Answer to Question #313379 in Statistics and Probability for Weihan

Question

Faculty salaries for a random sample of teacher in the public school system certain town recorded by dividing each salary 1,000 find the m a d and standard deviation of these salaries if the coded observation are 18,15,21,19,13,15,14,23,18 1nd 16pesos

Answer 1

The sorted sample is 13,14,15,15,16,18,18,19,21,23.

The median is the average of 5^th and 6^th element:

$med=\frac{16+18}{2}=17$

Next,

$\bar{x}=\frac{13+14+15+15+16+18+18+19+21+23}{10}=17.2\\s^2=\frac{\left( 13-17.2 \right) ^2+\left( 14-17.2 \right) ^2+2\cdot \left( 15-17.2 \right) ^2+\left( 16-17.2 \right) ^2+2\cdot \left( 18-17.2 \right) ^2+\left( 19-17.2 \right) ^2+\left( 21-17.2 \right) ^2+\left( 23-17.2 \right) ^2}{10-1}=10.1778\\s=\sqrt{s^2}=\sqrt{10.1778}=3.19027$