A class of 10 boys and 10 girls took a test.
The girls' marks were 4, 5, 6, 7, 7, 7, 8, 8, 8 and 10.

1. Find the most frequent mark(s) in the girls' marks

Girls' marks: $4, 5, 6, 7, 7, 7, 8, 8, 8, 10$.

$7$ occurs $3$ times and $8$ occurs $3$ times, more than any other mark.

So the modal marks are $7$ and $8$.

1. Calculate the mean mark for the girls

$\text{Mean} = \frac{4+5+6+7+7+7+8+8+8+10}{10}=\frac{70}{10}=7$

1. Find the boys' mean mark using the whole-class mean and the girls' mean

There are $20$ students in total.

Total mark for whole class:
$20 \times 7.5 = 150$

Total mark for girls from part (b):
$10 \times 7 = 70$

Total mark for boys:
$150 - 70 = 80$

Mean mark for boys:
$80 \div 10 = 8$

2. Compare the boys' mean with the girls' mean and justify the claim

Boys' mean $= 8$ and girls' mean $= 7$.

Since $8 > 7$, the boys did better on average.