Q13. - Algebra 1

Question

Find the mean absolute deviation to the nearest tenth.

Luci is keeping track of the number of candy bars each member of the drill team sold.

20, 25, 30, 50, 40, 60, 20, 10, 42

Step-by-Step Solution

Answer

The mean absolute deviation is 13.3.

Step 1. Define mean.

The mean is equal to the sum of all data values divided by the number of data values.

Step 2. Define the mean absolute deviation.

The mean absolute deviation is the average of the absolute values of the differences between the mean and each value in the data set.

Step 3. Calculate the mean absolute deviation for the given data.

The number of candy bars sold by each member of the drill team are : 

20, 25, 30, 50, 40, 60, 20, 10, 42

First, find the mean of the data.

Mean $=\frac{20+25+30+50+40+60+20+10+42}{9}=\frac{297}{9}=33$

Next, find the absolute value of the difference between the mean and each value.

$\begin{array}{c}\left|20-33\right|=13,\left|25-33\right|=8,\left|30-33\right|=3,\left|50-33\right|=17,\left|40-33\right|=7,\\ \left|60-33\right|=27,\left|20-33\right|=13,\left|10-33\right|=23,\left|42-33\right|=9\end{array}$

Now, find the mean of the differences.

$\frac{13+8+3+17+7+27+13+23+9}{9}=\frac{120}{9}=13.3$

 

Therefore, the mean absolute deviation is 13.3.