A Mathematics test was taken by 4 boys and 6 girls. The mean marks of the 10 students was 49.

a) Calculate the total marks obtained by 10 students.

b) If the mean marks of 6 girls was 51, calculate the mean marks of 4 boys.

Total population/Total number of observations = 10 (boys+girls)

a.) Combined mean = Total marks/Total population

49 = Total marks/10

∴ Total marks = 490

b.) Mean marks of girls is 51. Let m be the mean marks of boys.

Therefore,

Combined mean =

[mean marks of girls * (number of girls) + mean marks of boys * (number of boys) ]/Total population

49 = [51 (6) + m (4) ]/10

49*10 = 51 (6) + 4m

4m = 184

m=46