Statistics
Mean, median, mode for grouped data and cumulative frequency.
Chapter Overview
Class 10 Statistics covers mean, median, and mode for grouped data using assumed mean and step-deviation methods, plus cumulative frequency and ogives — essential for interpreting exam scores and surveys.
Mean of Grouped Data
Direct
x̄ = Σfᵢxᵢ / Σfᵢ
Assumed mean
x̄ = a + Σfᵢdᵢ / Σfᵢ, where dᵢ = xᵢ − a
Step deviation
x̄ = a + (Σfᵢuᵢ / Σfᵢ) × h, uᵢ = (xᵢ − a)/h
Median and Mode
Median
l + [(N/2 − cf)/f] × h
Mode
l + [(f₁−f₀)/(2f₁−f₀−f₂)] × h
- Median class: cumulative frequency just ≥ N/2
- Modal class has highest frequency
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Assumed mean
Classes 0–10, 10–20, 20–30 with frequencies 5, 8, 7. Find mean (mid-points 5, 15, 25).
- 1Σfx = 5×5 + 8×15 + 7×25 = 25 + 120 + 175 = 320
- 2Σf = 20
- 3Mean = 320/20 = 16
Answer
Mean = 16
Example 2: Median class
Total N = 50. Cumulative frequencies: 12, 28, 45. Which class contains median?
- 1N/2 = 25
- 2cf crosses 25 in second class
Answer
Second class (median class)
Key Points to Remember
- ✓ Use class marks (mid-points) for mean unless boundaries given
- ✓ Median divides data into two equal parts
- ✓ Empirical relation: Mode ≈ 3 Median − 2 Mean (approximate)
Exam Tips
- • Make cumulative frequency column for median
- • Identify modal class before applying formula
- • Show assumed mean a clearly in calculation
Practice MCQs — Statistics
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
For grouped data, mean uses: