Question

Calculate the variance and the standard deviation for the following sample data. Scores: 7, 9, 0, 1, 7, 4, 4, 7, 6

Answer 1

Answer:

Variance = 9

Standard deviation = 3

Step-by-step explanation:

Step 1

Find the Mean

Means = Sum of values/Number of values

= 0 + 1 + 4 + 4 + 6 + 7 + 7 + 7 + 9/9

= 45/9

= 5

Step 2

The formula for Sample variance

= (x - Mean)²/n - 1

Where

n = number of values = 9

Hence:

Sample variance =

( (0 - 5)² + (1 - 5)²+ (4 - 5)² + (4 - 5)² + (6 - 5)² + (7 - 5)² + (7 - 5)² + (7 - 5)² + (9 - 5)²)/9 - 1

= (-5² + -4²+ -1² + -1² + 1² + 2² + 2² + 2² + 4²) /8

= (25 + 16 + 1 + 1 + 1 + 4 + 4 + 4 + 16)/8

= 72/8

= 9

Sample Standard deviation = √Sample variance

= √9

= 3