Chapter 12.3, Problem 7PPE

To determine

To find: The mean, median, and mode of the given data set.

Answer to Problem 7PPE

  $\begin{array}{l}\text{Mean}=12\\ \text{Median}=11\\ \text{Mode}=\text{10}\\ \text{Mean is the best measure to describe the data set}\text{.}\end{array}$

Explanation of Solution

Given information:

A data set is given, weights of books (oz): $12,10,9,15,16,10$ .

Calculation:

Given data set is $12,10,9,15,16,10$ .

  $\begin{array}{l}\text{Mean}=\frac{\text{Sum of data values}}{\text{Total number of data values}}\\ \Rightarrow \text{Mean}=\frac{12+10+9+15+16+10}{6}\\ \Rightarrow \text{Mean}=12\end{array}$

Arranging data set in ascending order, $9,10,10,12,15,16$ .

Since number of data values are $6$ , an even number. So, median would be mean of two middle data values.

  $\text{Median}=\frac{10+12}{2}=11$ .

Mode is the data item that occurs the most times. Here mode is $10$ .

Since in the given data there is no outlier data value. Therefore, mean would be best measure to describe the data set.

Hence, for the given data set −

  $\begin{array}{l}\text{Mean}=12\\ \text{Median}=11\\ \text{Mode}=\text{10}\\ \text{Mean is the best measure to describe the data set}\text{.}\end{array}$