GCSE Secondary Maths Age 13-17 - Probability & Statistics: Mean - Explained

Mr. Brown gives a test to his class, where the girls have a mean mark of 70% and the boys 80%. Nick incorrectly assumes the overall mean is 75%. The teacher calculates the correct mean as 76% by finding the total marks for girls and boys, then dividing by the total number of students. The teacher emphasizes the importance of showing all work and concludes that Nick's assumption is incorrect.

What is the overall mean mark for the whole class?

Explain why Nick's calculation of the mean mark for the whole class is incorrect.

What justification can you provide to support your answer regarding the mean mark?