60,709 views
24 votes
24 votes
A class has an equal number of boys and girls. The boys all got 85% on a test and the girls all got 91%. What are the mean and standard deviation of the test scores for the entire class?

User Rgbflawed
by
2.7k points

1 Answer

26 votes
26 votes

In order to find the mean, consider that there are an equal number of girls and boy, then, if n is the number of boys, n is also the number of girls.

Then, for the mean, you have:


\operatorname{mean}=\bar{x}=(0.85n+0.91n)/(n+n)=(1.76n)/(2n)=(1.76)/(2)=0.88

Hence, the mean is 88%

To calculate the standar deviation, just consider that percentage for both boys and girls are 0.03 apart of the mean (0.88). Then, it is not necessary to calculate explicitly the standard deviation, because in this case, the 'distance' between the data and the mean is the same.

Hence, the standard deviation is 0.03, or simply 3%

User Inquam
by
2.8k points