Chapter 12.3, Problem 1LC

To determine

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

Answer to Problem 1LC

  $\begin{array}{l}\text{Mean}=26.167\\ \text{Median}=30.5\\ \text{Mode}=33\\ \text{Median is the best measure to describe the data set}\text{.}\end{array}$

Explanation of Solution

Given information:

A data set is given as − $1,29,33,31,30,33$ .

Calculation:

Given data set is $1,29,33,31,30,33$ .

  $\begin{array}{l}\text{Mean}=\frac{\text{Sum of data values}}{\text{Total number of data values}}\\ \Rightarrow \text{Mean}=\frac{1+29+33+31+30+33}{6}\\ \Rightarrow \text{Mean}=26.167\end{array}$

Arranging data set in ascending order, $1,29,30,31,33,33$ .

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

  $\text{Median}=\frac{30+31}{2}=30.5$ .

Mode is the data item that occurs the most times. Here mode is $33$ .

Since in the given data set there is an outlier value $1$ . Therefore, median would be best measure to describe the data set.

Hence, for the given data set −

  $\begin{array}{l}\text{Mean}=26.167\\ \text{Median}=30.5\\ \text{Mode}=33\\ \text{Median is the best measure to describe the data set}\text{.}\end{array}$