are $76$ beats per minute.