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. Fine the mean heart beats per minute for these women, choosing a suitable method.

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

Answer 1

Given data is,

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

To find the class mark of each interval $\left(x_i\right)$, the following relation is used.

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

Class size, $h$ of this data $=3$

Taking $75.5$ as assumed mean $\left(a\right)$, $d_i$ and $u_i$ are calculated as follows.

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

From the table,

$\sum f_i=30$

$\sum f_i{u}_i=4$

size of the class interval $h=3$.

Mean $=a+\left(\frac{\sum f_i{u}_i}{\sum f_i}\right)h$

$=75.5+\left(\frac{4}{30}\right)\times 3$

$=75.5+\frac{4}{10}$

$=75.5+0.4$

$=75.9$

Therefore, mean hear beats per minute for these women are $75.9$ beats per minute.