Question 19 - Set 9 - Try Out - Quantitative Knowledge - SNBT

Number 19

The average biology score in a class of $50$ students is $70$ . If the average score of male students is $76$ and the number of female students is $4$ more than the number of male students, then the average score of female students in the class is...

$64$

$64.88$

$65.09$

$65.20$

$65.34$

Explanation

Finding the Number of Male and Female Students

It is known that the total number of students is $50$ . Let $n_L$ be the number of male students and $n_P$ be the number of female students. It is also known that the number of female students is $4$ more than the number of male students, so:

n_P = n_L + 4

Since the total number of students is $50$ , then:

\begin{aligned} n_L + n_P &= 50 \\ n_L + (n_L + 4) &= 50 \\ 2n_L + 4 &= 50 \\ 2n_L &= 46 \\ n_L &= 23 \end{aligned}

So the number of female students is:

n_P = 23 + 4 = 27

Calculating Total Scores

Given that the average score of male students ( $\bar{x}_L$ ) is $76$ . Then the total score of male students is:

\sum x_L = n_L \times \bar{x}_L = 23 \times 76 = 1748

Given that the average score of the entire class ( $\bar{x}_{total}$ ) is $70$ . Then the total score of the entire class is:

\sum x_{total} = 50 \times 70 = 3500

Calculating the Average Score of Female Students

The total score of female students can be found by subtracting the total score of male students from the total score of the class:

\sum x_P = 3500 - 1748 = 1752

Thus, the average score of female students ( $\bar{x}_P$ ) is:

\bar{x}_P = \frac{\sum x_P}{n_P} = \frac{1752}{27} \approx 64.88

So, the average score of female students is $64.88$ .

Command Palette

Number 19

Explanation

Finding the Number of Male and Female Students

Calculating Total Scores

Calculating the Average Score of Female Students