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WAEC Further Mathematics 2006 Question 23

Question 23

Statistics

Calculate the standard deviation of the distribution below.
Age (in years): 1 − 5, 6 − 10, 11 − 15
Frequency: 3, 5, 2

  1. A.1.10
  2. B.2.36
  3. C.3.50
  4. D.7.50
Show the answer and explanation

Answer: C (3.50)

Explanation

Midpoints 3, 8, 13 with frequencies 3, 5, 2 give mean 75/10 = 7.5. Σf(x − x̄)² = 60.75 + 1.25 + 60.5 = 122.5, so SD = √(122.5/10) = √12.25 = 3.5.