CLASS 10 MATHS · STATISTICS

Median of grouped data

Median = l + [(n/2 − cf) ÷ f] × h, where l is the lower limit of the median class, cf the cumulative frequency before it, f its frequency, h the class width.

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Worked examples

Example 1 · level 1

Find the median of this grouped data (class: frequency) — 60–80: 13, 80–100: 2, 100–120: 14, 120–140: 14. Give your answer to 2 decimal places if needed.

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n = 43, n/2 = 21.5.
Median class 100–120: l = 100, f = 14, cf (before) = 15, h = 20.
Median = 100 + (21.5 − 15) ÷ 14 × 20 = 109.29.

Answer: 109.2857

Example 2 · level 2

Find the median of this grouped data (class: frequency) — 5–10: 4, 10–15: 10, 15–20: 14, 20–25: 8, 25–30: 5. Give your answer to 2 decimal places if needed.

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n = 41, n/2 = 20.5.
Median class 15–20: l = 15, f = 14, cf (before) = 14, h = 5.
Median = 15 + (20.5 − 14) ÷ 14 × 5 = 17.32.

Answer: 17.3214

Example 3 · level 3

Find the median of this grouped data (class: frequency) — 5–10: 2, 10–15: 15, 15–20: 6, 20–25: 6, 25–30: 12. Give your answer to 2 decimal places if needed.

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n = 41, n/2 = 20.5.
Median class 15–20: l = 15, f = 6, cf (before) = 17, h = 5.
Median = 15 + (20.5 − 17) ÷ 6 × 5 = 17.92.

Answer: 17.9167