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Mean of grouped data: Class 10 practice

For grouped data, use each class mark (mid-point) as x. Read the method, follow the three worked examples, then try the six questions.

What you should know first

  • Mean of ungrouped data

The idea behind mean of grouped data

For grouped data, use each class mark (mid-point) as x. Mean = Σfx ÷ Σf. The assumed-mean method subtracts a convenient value A to make the arithmetic smaller.

Step-by-step method

  1. Find each class mark.
  2. Multiply by frequency.
  3. Mean = Σfx ÷ Σf (or A + Σfd ÷ Σf).

Worked example 1 (Basic)

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

  1. Class marks: 15, 25, 35, 45
  2. Σf = 19, Σfx = 545
  3. Mean = 28.68
  4. Answer: 28.68

Worked example 2 (Standard)

Find the mean: classes 0–20, 20–40, 40–60, 60–80, 80–100 with frequencies 11, 7, 3, 7, 5.

  1. Class marks: 10, 30, 50, 70, 90
  2. Σf = 33, Σfx = 1410
  3. Mean = 42.73
  4. Answer: 42.73

Worked example 3 (Challenge)

Find the mean: classes 10–30, 30–50, 50–70, 70–90, 90–110, 110–130 with frequencies 7, 11, 9, 3, 5, 5.

  1. Class marks: 20, 40, 60, 80, 100, 120
  2. Σf = 40, Σfx = 2460
  3. Mean = 61.50
  4. Answer: 61.50

Common mistakes and misconceptions

  • Using class limits instead of class marks
  • Dividing by number of classes

Practice questions

  1. (Basic) Find the mean: classes 20–40, 40–60, 60–80, 80–100 with frequencies 6, 12, 9, 2.
  2. (Basic) Find the mean: classes 10–20, 20–30, 30–40, 40–50 with frequencies 5, 12, 7, 11.
  3. (Standard) Find the mean: classes 20–30, 30–40, 40–50, 50–60, 60–70 with frequencies 12, 9, 6, 7, 5.
  4. (Standard) Find the mean: classes 0–10, 10–20, 20–30, 30–40, 40–50 with frequencies 8, 9, 10, 3, 11.
  5. (Challenge) Find the mean: classes 10–30, 30–50, 50–70, 70–90, 90–110, 110–130 with frequencies 11, 4, 5, 9, 7, 11.
  6. (Challenge) Find the mean: classes 20–40, 40–60, 60–80, 80–100, 100–120, 120–140 with frequencies 4, 7, 8, 9, 2, 10.

Answer key with full working

  • Q1: Class marks: 30, 50, 70, 90 → Σf = 29, Σfx = 1590 → Mean = 54.83 → Answer: 54.83
  • Q2: Class marks: 15, 25, 35, 45 → Σf = 35, Σfx = 1115 → Mean = 31.86 → Answer: 31.86
  • Q3: Class marks: 25, 35, 45, 55, 65 → Σf = 39, Σfx = 1595 → Mean = 40.90 → Answer: 40.90
  • Q4: Class marks: 5, 15, 25, 35, 45 → Σf = 41, Σfx = 1025 → Mean = 25.00 → Answer: 25.00
  • Q5: Class marks: 20, 40, 60, 80, 100, 120 → Σf = 47, Σfx = 3420 → Mean = 72.77 → Answer: 72.77
  • Q6: Class marks: 30, 50, 70, 90, 110, 130 → Σf = 40, Σfx = 3360 → Mean = 84.00 → Answer: 84.00

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 mean 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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