CLASS 10 MATHS · STATISTICS

Mode of grouped data

Mode = l + [(f₁ − f₀) ÷ (2f₁ − f₀ − f₂)] × h, using the modal class (highest frequency) and its neighbours.

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Worked examples

Example 1 · level 1

Find the mode of this grouped data (class: frequency) — 15–20: 10, 20–25: 14, 25–30: 2, 30–35: 13. Give your answer to 2 decimal places if needed.

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Modal class 20–25: l = 20, h = 5, f₁ = 14, f₀ = 10, f₂ = 2.
Mode = 20 + (14 − 10) ÷ (28 − 10 − 2) × 5
= 20 + 4/16 × 5 = 21.25.

Answer: 21.25

Example 2 · level 2

Find the mode of this grouped data (class: frequency) — 20–30: 15, 30–40: 14, 40–50: 7, 50–60: 20, 60–70: 13. Give your answer to 2 decimal places if needed.

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Modal class 50–60: l = 50, h = 10, f₁ = 20, f₀ = 7, f₂ = 13.
Mode = 50 + (20 − 7) ÷ (40 − 7 − 13) × 10
= 50 + 13/20 × 10 = 56.5.

Answer: 56.5

Example 3 · level 3

Find the mode of this grouped data (class: frequency) — 20–30: 2, 30–40: 11, 40–50: 14, 50–60: 10, 60–70: 6. Give your answer to 2 decimal places if needed.

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Modal class 40–50: l = 40, h = 10, f₁ = 14, f₀ = 11, f₂ = 10.
Mode = 40 + (14 − 11) ÷ (28 − 11 − 10) × 10
= 40 + 3/7 × 10 = 44.29.

Answer: 44.2857