WAEC 2024 Mathematics · Question 38

The following are the masses (in kg) of members in a club: 59, 44, 53, 49, 57, 40, 48, and 50. Calculate the variance of the distribution.

Options

A.35
B.36
C.40
D.50

Answer: A. 35

Explanation written with AI and checked against the answer key

Step 1: Find the mean Sum = 59 + 44 + 53 + 49 + 57 + 40 + 48 + 50 = 59+44 = 103; +53 = 156; +49 = 205; +57 = 262; +40 = 302; +48 = 350; +50 = 400 Mean = 400 / 8 = 50 Step 2: Find the deviations from the mean and square them | x | x − 50 | (x − 50)² | |---|---|---| | 59 | 9 | 81 | | 44 | −6 | 36 | | 53 | 3 | 9 | | 49 | −1 | 1 | | 57 | 7 | 49 | | 40 | −10 | 100 | | 48 | −2 | 4 | | 50 | 0 | 0 | Sum of squares = 81 + 36 + 9 + 1 + 49 + 100 + 4 + 0 = 280 Step 3: Calculate the variance Variance = Σ(x − mean)² / n = 280 / 8 = 35 (Using n − 1 would give 280/7 = 40, which is option C. But WASSCE questions on "variance of a distribution" use the population formula, dividing by n.) Answer: A (35) Tip: Always compute the mean first, then the deviations. Check that the deviations sum to zero (9 − 6 + 3 − 1 + 7 − 10 − 2 + 0 = 0), which confirms your mean is right. In WASSCE, variance = Σ(x − x̄)²/n unless the question says "sample variance."

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