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VARVARA [1.3K]
2 years ago
14

What are the mean absolute deviation and population standard deviation of this data set? Round to the nearest tenth if necessary

. 2, 4, 6, 9, 14
Mathematics
1 answer:
tekilochka [14]2 years ago
6 0

Answer:

For a data set of N elements:

{x₁, x₂, ..., xₙ}

The mean is:

M = \frac{x_1 + x_2 + ... + x_n}{N}

The mean absolute deviation is:

MAD = \frac{|x_1 - M| + ... + |x_n - M|}{N}

And the population standard deviation is:

PSD = \frac{\sqrt{|x_1 - M|^2 + ... + |x_n - M|^2} }{\sqrt{N}}

In this case, our set has 5 elements, and the set is:

{2, 4, 6, 9, 14}

The mean of this set is:

M = \frac{2 + 4 + 6 + 9 + 14}{5} = 7

The mean absolute deviation is:

MAD = \frac{|2 - 7| + |4 - 7| + |6 - 7|+ |9 - 7| + |14 - 7| }{5} = 3.6

And the population standard deviation is:

PSD =  \sqrt{\frac{|2 - 7|^2 + |4 - 7|^2 + |6 - 7|^2+ |9 - 7|^2 + |14 - 7|^2 }{5}} = 4.2

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