Given:
The scores that Jenna has received on her seven quizzes is 16, 13, 20, 16, 12, 17, 18.
We need to determine the variance.
Mean:
The mean of the data is given by
[tex]Mean=\frac{16+13+20+16+12+17+18}{7}[/tex]
[tex]Mean=\frac{112}{7}[/tex]
[tex]Mean=16[/tex]
Thus, the mean of the given data is 16.
Variance:
The variance of the data can be determined using the formula,
[tex]variance =\frac{\sum(X-\mu)^{2}}{n}[/tex]
where [tex]\mu[/tex] is the mean and n is the number of terms in the distribution.
Thus, we have;
[tex]variance=\frac{(16-16)^2+(13-16)^2+(20-16)^2+(16-16)^2+(12-16)^2+(17-16)^2+(18-16)^2}{7}[/tex]
Simplifying the terms, we get;
[tex]variance=\frac{(0)^2+(-3)^2+(4)^2+(0)^2+(4)^2+(1)^2+(2)^2}{7}[/tex]
[tex]variance=\frac{0+9+16+0+16+1+4}{7}[/tex]
[tex]variance=\frac{46}{7}[/tex]
[tex]variance=6.57[/tex]
Rounding off to the nearest tenth, we get;
[tex]variance=6.6[/tex]
Thus, the variance is 6.6
