Problem Bank | IB Math AAHL

[Maximum mark: 19]

An aquarium is home to three kinds of parrotfish, blue, rainbow and princess.

A group of 60 blue parrotfish are randomly selected, and their length is measured to the nearest centimeter. The results are represented in the following cumulative frequency diagram.

Using the diagram find
1. the median length,
  [2]
  median=cm
2. the interquartile range.
  [4]

20% of these blue parrotfish are longer than L.

Find the value of l.
[3]

The recorded length of these same blue parrotfish is represented in the following table.

Length (l) in cm	0<l≤5	5<l≤12	12<l≤b	b<l≤25
Frequency	4	a	24	c

Find the value of a and the value of b.
[5]

There are a total of 270 parrotfish in the aquarium. A parrotfish is said to be juvenile if its length does not exceed 5cm.

Estimate the total number of juvenile parrotfish in the aquarium.
[3]
Explain why the result in (d) is unlikely to be a good estimate, and suggest a more appropriate sampling technique.
[2]

Ask Plex AI about this problem

Get hints, ask questions, and work through this problem step by step

I'm Plex, here to help with problems on this worksheet!