Calculate the variance of 2, 3, 3, 4, 5, 5, 5, 7, 7 and 9

Step 1: Analyze the question We need the variance of 10 numbers: 2, 3, 3, 4, 5, 5, 5, 7, 7, 9.

Step 2: The concept Variance = Σ(x − mean)² / n (the population formula, which WASSCE uses for this type of question).

Step 3: Solve

Sum: 2 + 3 + 3 + 4 + 5 + 5 + 5 + 7 + 7 + 9 = 50 n = 10 Mean = 50 / 10 = 5

Deviations from the mean (x − 5), squared:

• 2 → −3 → 9
• 3 → −2 → 4
• 3 → −2 → 4
• 4 → −1 → 1
• 5 → 0 → 0
• 5 → 0 → 0
• 5 → 0 → 0
• 7 → 2 → 4
• 7 → 2 → 4
• 9 → 4 → 16

Σ(x − mean)² = 9 + 4 + 4 + 1 + 0 + 0 + 0 + 4 + 4 + 16 = 42

Variance = 42 / 10 = 4.2

Step 4: Answer The variance is 4.2, which matches option D.

Tip: Always find the mean first, then square the deviations. Check that your deviations add up to zero (here: −3 −2 −2 −1 + 0 + 0 + 0 + 2 + 2 + 4 = 0). If they do not, you have made an error in the mean or subtraction. Also, in WASSCE, divide by n (not n − 1) unless the question says "sample variance."