Chapter 12.3, Problem 10P

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

100, 112, 98, 235, x; mean 127

To determine

Find the value of x .

Answer to Problem 10P

  $x=90$

Explanation of Solution

Given:

100 , 112 , 98 , 235 , x ; mean is 127

Calculation:

Mean =

  $\begin{array}{l}\frac{sum\text{ of all the entries}}{\text{total number of entries}}=\frac{100+112+98+235+x}{5}=\frac{545+x}{5}=127(given)\\ \Rightarrow 545+x=127\times \mathrm{5.................}[\text{multiply each side by 5]}\\ \Rightarrow 545+x=635\\ \Rightarrow x=635-\mathrm{545...................}[\text{subtract 545 from each side]}\\ \Rightarrow x=90\end{array}$