Example 1 · level 1
Find the mean of this grouped data (class: frequency) — 0–20: 4, 20–40: 8, 40–60: 4.
Show solution
- Class marks x: 10, 30, 50.
- fx: 10 × 4 = 40, 30 × 8 = 240, 50 × 4 = 200.
- Σfx = 480, Σf = 16.
- Mean = 480 ÷ 16 = 30.
Answer: 30
CLASS 10 MATHS · STATISTICS
Mean of grouped data
Use the class marks (midpoints) xᵢ: mean = Σfᵢxᵢ ÷ Σfᵢ.
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Worked examples
Example 2 · level 2
Find the mean of this grouped data (class: frequency) — 60–80: 6, 80–100: 12, 100–120: 4, 120–140: 12. Give your answer to 2 decimal places.
Show solution
- Class marks x: 70, 90, 110, 130.
- fx: 70 × 6 = 420, 90 × 12 = 1080, 110 × 4 = 440, 130 × 12 = 1560.
- Σfx = 3,500, Σf = 34.
- Mean = 3,500 ÷ 34 = 102.94.
Answer: 102.9412
Example 3 · level 3
Find the mean of this grouped data (class: frequency) — 10–20: 8, 20–30: 10, 30–40: 13, 40–50: 5, 50–60: 14. Give your answer to 2 decimal places.
Show solution
- Class marks x: 15, 25, 35, 45, 55.
- fx: 15 × 8 = 120, 25 × 10 = 250, 35 × 13 = 455, 45 × 5 = 225, 55 × 14 = 770.
- Σfx = 1,820, Σf = 50.
- Mean = 1,820 ÷ 50 = 36.4.
Answer: 36.4