Calculate the mean (x) of the ages.

Question

ScanSolve AI Tutor · Accepted Answer

To calculate the mean deviation, we first need to find the mean of the given ages.

Calculate the mean ( $\bar{x}$ ) of the ages.
The ages are 17, 11, 31, 18, 25, 12, 29, 13, and 15.
There are $N=9$ members.
$\bar{x} = \frac{\sum x_i}{N}$ $\sum x_i = 17 + 11 + 31 + 18 + 25 + 12 + 29 + 13 + 15 = 171$ $\bar{x} = \frac{171}{9} = 19$
Calculate the absolute deviation of each age from the mean, $|x_i - \bar{x}|$ .
- $|17 - 19| = |-2| = 2$
- $|11 - 19| = |-8| = 8$
- $|31 - 19| = |12| = 12$
- $|18 - 19| = |-1| = 1$
- $|25 - 19| = |6| = 6$
- $|12 - 19| = |-7| = 7$
- $|29 - 19| = |10| = 10$
- $|13 - 19| = |-6| = 6$
- $|15 - 19| = |-4| = 4$
Sum the absolute deviations.
$\sum |x_i - \bar{x}| = 2 + 8 + 12 + 1 + 6 + 7 + 10 + 6 + 4 = 56$
Calculate the mean deviation.
$\text{Mean Deviation} = \frac{\sum |x_i - \bar{x}|}{N}$ $\text{Mean Deviation} = \frac{56}{9}$ $\text{Mean Deviation} \approx 6.22$
The mean deviation is $\boxed{\frac{56}{9}}$ or approximately $\boxed{6.22}$ .

Answer