Question 1022940
We treat the entire class as a population.

Let n = number of boys = number of girls ==> total number of students is 2n.

==> The mean of the test scores would be {{{mu = (0.85n+0.91n)/(2n) = (1.76n)/(2n) = 0.88}}}, or {{{highlight(88)}}}%.

To find the standard deviation, use the formula {{{sigma^2 = (1/(2n))sum(x[i]^2, 1, 2n ) - mu^2}}} for the population variance.

==> {{{sigma^2 = (1/(2n))(n(0.85^2)+n(0.91^2)) - 0.88^2}}}

==> {{{sigma^2 = (0.85^2+0.91^2)/2 - 0.88^2 = 0.0009}}}

==> {{{sigma = 0.03}}}, to three decimal places.

The standard deviation is {{{highlight(0.03)}}}.

(Note that both averages of 85% and 91% are exactly one standard deviation from the mean!)