📖 Chapter 13 — Statistics (CBSE Class 10 Maths): Detailed notes — mean, mode and median of grouped data, with formulas and worked steps.
Chapter 13 — Statistics
📊 1. Mean of Grouped Data (3 methods)
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)
📈 2. Mode of Grouped Data
Mode = l + [ (f₁ − f₀) / (2f₁ − f₀ − f₂) ] × h
where l = lower limit of the modal class (highest frequency), f₁ = frequency of modal class, f₀ = frequency of the class before it, f₂ = of the class after it, h = class size.
📉 3. Median of Grouped Data
Median = l + [ (n/2 − cf) / f ] × h
where l = lower limit of the median class (where cumulative frequency first reaches n/2), cf = cumulative frequency before it, f = frequency of the median class, h = class size, n = Σfᵢ.
🔗 4. Empirical Relationship
Mode = 3 × Median − 2 × Mean
🧠 Remember: Mean = Σfx/Σf. Mode uses the modal class (max frequency). Median uses the median class (cf reaches n/2). Mode = 3 Median − 2 Mean. Class mark xᵢ = (lower+upper)/2.
⭐ Exam Tips: ① Make a table of xᵢ, fᵢ, fᵢxᵢ (or dᵢ, uᵢ). ② Mean by any of the three methods. ③ Mode — identify the modal class, apply the formula. ④ Median — build cumulative frequency, find the median class. ⑤ Use the empirical relation if two measures are known.