Statistics Class 10 Notes: Mean, Median, Mode Formulas and Solved Examples

Quick answer: Statistics is 6–8 marks in Class 10 boards and is pure procedure — one full example done correctly teaches the whole chapter.

Mean of grouped data

• Direct: x̄ = Σfᵢxᵢ/Σfᵢ (xᵢ = class mark = (lower + upper)/2)
• Assumed mean: x̄ = a + Σfᵢdᵢ/Σfᵢ, dᵢ = xᵢ − a
• Step deviation: x̄ = a + h(Σfᵢuᵢ/Σfᵢ), uᵢ = (xᵢ − a)/h

Median

Find n/2, locate the median class (cumulative frequency just ≥ n/2). Median = l + [(n/2 − cf)/f] × h, where l = lower limit, cf = cumulative frequency of the previous class, f = frequency of median class, h = class width.

Mode

Modal class = highest frequency. Mode = l + [(f₁ − f₀)/(2f₁ − f₀ − f₂)] × h, f₁ = modal frequency, f₀ = previous, f₂ = next.

Empirical relation

3 Median = Mode + 2 Mean.

Solved example

Marks: 0–10 (5), 10–20 (8), 20–30 (15), 30–40 (10), 40–50 (7); n = 45.

Mean (direct): Σfx = 5×5 + 8×15 + 15×25 + 10×35 + 7×45 = 25 + 120 + 375 + 350 + 315 = 1185 → x̄ = 1185/45 = 26.33.

Median: n/2 = 22.5; cf: 5, 13, 28 → median class 20–30, cf = 13, f = 15. Median = 20 + (22.5 − 13)/15 × 10 = 20 + 6.33 = 26.33.

Mode: modal class 20–30; f₁ = 15, f₀ = 8, f₂ = 10. Mode = 20 + (7/(30 − 18)) × 10 = 20 + 5.83 = 25.83.

Check: 3 × 26.33 ≈ 25.83 + 2 × 26.33 ✓ (approximately).

Ogives

Less-than ogive (plot upper limits vs cumulative frequency) and more-than ogive (lower limits); they intersect at the median.

Common mistakes

• Using the class mark as the lower limit in median/mode
• Taking cf of the median class instead of the previous class
• Forgetting to convert inclusive classes (1–10, 11–20) to exclusive (0.5–10.5)

Related: Trigonometry Class 10.

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Frequently asked questions

Are these Statistics Class 10 Notes notes enough for the exam?

They cover every formula, definition and question type that appears in school and board papers for this chapter. Use them with the NCERT examples, exercise questions and the last five years' papers to be fully prepared.

How should I revise Statistics Class 10 Notes?

Revise the notes after 1 day, 7 days and 30 days. Solve five questions each time instead of only reading, and keep an error list of the steps you get wrong.

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