Question

Question 4
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.

$\begin{array}{cccccccc}\text{Number of heart beats per minute}& 65-68& 68-71& 71-74& 74-77& 77-80& 80-83& 83-86\\ \text{Number of women}& 2& 4& 3& 8& 7& 4& 2\end{array}$

Answer 1

We may find the class mark of each interval $\left(x_i\right)$ by using the relation:

$x_i=\frac{\text{Upper class limit + lower class limit}}{2}$

Class size h of this data = 3

Now, taking 75.5 as assumed mean $a$; we may calculate $d_i,u_i,f_i{u}_i$ as following:

$\begin{array}{cccccc}\text{Number of heart beats per minute}& \text{Number of women}{f}_i& x_i& d_i=x_i-75.5& u_i=\frac{x_i-75.5}{h}& f_i{u}_i\\ 65-68& 2& 66.5& -9& -3& -6\\ 68-71& 4& 69.5& -6& -2& -8\\ 71-74& 3& 72.5& -3& -1& -3\\ 74-77& 8& 75.5& 0& 0& 0\\ 77-80& 7& 78.5& 3& 1& 7\\ 80-83& 4& 81.5& 6& 2& 8\\ 83-86& 2& 84.5& 9& 3& 6\\ Total& 30& & & & 4\end{array}$

Now, we may observe from the table that:

$\sum f_i=30\sum f_i{u}_i=4Mean\overline{x}=a+\left(\frac{\sum f_i{u}_i}{\sum f_i}\right)\times h=75.5+\left(\frac{4}{30}\right)\times 3=75.5+0.4=75.9$

So, mean heart beats per minute for these women are 75.9 beats per minute.