Chapter 12.3, Problem 30PPE

To determine

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

Answer to Problem 30PPE

  $\begin{array}{l}\text{Mean}=\frac{20}{3}x\\ \text{Median}=6x\\ \text{Mode}=4x.\end{array}$

Explanation of Solution

Given information:

A data set is given : $9x,4x,11x,7x,5x,4x$ ; $x>0$ .

Calculation:

Given data set is $9x,4x,11x,7x,5x,4x$ ; $x>0$ .

  $\begin{array}{l}\text{Mean}=\frac{\text{Sum of data values}}{\text{Total number of data values}}\\ \Rightarrow \text{Mean}=\frac{9x+4x+11x+7x+5x+4x}{6}\\ \Rightarrow \text{Mean}=\frac{20}{3}x\end{array}$

Arranging data set in ascending order, $4x,4x,5x,7x,9x,11x$ .

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

  $\text{Median}=\frac{5x+7x}{2}=6x$ .

Mode is the data item that occurs the most times. Here mode is $4x$ .

Hence, for the given data set −

  $\begin{array}{l}\text{Mean}=\frac{20}{3}x\\ \text{Median}=6x\\ \text{Mode}=4x.\end{array}$