Answer :
Answer:
[tex]\sigma_x = 5.68[/tex]
Explanation:
Given
[tex]x = 4, 14, 6, 2, 7, 12 2,17[/tex]
Required
The standard deviation
First, calculate the mean
[tex]\bar x =\frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x = \frac{4+ 14+ 6+ 2+ 7+ 12 +2+17}{8}[/tex]
[tex]\bar x = \frac{64}{8}[/tex]
[tex]\bar x = 8[/tex]
The standard deviation is:
[tex]\sigma_x = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]
So, we have:
[tex]\sigma_x = \sqrt{\frac{(4 - 8)^2+ (14 - 8)^2+ (6 - 8)^2+ (2 - 8)^2+ (7 - 8)^2+ (12 - 8)^2+ (2 - 8)^2+ (17 - 8)^2}{8-1}}[/tex]
[tex]\sigma_x = \sqrt{\frac{226}{7}}[/tex]
[tex]\sigma_x = \sqrt{32.2857}[/tex]
[tex]\sigma_x = 5.68[/tex]