Chapter 12.3, Problem 13PPE

To determine

To find: The value of $x$ such that the data set has the given mean.

Answer to Problem 13PPE

  $x=125$ .

Explanation of Solution

Given information:

A data set is given as $100,121,105,113,108,x\text{ and mean is 112}$ .

Calculation:

Given data set is $100,121,105,113,108,x\text{ and mean is 112}$ .

  $\begin{array}{l}\text{Mean}=\frac{\text{Sum of data values}}{\text{Total number of data values}}\\ \Rightarrow \text{112}=\frac{100+121+105+113+108+x}{6}\\ \Rightarrow \text{672}=547+x\\ \Rightarrow x=672-547\\ \Rightarrow x=125\end{array}$

Hence, desired value is $x=125$ .