Question 17

Explanation

Defining Variables

Let:

• $\bar{x} = 62$ be the combined average.
• $\bar{x}_L = 50$ be the average score of male students.
• $\bar{x}_P = 70$ be the average score of female students.
• $n_L$ be the number of male students.
• $n_P$ be the number of female students.

Using the Combined Average Formula

The formula for the combined average is:

Substitute the known values:

Multiply both sides by $(n_L + n_P)$:

Group like terms:

Determining the Ratio

To find the ratio $n_L : n_P$, rearrange the equation:

Simplify the fraction by dividing both numerator and denominator by $4$:

Thus, the ratio of the number of male students to female students is $2 : 3$.