WAEC 2020 Mathematics · Question 12

The interquartile range of distribution is 7. If the 25th percentile is 16, find the upper quartile.

Options

A.35
B.30
C.23
D.9

Answer: C. 23

Explanation written with AI and checked against the answer key

Analyze the question We're given the interquartile range (IQR) and the 25th percentile, and we need the upper quartile.

Concept

Lower quartile (Q₁) = 25th percentile
Upper quartile (Q₃) = 75th percentile
Interquartile range = Q₃ − Q₁

Solution Given: IQR = 7 and Q₁ = 16

IQR = Q₃ − Q₁

7 = Q₃ − 16

Q₃ = 7 + 16 = 23

Answer The upper quartile is 23, which is option C.

Tip The 25th percentile is the same as the lower quartile. The "upper" quartile is always the 75th percentile, so just add the IQR to Q₁. Be careful of option D (9), which comes from wrongly subtracting (16 − 7).

AI can make mistakes. Report anything that looks wrong.