What is the mean score of all students together? (Please show work)

Question

In a psychology class, 43 students have a mean score of 82.4 on a test. Then 9 more students take the test and their mean score is 61.5.

What is the mean score of all of these students together? Round to one decimal place.

Answer 1

43(82.4) + 9(61.5) = 3,543.2 + 553.5 = 4,096.7

divide by 52, to get the weighted average of all 43+9 = 52 grades

= about 78.7827

= 78.8 rounded off to one decimal place

= mean of all 52 students

61.5 is within 17.6 of 78.8

82.4 is within 3.6 of 78.8

17.6/3.6 = 4.8

43/9 = 4.8

You need 4.8 times as many grades of 82.4 as grades of 61.5 to get an average 78.8

Answer 2