Question

23,17,29,36,15,6,18,24,32,41,14,27,33,18,24

Calculate the mean deviation.

Answer 1

Answer on Question 54704, Math, Statistics and Probability

Question:

23, 17, 29, 36, 15, 6, 18, 24, 32, 41, 14, 27, 33, 18, 24

Calculate the mean deviation.

Solution:

The formula for mean deviation looks like:

$$MD = \frac{1}{N} \sum_{i=1}^{N} |x_i - \bar{x}|,$$

where, $\bar{x}$ is the mean of the distribution, $x_i, i = 1, 2, \ldots, N$ is each value of a set of data and $N$ is the number of values.

Let's first obtain the mean:

$$\bar{x} = \frac{23 + 17 + 29 + 36 + 15 + 6 + 18 + 24 + 32 + 41 + 14 + 27 + 33 + 18 + 24}{15} = \frac{357}{15} = 23.8.$$

Let's find the distance of each value, $|x_i - \bar{x}|$, from that mean:

So, we can get the mean deviation:

$$MD = \frac{0.8 + 6.8 + 5.2 + 12.2 + 8.8 + 17.8 + 5.8 + 0.2 + 8.2 + 17.2 + 9.8 + 3.2 + 9.2 + 5.8 + 0.2}{15} = \frac{111.2}{15} = 7.41(3).$$

Answer:

$$MD = 7.41(3).$$

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