Answer:
The standard deviation = 7.65
The variance = 58.55
Explanation:
The given data are:
x = 19.9, 3.7, 24.6, 4.9, 13.5, 4.4, 19, 18.1
The mean is calculated as:
[tex]\begin{gathered} \mu=\frac{\sum x}{N} \\ \mu=\frac{19.9+3.7+24.6+4.9+13.5+4.4+19+18.1}{8} \\ \mu=\frac{108.1}{8} \\ \mu=13.5125 \end{gathered}[/tex]
The standard deviation is given by the formula:
[tex]\begin{gathered} SD=\sqrt{\frac{\sum(x-\mu)^2}{N}} \\ SD=\sqrt{\frac{(19.9-13.5125)^2+(3.7-13.5125)^2+(24.6-13.5125)^2+(4.9-13.5125)^2+(13.5-13.5125)^2+(4.4-13.5125)^2+(19-13.5125)^2+(18.1-13.5125)^2}{8}} \\ SD=7.65 \end{gathered}[/tex]
The variance = SD²
The variance = 7.65²
The variance = 58.55
