Question

Find the mean and the MAD of the following data set.10, 15, 20, 25, 30, 35

Answer 1

Answer:

Mean = 22.5

MAD = 7.5

Explanation:

The mean is equal to the sum of all the values divided by the number of values, so the mean of the data set is:

$\begin{gathered} \text{Mean = }\frac{10+15+20+25+30+35}{6} \\ \text{Mean = }\frac{135}{6} \\ \text{Mean = 22.5} \end{gathered}$

Then, to calculate the mean absolute deviation, we need to find the absolute difference between each value and the mean, so:

| 10 - 22.5 | = | -12.5| = 12.5

| 15 - 22.5 | = | -7.5| = 7.5

| 20 - 22.5 | = | -2.5| = 2.5

| 25 - 22.5 | = | 2.5| = 2.5

| 30 - 22.5 | = | 7.5| = 7.5

| 35 - 22.5 | = |12.5| = 12.5

Finally, add all the differences and divide them by the number of values to get that mean absolute deviation is equal to:

$\begin{gathered} \text{MAD}=\frac{12.5+7.5+2.5+2.5+7.5+12.5}{6} \\ \text{MAD = }\frac{45}{6}=7.5 \end{gathered}$

Therefore, the mean is 22.5 and the MAD is 7.5