Question

If the test scores of a class of 35 students have a mean of 74.3 and the test scores of another class of 28 students have a mean of 67.6, then the mean of the combined group is

Answer 1

Let the total sum of the scores of the first class of 35 students be a. The mean is 74.3 .

So 
$\frac{a}{35}=74.3\\\\a=35\cdot74.3= 2600.5$

Also, let the total sum of the scores of the second class of 28 students be b. The mean is 67.6 .

so 
$\frac{b}{28}=67.6\\\\ b=28\cdot67.6= 1892.8$



The combined group has 35+28=63 students. The sum of their scores is 

a+b=2600.5+1892.8=4493.3


Thus, the mean of the combined group is $\frac{4493.3}{63}= 71.32$