Chapter 12.3, Problem 20PPS

To determine

To calculate : the mean absolute deviation of the given data to the nearest tenth.

Answer to Problem 20PPS

The mean absolute deviation of the given data is $\underset{\_}{0.6}$ .

Explanation of Solution

Given information :

Consider the information given in the question:

The amount charged per hour by Samantha’s friends for babysitting :

  $\$8,\$8.5,\$9,\$7.5,\$10,\$8.25,\$8.75$

Formula used :

Step1: Find the mean, $\overline{x}$

Step2: Find the sum of the absolute values of the difference between each value in the set of data and the mean.

Step3: divide the sum by the number of values in the set of data.

Calculation :

As per problem,

The data set: $\$8,\$8.5,\$9,\$7.5,\$10,\$8.25,\$8.75$

The number of values in the data set $\text{=7}$

Step1: To find the mean, add the values in the data and then divide by the number of values in the data set.

  $\begin{array}{l}\overline{x}=\frac{8+8.5+9+7.5+10+8.25+8.75}{7}\\ \overline{x}=\frac{60}{7}=8.57\end{array}$

Step2: To find the sum of the absolute values, add the difference between each value and the mean.

The sum of absolute values

  $\begin{array}{l}=\left|8-8.57\right|+\left|8.5-8.57\right|+\left|9-8.57\right|+\left|7.5-8.57\right|+\left|10-8.57\right|+\left|8.25-8.57\right|+\left|8.757-8.57\right|\\ =0.57+0.07+0.43+1.07+1.43+0.32+0.18\\ =4.07\end{array}$

Step 3: Divide the sum by the number of values

  $\text{mean absolute deviation =}\frac{4.07}{7}=0.58\approx 0.6$