Mode of grouped data: Class 10 practice

What you should know first

• Reading frequency tables

The idea behind mode of grouped data

The modal class has the highest frequency. Mode = l + [(f₁ − f₀)/(2f₁ − f₀ − f₂)] × h, where l is its lower limit, f₁ its frequency, f₀ and f₂ the neighbouring frequencies and h the class width.

Step-by-step method

1. Find the modal class.
2. Note l, h, f₁, f₀, f₂.
3. Substitute into the formula.

Worked example 1 (Basic)

Find the mode: classes 10–20, 20–30, 30–40, 40–50, 50–60 with frequencies 4, 5, 13, 9, 3.

1. Modal class 30–40; f₁ = 13, f₀ = 5, f₂ = 9
2. Mode = 30 + (8/12) × 10 = 36.67
3. Answer: 36.67

Worked example 2 (Standard)

Find the mode: classes 20–30, 30–40, 40–50, 50–60, 60–70 with frequencies 6, 6, 8, 4, 2.

1. Modal class 40–50; f₁ = 8, f₀ = 6, f₂ = 4
2. Mode = 40 + (2/6) × 10 = 43.33
3. Answer: 43.33

Worked example 3 (Challenge)

Find the mode: classes 0–10, 10–20, 20–30, 30–40, 40–50 with frequencies 5, 4, 7, 5, 3.

1. Modal class 20–30; f₁ = 7, f₀ = 4, f₂ = 5
2. Mode = 20 + (3/5) × 10 = 26.00
3. Answer: 26.00

Common mistakes and misconceptions

• Using the wrong neighbours
• Forgetting h

Practice questions

1. (Basic) Find the mode: classes 0–10, 10–20, 20–30, 30–40, 40–50 with frequencies 2, 8, 13, 6, 6.
2. (Basic) Find the mode: classes 20–30, 30–40, 40–50, 50–60, 60–70 with frequencies 3, 9, 11, 9, 2.
3. (Standard) Find the mode: classes 20–30, 30–40, 40–50, 50–60, 60–70 with frequencies 2, 8, 14, 8, 4.
4. (Standard) Find the mode: classes 20–30, 30–40, 40–50, 50–60, 60–70 with frequencies 2, 9, 11, 8, 4.
5. (Challenge) Find the mode: classes 20–30, 30–40, 40–50, 50–60, 60–70 with frequencies 5, 6, 12, 4, 3.
6. (Challenge) Find the mode: classes 10–20, 20–30, 30–40, 40–50, 50–60 with frequencies 6, 6, 13, 9, 2.

Answer key with full working

• Q1: Modal class 20–30; f₁ = 13, f₀ = 8, f₂ = 6 → Mode = 20 + (5/12) × 10 = 24.17 → Answer: 24.17
• Q2: Modal class 40–50; f₁ = 11, f₀ = 9, f₂ = 9 → Mode = 40 + (2/4) × 10 = 45.00 → Answer: 45.00
• Q3: Modal class 40–50; f₁ = 14, f₀ = 8, f₂ = 8 → Mode = 40 + (6/12) × 10 = 45.00 → Answer: 45.00
• Q4: Modal class 40–50; f₁ = 11, f₀ = 9, f₂ = 8 → Mode = 40 + (2/5) × 10 = 44.00 → Answer: 44.00
• Q5: Modal class 40–50; f₁ = 12, f₀ = 6, f₂ = 4 → Mode = 40 + (6/14) × 10 = 44.29 → Answer: 44.29
• Q6: Modal class 30–40; f₁ = 13, f₀ = 6, f₂ = 9 → Mode = 30 + (7/11) × 10 = 36.36 → Answer: 36.36

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

• Statistics chapter notes (Class 10)
• Mean of grouped data
• Median of grouped data
• Cumulative frequency tables
• Solving quadratic equations
• AP nth term and sum
• Distance formula and section formula
• Finding all trigonometric ratios from one
• All Class 10 practice

Frequently asked questions

Which chapter is mode 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.