Chapter 15.1, Problem 17WE

To determine

Find the mean score of the $90$ students.

Answer to Problem 17WE

  $77.22$

Explanation of Solution

Given information:

At high school $A,$ the mean score of $50$ students on a science test is $75$ . At high school $B$ , the mean score of $40$ students on the same test is $80$ .

Calculation:

Let the scores of $50$ students be $A_1$ . Then, mean score will be $Mean=\frac{A_1}{50}$ .

Substitute $75$ for mean in the formula.

  $75=\frac{A_1}{50}$

Multiply each side of the equation by $50$ and simplify.

  $\begin{array}{l}50\left(75\right)=50\left(\frac{A_1}{50}\right)\\ 3750=A_1\end{array}$

The scores of $50$ student is $3750$ .

Find the scores of $40$ students.

Assume the scores of $40$ students be $A_2$ . Then, mean score will be $Mean=\frac{A_2}{40}$ .

Substitute $80$ for mean in the formula.

  $80=\frac{A_2}{40}$

Multiply each side of the equation by $40$ and simplify.

  $\begin{array}{l}40(80)=40\left(\frac{A_2}{40}\right)\\ 3200=A_2\end{array}$

The scores of $40$ students is $3200$ .

The mean score of $90$ students= $\frac{Thescoreof50students+Thescoresof40students}{90}$

Substitute $3750$ for the scores of $50$ students, and $3200$ for the score of $40$ students in the equation.

Mean score of $90$ students $=\frac{3750+3200}{90}$

  $\begin{array}{l}=\frac{6950}{90}\\ \approx 77.22\end{array}$

Hence, the mean score of $90$ students is about $77.22$ .