Chapter 12.3, Problem 2LC

To determine

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

Answer to Problem 2LC

  $\begin{array}{l}\text{Mean}=8.76\\ \text{Median}=8.8\\ \text{Mode}=\text{None}\\ \text{Mean is the best measure to describe the data set}\text{.}\end{array}$

Explanation of Solution

Given information:

A data set is given as − $\mathrm{8.2.9.3},8.5,8.8,9.0$ .

Calculation:

Given data set is $\mathrm{8.2.9.3},8.5,8.8,9.0$ .

  $\begin{array}{l}\text{Mean}=\frac{\text{Sum of data values}}{\text{Total number of data values}}\\ \Rightarrow \text{Mean}=\frac{8.2+9.3+8.5+8.8+9.0}{5}\\ \Rightarrow \text{Mean}=8.76\end{array}$

Arranging data set in ascending order, $8.2,8.5,8.8,9.0,9.3$ .

Since number of data values are $5$ , an odd number. So, median would be the middle data values.

  $\text{Median}=8.8$ .

Mode is the data item that occurs the most times. Here all data value occurs once, there is no mode.

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 −

  $\begin{array}{l}\text{Mean}=8.76\\ \text{Median}=8.8\\ \text{Mode}=\text{None}\\ \text{Mean is the best measure to describe the data set}\text{.}\end{array}$