Word Problems Involving the Mean of a Data Set

Example 1 :

When a number $x$ is added to the data set $\text{4, 8, 20, 25, 32,}$ the new mean is $15$ . Find the value of $x$ .

Including $x$ , there are 6 numbers in the set. Write an equation for calculating the mean with the unknown value.

$\frac{4+8+20+25+32+x}{6}=15$

Simplify.

$\frac{89+x}{6}=15$

Multiply both sides by $6$ .

$89+x=90$

Subtract $89$ from both sides.

$x=1$

Example 2 :

Kalief's scores on his first four History tests were $\text{80, 85, 88 and 95}$ .

To get an $A$ in the class, he needs to have an average of $90$ or better.

What score must he make on the fifth test to get an $A$ ?

Let $x$ be the required score on the fifth test. Write an equation for calculating the mean with the unknown value.

$\frac{80+85+88+95+x}{5}=90$

Simplify.

$\frac{348+x}{5}=90$

Multiply both sides by $5$ .

$348+x=450$

Subtract $348$ from both sides.

$x=98$

He needs to score a $98$ or higher in order to get an $A$ .