Core stretch The table shows the heights, $h$ cm, of a group of students. The frequency $p$ is a

Question

Core stretch

The table shows the heights, $h$ cm, of a group of students. The frequency $p$ is a non-negative integer.

The conditions in parts (a) and (c) are independent.

Find the greatest possible value of $p$ for which the middle observation, or both middle observations when the total frequency is even, lies or lie in the class $130\le h<140$.[3]
A student claims that a suitable choice of $p$ can make $150\le h<160$ the unique modal class. Explain why this is impossible.[2]
Given instead that there are 60 students, find $p$ and calculate an estimate of their mean height, correct to 1 decimal place.[3]

Accepted Answer

(a) $p=9$. (b) Impossible: the fourth-class frequency 15 is less than the second-class frequency 18. (c) $p=10$; estimated mean $142.2$ cm.

Reasoning with grouped frequencies