Combine geometric heights with a weighted class mean

A class has $16$ boys with AP heights and $10$ girls with GP heights. The shortest boy and girl are each $150.0$ cm. The tallest boy is $180.0$ cm, and the fourth-shortest girl is $157.5$ cm.

(i) Show the girls’ common ratio is $1.05^{1/3}$ and find the tallest girl’s height to 1 d.p.2 marks

(ii) Find how many girls are taller than $164.0$ cm.3 marks

(iii) Find the girls’ mean height to 1 d.p.3 marks

(iv) Find the class mean to 1 d.p.2 marks