Question

The table shows your scores on $9$ out of $10$ quizzes that are each worth $20$ points. What score do you need on the final quiz to have a mean score of at least $17$ points?

Answer 1

Step 1 : Form an inequality

Let the score in final quiz $=x$

From the given data in table the total score on quiz

$$\begin{gathered} =(15+14+16+19+18+19+20+15+16+x) \\ =152+x \end{gathered}$$

Mean value$=\frac{\text{sum of all terms}}{\text{number of total terms}}$

Mean of total score $=\frac{(152+x)}{10}$

As given total score should be at least $17$ so inequality becomes:
$\therefore \frac{(152+x)}{10}\ge 17$

Step 2 : solve the inequality

We have,

$\Rightarrow \frac{(152+x)}{10}\ge 17$

$\Rightarrow 152+x\ge 17\times 10$ [ Multiply both sides by $10$ ]

$\Rightarrow x\ge 170–152$ [ Subtract $152$ from both sides ]
$\therefore x\ge 18$
Hence, we need to score at least $18$ points