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Median of grouped data: Class 10 practice

Find n/2, locate the median class using cumulative frequency, then Median = l + [(n/2 − cf)/f] × h, where cf is the cumulative frequency before the median class.. Read the method, follow the three worked examples, then try the six questions.

What you should know first

  • Cumulative frequency

The idea behind median of grouped data

Find n/2, locate the median class using cumulative frequency, then Median = l + [(n/2 − cf)/f] × h, where cf is the cumulative frequency before the median class.

Step-by-step method

  1. Build the cumulative frequency column.
  2. Find n/2 and the class containing it.
  3. Substitute l, cf, f, h.

Worked example 1 (Basic)

Find the median: classes 0–10, 10–20, 20–30, 30–40, 40–50 with frequencies 6, 5, 10, 6, 3.

  1. n = 30, n/2 = 15
  2. Cumulative: 6, 11, 21, 27, 30 → median class 20–30
  3. Median = 20 + ((15 − 11)/10) × 10 = 24.00
  4. Answer: 24.00

Worked example 2 (Standard)

Find the median: classes 20–30, 30–40, 40–50, 50–60, 60–70 with frequencies 10, 9, 4, 10, 4.

  1. n = 37, n/2 = 18.5
  2. Cumulative: 10, 19, 23, 33, 37 → median class 30–40
  3. Median = 30 + ((18.5 − 10)/9) × 10 = 39.44
  4. Answer: 39.44

Worked example 3 (Challenge)

Find the median: classes 20–30, 30–40, 40–50, 50–60, 60–70 with frequencies 7, 12, 6, 6, 6.

  1. n = 37, n/2 = 18.5
  2. Cumulative: 7, 19, 25, 31, 37 → median class 30–40
  3. Median = 30 + ((18.5 − 7)/12) × 10 = 39.58
  4. Answer: 39.58

Common mistakes and misconceptions

  • Using the median class's own cf
  • Using n instead of n/2

Practice questions

  1. (Basic) Find the median: classes 0–10, 10–20, 20–30, 30–40, 40–50 with frequencies 8, 6, 12, 6, 8.
  2. (Basic) Find the median: classes 20–30, 30–40, 40–50, 50–60, 60–70 with frequencies 11, 5, 6, 3, 4.
  3. (Standard) Find the median: classes 0–10, 10–20, 20–30, 30–40, 40–50 with frequencies 3, 10, 10, 7, 10.
  4. (Standard) Find the median: classes 0–10, 10–20, 20–30, 30–40, 40–50 with frequencies 5, 5, 7, 9, 11.
  5. (Challenge) Find the median: classes 10–20, 20–30, 30–40, 40–50, 50–60 with frequencies 10, 10, 9, 9, 6.
  6. (Challenge) Find the median: classes 0–10, 10–20, 20–30, 30–40, 40–50 with frequencies 12, 7, 10, 12, 9.

Answer key with full working

  • Q1: n = 40, n/2 = 20 → Cumulative: 8, 14, 26, 32, 40 → median class 20–30 → Median = 20 + ((20 − 14)/12) × 10 = 25.00 → Answer: 25.00
  • Q2: n = 29, n/2 = 14.5 → Cumulative: 11, 16, 22, 25, 29 → median class 30–40 → Median = 30 + ((14.5 − 11)/5) × 10 = 37.00 → Answer: 37.00
  • Q3: n = 40, n/2 = 20 → Cumulative: 3, 13, 23, 30, 40 → median class 20–30 → Median = 20 + ((20 − 13)/10) × 10 = 27.00 → Answer: 27.00
  • Q4: n = 37, n/2 = 18.5 → Cumulative: 5, 10, 17, 26, 37 → median class 30–40 → Median = 30 + ((18.5 − 17)/9) × 10 = 31.67 → Answer: 31.67
  • Q5: n = 44, n/2 = 22 → Cumulative: 10, 20, 29, 38, 44 → median class 30–40 → Median = 30 + ((22 − 20)/9) × 10 = 32.22 → Answer: 32.22
  • Q6: n = 50, n/2 = 25 → Cumulative: 12, 19, 29, 41, 50 → median class 20–30 → Median = 20 + ((25 − 19)/10) × 10 = 26.00 → Answer: 26.00

Syllabus note

This skill is listed under "Statistics" for Class 10 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.

Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.

Related practice and notes

Frequently asked questions

Which chapter is median of grouped data in?

"Statistics", Class 10 Maths (NCERT/CBSE). Other boards may place it differently.

How were the answers checked?

Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.

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