Chapter 12.3, Problem 11P

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

1.2, 3.4, 6.7, 5.9, x; mean 4.0

To determine

Find the value of x .

Answer to Problem 11P

  $x=2.8$

Explanation of Solution

Given:

1.2 , 3.4 , 6.7 , 5.9 , x ; mean is 4

Calculation:

Mean =

  $\begin{array}{l}\frac{sum\text{ of all the entries}}{\text{total number of entries}}=\frac{1.2+3.4+6.7+5.9+x}{5}=\frac{17.2+x}{5}=4(given)\\ \Rightarrow 17.2+x=4\times \mathrm{5.................}[\text{multiply each side by 5]}\\ \Rightarrow 17.2+x=20\\ \Rightarrow x=20-\mathrm{17.2...................}[\text{subtract 17}\text{.2 from each side]}\\ \Rightarrow x=2.8\end{array}$