Given
sample Epworth Sleepiness Scores for the problems below;
6, 4, 3, 5, 4, 2, 4, 5, 4, 6, 1, 4, 5, 2
Find
Sample variance and Sample Standard Deviation
Explanation
sample variance is given by
[tex]S^2=\frac{\sum_^(x-\bar{x})^2}{n-1}[/tex]here n = 14
mean = 6+4+3+5+4+2+4+5+4+6+1+4+5+2/14
mean = 3.14
[tex]\sum_^(x-\bar{x})^2=28.9296[/tex]so variance =
[tex]\begin{gathered} \frac{28.9296}{14-1} \\ \\ \frac{28.9296}{13} \\ \\ 2.22 \end{gathered}[/tex]sample standard deviation = square root of variance
so ,
[tex]\begin{gathered} \sqrt{2.22} \\ 1.48996644258\approx1.49 \end{gathered}[/tex]Final Answer
Hence ,
Sample variance = 2.22
Sample Standard Deviation = 1.49
