Given:
The dataset : 19, 11, 21, 9, 15
Mean
The sum of the values divided by the number of values.
[tex]\begin{gathered} mean\text{ = }\frac{\sum_^x}{n} \\ =\text{ }\frac{19\text{ + 11 + 21 +}9\text{ + 15}}{5} \\ =\text{ }\frac{75}{5} \\ =\text{ 15} \end{gathered}[/tex]
The mean is 15
Variance
Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value.
[tex]\begin{gathered} variance\text{ = }\frac{\sum^(x-x*)^2}{n-1} \\ =\text{ }\frac{(19-15)^2\text{ + \lparen11-15\rparen}^2+(21-15)^2\text{ +}(9-15)^2\text{ + \lparen15-15\rparen}^2\text{ }}{5-1} \\ =\text{ 26} \end{gathered}[/tex]
The variance is 26
Standard deviation
The standard deviation is square root of the variance
[tex]\begin{gathered} \sigma\text{ = }\sqrt{26} \\ =\text{ 5.099} \\ \approx\text{ 5.10} \end{gathered}[/tex]
The standard deviation is 5.10
