WAEC 2022 Mathematics · Question 17

The age (years) of some members in a singing group are: 12, 47, 49, 15, 43, 41, 13, 39, 43, 41 and 36. Find the lower quartile

Options

A.12
B.13
C.15
D.20

Answer: C. 15

Explanation written with AI and checked against the answer key

Analyze the question: We need the lower quartile (Q1) of 11 ages. Concept: The lower quartile is the value one-quarter of the way through the ordered data. For n data values, Q1 is commonly found at the position (n+1)/4 (or, equivalently in WASSCE, the median of the lower half). Step 1: Arrange in ascending order 12, 13, 15, 36, 39, 41, 41, 43, 43, 47, 49 Count: n = 11. Step 2: Find the position of Q1 Position = (n+1)/4 = 12/4 = 3rd value The 3rd value is 15. Check with the median-of-lower-half method: The median is the 6th value (41). The lower half is 12, 13, 15, 36, 39. Its median is the 3rd value, which is 15. Both methods agree. Tip: Always sort the data first. With n = 11, Q1 is the 3rd value, the median is the 6th, and Q3 is the 9th. Many students lose marks by skipping the sorting step.

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