Worked example 1
Question: Find the mean for classes 0–10,10–20,20–30 with frequencies 2,3,5.
Solution: Class marks 5,15,25. Σfx=10+45+125=180; N=10. Mean=18.
What this chapter covers
Calculate the mean, median and mode of grouped frequency distributions using suitable methods and interpret the result in context.
Mean
Use class marks xᵢ and frequencies fᵢ. The direct method uses Σfᵢxᵢ/Σfᵢ. Assumed-mean and step-deviation methods reduce arithmetic for large tables.
Median and mode
For grouped data, locate the median class using cumulative frequency and N/2. The modal class has the highest frequency. Use continuous class boundaries and keep h as class width. Avoid bimodal cases when applying the standard mode formula.
Key formulae: Mean x̄=Σfᵢxᵢ/N. Median=l+[(N/2−cf)/f]h. Mode=l+[(f₁−f₀)/(2f₁−f₀−f₂)]h.
Worked examples: CBSE question patterns
These are original practice questions modeled on common board-exam patterns; they are not reproduced past-paper questions.
Worked example 2
Question: For a grouped distribution, median class is 20–30; l=20, N=40, cf=16, f=12, h=10. Find the median.
Solution: Median=20+[(20−16)/12]×10=20+10/3≈23.33.
Practical activity / investigation
Collect the number of minutes classmates spend reading in one evening, group the data into equal intervals, and calculate mean, median and mode. Compare what each measure says about a “typical” value.
Record: Write the aim, materials, steps, observations and conclusion in your notebook. Follow teacher supervision for any classroom activity.
Quick practice with answers
Try each question before opening its solution.
Practice 1: For class marks 5,15,25 and frequencies 1,4,5, find the mean.
Σfx=5+60+125=190; N=10; mean=19.
Practice 2: If N=50, which cumulative position is used to locate the median class?
N/2=25; locate the class whose cumulative frequency first reaches or exceeds 25.
Practice 3: What is the modal class?
The class interval with the greatest frequency.
Revision checklist
- Can I explain the key idea without memorising a worked solution?
- Have I selected the right formula and written units where needed?
- Can I show each algebraic or geometric step clearly?
- Can I check my answer by substitution, estimation or a diagram?
Aligned to the Class X Mathematics curriculum for 2026–27 and the NCERT Mathematics textbook. Always confirm any school-specific internal assessment with your teacher.