In short: Statistics (Chapter 13) carries 8-10 marks in CBSE Class 10 Maths. It is the most scoring chapter because the question types are 100% predictable — you either calculate mean, median, or mode from grouped data. There are no proofs, no theorems, just formulas and arithmetic. If you practice 10 problems, you can score full marks from this chapter.
Why Statistics Is the Easiest 10 Marks
- Only 3 question types: Mean, Median, Mode
- Every question gives you a frequency table — you just apply the formula
- No conceptual traps — if your arithmetic is correct, your answer is correct
- Appears every year as a 5-mark question
Mean of Grouped Data
Three Methods
1. Direct Method: Mean = Σfᵢxᵢ / Σfᵢ
Where xᵢ = class mark (midpoint), fᵢ = frequency
2. Assumed Mean Method (Shortcut): Mean = a + (Σfᵢdᵢ / Σfᵢ)
Where a = assumed mean, dᵢ = xᵢ - a
3. Step-Deviation Method (Most used in exams): Mean = a + (Σfᵢuᵢ / Σfᵢ) × h
Where uᵢ = (xᵢ - a) / h, h = class size
Solved Example: Step-Deviation Method
Find the mean of the following data:
| Class Interval | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
|---|---|---|---|---|---|
| Frequency (fᵢ) | 5 | 8 | 15 | 10 | 7 |
Solution:
Take a = 25 (assumed mean), h = 10
| CI | fᵢ | xᵢ | uᵢ = (xᵢ-25)/10 | fᵢuᵢ |
|---|---|---|---|---|
| 0-10 | 5 | 5 | -2 | -10 |
| 10-20 | 8 | 15 | -1 | -8 |
| 20-30 | 15 | 25 | 0 | 0 |
| 30-40 | 10 | 35 | 1 | 10 |
| 40-50 | 7 | 45 | 2 | 14 |
| Total | 45 | 6 |
Mean = 25 + (6/45) × 10 = 25 + 1.33 = 26.33
Median of Grouped Data
Formula: Median = l + [(n/2 - cf) / f] × h
Where:
- l = lower limit of the median class
- n = total frequency (Σfᵢ)
- cf = cumulative frequency of the class before the median class
- f = frequency of the median class
- h = class size
How to Find the Median Class
- Calculate n/2
- Find the cumulative frequency (cf) column
- The class where cf first exceeds n/2 is the median class
Solved Example
Find the median:
| CI | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
|---|---|---|---|---|---|
| f | 5 | 8 | 15 | 10 | 7 |
Step 1: n = 45, n/2 = 22.5
Step 2: Cumulative frequency: 5, 13, 28, 38, 45
Step 3: 28 is the first cf ≥ 22.5 → Median class = 20-30
Step 4: l = 20, cf = 13 (class before), f = 15, h = 10
Median = 20 + [(22.5 - 13) / 15] × 10 = 20 + (9.5/15) × 10 = 20 + 6.33 = 26.33
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Mode of Grouped Data
Formula: Mode = l + [(f₁ - f₀) / (2f₁ - f₀ - f₂)] × h
Where:
- l = lower limit of the modal class
- f₁ = frequency of the modal class
- f₀ = frequency of the class before the modal class
- f₂ = frequency of the class after the modal class
- h = class size
How to Find the Modal Class
The class with the highest frequency is the modal class.
Solved Example
Find the mode:
| CI | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
|---|---|---|---|---|---|
| f | 5 | 8 | 15 | 10 | 7 |
Modal class = 20-30 (highest frequency = 15)
l = 20, f₁ = 15, f₀ = 8, f₂ = 10, h = 10
Mode = 20 + [(15 - 8) / (2×15 - 8 - 10)] × 10 = 20 + (7/12) × 10 = 20 + 5.83 = 25.83
Ogive (Cumulative Frequency Curve)
An ogive is a graph of cumulative frequency vs upper class boundaries.
Types:
- Less than ogive: plot cumulative frequency against upper class limits
- More than ogive: plot cumulative frequency against lower class limits
Finding median from ogive: Draw a horizontal line from n/2 on the y-axis to the curve, then drop vertically to the x-axis. The point on the x-axis is the median.
Relationship Between Mean, Median, and Mode
Empirical formula: 3 × Median = Mode + 2 × Mean
This is an approximate relationship. If you know two of the three, you can estimate the third.
Board Exam Tips
- Use the step-deviation method for mean — it is the fastest and least error-prone.
- Always make a complete table with all columns (xᵢ, fᵢ, uᵢ, fᵢuᵢ, cf). The table earns step marks.
- Double-check your arithmetic — calculation errors are the #1 reason students lose marks in Statistics.
- Show the formula before substituting — formula = 1 mark.
- Write the answer with "∴" — "∴ Mean = 26.33" signals completion.
For the complete marks distribution, see the CBSE Class 10 Maths marks weightage. For all formulas, see the Maths formulas list.
Frequently Asked Questions
How many marks does Statistics carry?
8-10 marks in CBSE Class 10 Maths (combined with Probability, the unit carries 11 marks).
Which method should I use for Mean?
Step-deviation method is recommended. It works for all problems and reduces calculation errors. The direct method is simpler but only for small numbers.
Is the Ogive important for the exam?
Ogive appears occasionally as a 3-5 mark question. Know how to plot it and find the median graphically. It is less frequently asked than Mean, Median, and Mode calculations.
How many practice problems should I solve?
At least 10 — 3 Mean, 3 Median, 2 Mode, 2 Ogive. The question patterns repeat with different numbers.
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