Answer to Question #142752 in Statistics and Probability for Jhinree

Question

Faculty salaries for a random sample of teachers in the public-school system of a certain town were
coded by dividing each salary by 1000. Find the MAD and standard deviation of these salaries if the
coded observations are 18, 15, 21, 19, 13, 15, 14, 23, 18, and 16 pesos.

Answer 1

Solution

Mean

$$\bar{x}= {\sum x \over n} = {172000 \over 10} = 17200$$

Mean Absolute Deviation

$$MAD={1 \over n}\sum|x-\bar{x}|$$ $$={1 \over 10}(26000)$$ $$=2600$$

Standard Deviation

$$sd=\sqrt {\sum {(x- \bar{x})}^2 \over n-1}$$

$$=\sqrt{916000000 \over 9}$$ $$= 3190.2630$$