Chapter 12.3, Problem 8P

Find the value of x such that the data set has the given mean.

55, 60, 35, 90, x: mean 51

To determine

Find the value of x .

Answer to Problem 8P

  $x=15$

Explanation of Solution

Given:

55 , 60 , 35 , 90 , x ; mean is 51

Calculation:

Mean =

  $\begin{array}{l}\frac{sum\text{ of all the entries}}{\text{total number of entries}}=\frac{55+60+35+90+x}{5}=\frac{240+x}{5}=51(given)\\ \Rightarrow 240+x=51\times \mathrm{5.................}[\text{multiply each side by 5]}\\ \Rightarrow 240+x=255\\ \Rightarrow x=255-\mathrm{240...................}[\text{subtract 240 from each side]}\\ \Rightarrow x=15\end{array}$