91Ó°ÊÓ

The frequency distribution of the number of births that occur on different days of the week is provided.

The relative frequency of a class interval in a grouped frequency distribution is obtained using the given formula:

$\text{Relative}\text{frequency}\text{of}\text{a}\text{class}\text{interval}=\frac{\text{Frequency}\text{of}\text{a}\text{class}\text{interval}}{\text{Sum}\text{of}\text{all}\text{frequencies}}×100\%$

The table below shows the frequencies of births on the days of the week

The sum of all frequencies is shown below:

$$\begin{gathered} \text{Sum}\text{of}\text{all}\text{frequencies}=52+66+72+57+57+43+53 \\ =400 \end{gathered}$$

Using the formula mentioned above, the relative frequencies for the different categories are calculated as shown below:

$$\begin{gathered} \text{Relative}{\text{freq}}_1=\frac{52}{400}×100\% \\ =13\% \\ \text{Relative}{\text{freq}}_2=\frac{66}{400}×100\% \\ =17\% \end{gathered}$$

$$\begin{gathered} \text{Relative}{\text{freq}}_3=\frac{72}{400}×100\% \\ =18\% \\ \text{Relative}{\text{freq}}_4=\frac{57}{400}×100\% \\ =14\% \end{gathered}$$

$$\begin{gathered} \text{Relative}{\text{freq}}_5=\frac{57}{400}×100\% \\ =14\% \\ \text{Relative}{\text{freq}}_6=\frac{43}{400}×100\% \\ =11\% \end{gathered}$$

$$\begin{gathered} \text{Relative}{\text{freq}}_7=\frac{53}{400}×100\% \\ =13\% \end{gathered}$$

Thus, the relative frequency distribution is constructed as follows:

It can be observed that almost all days have an approximately equal relative frequency.

Therefore, it can be said that the births occur equally frequently on different days of the week.