to find the mean of a data set, we follow the following formula
Mean = sum of values in data set ÷ number of values in data set
We have three values in given data set: 83, 91, and an unknown value [tex]x[/tex]
We want to work out a range of possible value of [tex]x[/tex] such as the mean is in between 85 and 90 inclusive
We first set the inequality
[tex]85 \leq Mean \leq 90[/tex]
[tex]85 \leq \frac{83+91+x}{3} \leq 90 [/tex]
[tex]85 \leq \frac{174+x}{3} \leq 90 [/tex], multiply each term by 3
[tex]255 \leq 174+x \leq 270[/tex], subtract 174 from each term
[tex]81 \leq x \leq 96[/tex]
So the possible values of x are in between 81 and 96 inclusive
