Cumulative frequency tables: Class 10 practice
A 'less than' cumulative frequency adds frequencies from the top; a 'more than' cumulative frequency adds from the bottom. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Frequency tables
The idea behind cumulative frequency tables
A 'less than' cumulative frequency adds frequencies from the top; a 'more than' cumulative frequency adds from the bottom. The ogive plots these and the median is where cf = n/2.
Step-by-step method
- Add frequencies progressively.
- Less-than: pair with upper limits; more-than: lower limits.
- Locate n/2 for the median class.
Worked example 1 (Basic)
Classes 10–20, 20–30, 30–40, 40–50, 50–60 have frequencies 11, 4, 4, 8, 10. Write the "less than" cumulative frequencies.
- < 20: 11, < 30: 15, < 40: 19, < 50: 27, < 60: 37
- Answer: 11, 15, 19, 27, 37
Worked example 2 (Standard)
Classes 0–10, 10–20, 20–30, 30–40, 40–50 have frequencies 13, 7, 13, 7, 4. Write the "more than" cumulative frequencies.
- Add from the bottom
- ≥ 0: 44, ≥ 10: 31, ≥ 20: 24, ≥ 30: 11, ≥ 40: 4
- Answer: 44, 31, 24, 11, 4
Worked example 3 (Challenge)
Classes 0–10, 10–20, 20–30, 30–40, 40–50 have frequencies 7, 15, 2, 8, 12. Write the "less than" cumulative frequencies and the median class.
- < 10: 7, < 20: 22, < 30: 24, < 40: 32, < 50: 44
- n/2 = 22 → median class 10–20
- Answer: 7, 22, 24, 32, 44; median class 10–20
Common mistakes and misconceptions
- Pairing less-than cf with lower limits
- Skipping a class
Practice questions
- (Basic) Classes 10–20, 20–30, 30–40, 40–50, 50–60 have frequencies 9, 3, 9, 7, 11. Write the "less than" cumulative frequencies.
- (Basic) Classes 20–30, 30–40, 40–50, 50–60, 60–70 have frequencies 14, 13, 8, 5, 10. Write the "less than" cumulative frequencies.
- (Standard) Classes 20–30, 30–40, 40–50, 50–60, 60–70 have frequencies 2, 8, 9, 15, 3. Write the "more than" cumulative frequencies.
- (Standard) Classes 10–20, 20–30, 30–40, 40–50, 50–60 have frequencies 12, 7, 5, 2, 7. Write the "more than" cumulative frequencies.
- (Challenge) Classes 10–20, 20–30, 30–40, 40–50, 50–60 have frequencies 7, 12, 5, 5, 4. Write the "less than" cumulative frequencies and the median class.
- (Challenge) Classes 20–30, 30–40, 40–50, 50–60, 60–70 have frequencies 10, 13, 12, 9, 10. Write the "less than" cumulative frequencies and the median class.
Answer key with full working
- Q1: < 20: 9, < 30: 12, < 40: 21, < 50: 28, < 60: 39 → Answer: 9, 12, 21, 28, 39
- Q2: < 30: 14, < 40: 27, < 50: 35, < 60: 40, < 70: 50 → Answer: 14, 27, 35, 40, 50
- Q3: Add from the bottom → ≥ 20: 37, ≥ 30: 35, ≥ 40: 27, ≥ 50: 18, ≥ 60: 3 → Answer: 37, 35, 27, 18, 3
- Q4: Add from the bottom → ≥ 10: 33, ≥ 20: 21, ≥ 30: 14, ≥ 40: 9, ≥ 50: 7 → Answer: 33, 21, 14, 9, 7
- Q5: < 20: 7, < 30: 19, < 40: 24, < 50: 29, < 60: 33 → n/2 = 16.5 → median class 20–30 → Answer: 7, 19, 24, 29, 33; median class 20–30
- Q6: < 30: 10, < 40: 23, < 50: 35, < 60: 44, < 70: 54 → n/2 = 27 → median class 40–50 → Answer: 10, 23, 35, 44, 54; median class 40–50
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 cumulative frequency tables 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.