Question

in the data set below, what is the mean absolute deviation?
10 18 74 82 81 65
if the answer is a decimal, round it to the nearest tenth.
mean absolute deviation (mad):

Explanation:

Step1: Calculate the data mean

First sum all values, divide by count.
$$\text{Mean} = \frac{10 + 18 + 74 + 82 + 81 + 65}{6} = \frac{330}{6} = 55$$

Step2: Find absolute deviations

Subtract mean from each value, take absolute value.
$|10-55|=45$, $|18-55|=37$, $|74-55|=19$, $|82-55|=27$, $|81-55|=26$, $|65-55|=10$

Step3: Calculate MAD of deviations

Sum absolute deviations, divide by count.
$$\text{MAD} = \frac{45 + 37 + 19 + 27 + 26 + 10}{6} = \frac{164}{6} \approx 27.3$$

Answer:

27.3