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

Let us assume the mean as $A=75.5$.

$x_i=\frac{(Upperlimit+Lowerlimit)}{2}$

$Classsize\left(h\right)=3$

Now, will determine the $u_i$and $f_i{u}_i$ as follows:

Class Interval	Number of women $\left(fi\right)$	Mid-point $\left(xi\right)$	$ui=(xi–75.5)/h$	$fiui$
$65-68$	$2$	$66.5$	$-3$	$-6$
$68-71$	$4$	$69.5$	$-2$	$-8$
$71-74$	$3$	$72.5$	$-1$	$-3$
$74-77$	$8$	$75.5$	$0$	$0$
$77-80$	$7$	$78.5$	$1$	$7$
$80-83$	$4$	$81.5$	$3$	$8$
$83-86$	$2$	$84.5$	$3$	$6$
	$Sumfi=30$			$Sumfiui=4$

The mean formula is

$Mean=\mathrm{x̄}=A+h\sum f_i{u}_i/\sum f_i$

$=75.5+(12/30)$

$=75.5+2/5$

$=75.5+0.4$

$=75.9$

Therefore, the mean heartbeats per minute for these women is $75.9$.