To find the mean deviation, we first need to calculate the mean (x) of the given ages, and then find the…

Question

To find the mean deviation, we first need to calculate the mean (x) of the given ages, and then find the average of the absolute differences between each age and the mean.

ScanSolve AI Tutor · Accepted Answer

To find the mean deviation, we first need to calculate the mean ( $\bar{x}$ ) of the given ages, and then find the average of the absolute differences between each age and the mean.

The ages are: $17, 11, 31, 18, 25, 29, 13, 15$ .
The number of observations is $N=8$ .

Calculate the mean ( $\bar{x}$ ).
The mean is the sum of all ages divided by the number of ages.
$\bar{x} = \frac{17 + 11 + 31 + 18 + 25 + 29 + 13 + 15}{8}$ $\bar{x} = \frac{159}{8}$ $\bar{x} = 19.875$
Calculate the absolute deviation of each age from the mean, $|x_i - \bar{x}|$ .
- $|17 - 19.875| = |-2.875| = 2.875$
- $|11 - 19.875| = |-8.875| = 8.875$
- $|31 - 19.875| = |11.125| = 11.125$
- $|18 - 19.875| = |-1.875| = 1.875$
- $|25 - 19.875| = |5.125| = 5.125$
- $|29 - 19.875| = |9.125| = 9.125$
- $|13 - 19.875| = |-6.875| = 6.875$
- $|15 - 19.875| = |-4.875| = 4.875$
Calculate the sum of the absolute deviations.
$\sum |x_i - \bar{x}| = 2.875 + 8.875 + 11.125 + 1.875 + 5.125 + 9.125 + 6.875 + 4.875$ $\sum |x_i - \bar{x}| = 50.75$
Calculate the mean deviation.
The mean deviation is the sum of the absolute deviations divided by the number of observations.
$\text{Mean Deviation} = \frac{\sum |x_i - \bar{x}|}{N}$ $\text{Mean Deviation} = \frac{50.75}{8}$ $\text{Mean Deviation} = 6.34375$
The final answer is 6.34375.

To find the mean deviation, we first need to calculate the mean (x) of the given ages, and then find the average of the absolute differences between each age and the mean.

Answer

Step-by-step solution

Calculate the mean ( $\bar{x}$ ).

Calculate the absolute deviation of each age from the mean, $|x_i - \bar{x}|$ .

Calculate the sum of the absolute deviations.

Calculate the mean deviation.

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To find the mean deviation, we first need to calculate the mean (x) of the given ages, and then find the average of the absolute differences between each age and the mean.

Answer

Step-by-step solution

Calculate the mean (xˉ\bar{x}xˉ).

Calculate the absolute deviation of each age from the mean, ∣xi−xˉ∣|x_i - \bar{x}|∣xi​−xˉ∣.

Calculate the sum of the absolute deviations.

Calculate the mean deviation.

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Still stuck on this one?

More Mathematics Questions

Calculate the mean ( $\bar{x}$ ).

Calculate the absolute deviation of each age from the mean, $|x_i - \bar{x}|$ .