Question

Find and interpret the mean absolute deviation of the data. Round your answer to the nearest tenth, if necessary. Prices of microphones (dollars) 25 28 20 22 32 28 35 34 30 36

Answer 1

Answer:

The Mean Absolute Vale (MAD) is 4.4

Step-by-step explanation:

The mean absolute deviation is defined as

$MAD=\frac{\sum |x_{i}-\mu |}{N}$

Where $\mu$ is the mean and $N$ is the total number of data.

The means is defined as

$\mu = \frac{\sum x_{i} }{N}=\frac{25+28+20+22+32+28+35+34+30+36}{10}=\frac{290}{10}=29$

And, $N=10$

Replacing these values, in the MAD formula, we have

$MAD=\frac{|25-29|+|28-29|+|20-29|+|22-29|+|32-29|+|28-29|+|35-29|+|34-29|+|30-29|+|36-29|}{10} \\MAD=\frac{|-4|+|-1|+|-9|+|-7|+|3|+|-1|+|6|+|5|+|1|+|7|}{10}=\frac{44}{10}\\ MAD = 4.4$

Therefore, the Mean Absolute Vale (MAD) is 4.4