Answer:
[tex]s = 0.0394[/tex]
Step-by-step explanation:
Given:
0.612 0.523 0.606 0.631 0.584 0.592 0.644 0.597 0.639 0.607 0.564 0.673
Required
Calculate the sample standard deviation
First, calculate the mean
[tex]\bar x = \frac{\sum x}{n}[/tex]
[tex]\bar x = \frac{0.612 +0.523 +0.606 +0.631+ 0.584 + 0.592+ 0.644 +0.597 +0.639 +0.607 +0.564+ 0.673}{12}[/tex]
[tex]\bar x = \frac{7.272}{12}[/tex]
[tex]\bar x = 0.606[/tex]
The sample standard deviation is then calculated using:
[tex]s = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]
[tex]\sum (x - \bar x)^2 = (0.612 -0.606)^2+(0.523 -0.606)^2+(0.606 -0.606)^2+(0.631 -0.606)^2+(0.584 -0.606)^2+(0.592 -0.606)^2+(0.644 -0.606)^2+(0.597 -0.606)^2+(0.639 -0.606)^2+(0.607 -0.606)^2+(0.564 -0.606)^2+(0.673 -0.606)^2[/tex]
[tex]\sum (x - \bar x)^2 = 0.017098[/tex]
So, we have:
[tex]s = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]
[tex]s = \sqrt{\frac{0.017098}{12-1}}[/tex]
[tex]s = \sqrt{\frac{0.017098}{11}}[/tex]
[tex]s = \sqrt{0.00155436363}[/tex]
[tex]s = 0.0394[/tex] -- approximated
