The standard deviation of a sample is the square root of the variance
The sample is given as: 11, 6, 10, 6, and 7
Start by calculating the mean
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x = \frac{11+ 6+ 10+ 6+ 7}{5}[/tex]
[tex]\bar x = 8[/tex]
The variance is then calculated as:
[tex]\sigma^2 = \frac{\sum(x - \bar x)^2}{n -1}[/tex]
This gives
[tex]\sigma^2 = \frac{(11 - 8)^2 + (6 - 8)^2 + (10 - 8)^2 + (6 - 8)^2+(7 - 8)^2}{5 -1}[/tex]
[tex]\sigma^2 = 5.5[/tex]
Hence, the variance is 5.5
In (a), we have:
[tex]\sigma^2 = 5.5[/tex]
Take the square roots of both sides
[tex]\sqrt{\sigma^2} = \sqrt{5.5[/tex]
[tex]\sigma = 2.35[/tex]
Hence, the standard deviation is 2.35
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