SaiBook.us Statistics

Example

Title: Measures of variation- Population Standard deviation

Grade: 9-a Lesson: S2-L2

Explanation: The best way to understand statistics is by looking at some examples. Take turns and read each example for easy understanding.

Examples:

Five people took a test.Their scores were 85,92,64,99,56.Find the population standard deviation.

Step 1a

Find the mean

Explanation: Let us add all the scores and divide by total number of scores

\$\mu\$ = \$(85+92+64+99+56)/(5)\$ = \$396/5\$ = 79.2

Step 1b

subtracting each score from mean and square each deviation

Explanation:

$1$

Step 1c

Calculate the Population standard deviation.

Explanation: Add the squared deviation \${X_i - \mu}^2\$ = 33.64+163.84+231.04+392.04+538.24 = 1358.8

Divide the sum by number of scores to get the variance \$frac\{1358.8}{5}\$ = 271.76

Take the square root of the squared deviation (or) variance \$\sqrt(271.76)\$ \$\approx\$ 16.485

Population standard deviation \$\sigma\$ = 16.485