FRQ — Statistics and Probability

Long answer·Challenge (5/5)·No calculator

Difficulty guide

The label describes the problem, not your ability.

1/5 - Foundational

Warm-up setup; checks one basic idea.

2/5 - Routine exam skill

Normal syllabus skill; usually one main rule or interpretation.

3/5 - Standard multi-step

Exam-style problem with multiple steps or a common trap.

4/5 - Hard exam skill

High-end exam problem; combines methods carefully.

5/5 - Challenge

Stretch problem beyond normal exam pressure.

Question

A grouped table has class intervals

0

10

10

20

20

30

30

40

40

50

and frequencies

4,a,12,b,6

. The total frequency is

40

and the mean is

28

. Find

a

and

b

, and then find the median.

Total: 6 marks

(a) Use the total frequency and mean conditions to find $a$ and $b$ . (3 marks)

(b) Find the median class. (1 mark)

Your response (optional — you can also work on paper)

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