CBSE Class 10 Maths: Statistics & Probability — Notes 2026

Mean for Grouped Data

• Direct method: x̄ = Σfᵢxᵢ/Σfᵢ
• Assumed mean method: a = assumed mean; dᵢ = xᵢ−a; x̄ = a + Σfᵢdᵢ/Σfᵢ
• Step deviation method: uᵢ = (xᵢ−a)/h; x̄ = a + h × Σfᵢuᵢ/Σfᵢ

Median for Grouped Data

• Identify median class (cumulative freq just ≥ n/2)
• Formula: M = l + [(n/2 − cf)/f] × h
• Where l = lower boundary, cf = preceding cumulative freq, f = median class freq, h = width

Mode for Grouped Data

• Modal class = class with maximum frequency
• Mode = l + [(f₁−f₀)/(2f₁−f₀−f₂)] × h (f₀=preceding, f₂=following class freq)
• Empirical relation: 3 Median = Mode + 2 Mean

Ogive — Graphical Method

• Less than ogive: plot (upper boundary, cumulative freq); rising curve
• More than ogive: plot (lower boundary, decreasing cumulative freq)
• Intersection of both ogives gives median on x-axis

Probability — Basic Concepts

• P(E) = number of favourable outcomes / total outcomes; 0 ≤ P ≤ 1
• P(E) + P(Ē) = 1; mutually exclusive events: P(A or B) = P(A) + P(B)
• Sample space: set of all possible outcomes

CBSE Probability Problems

• One card drawn from deck of 52; P(face card), P(ace of spades), P(red card)
• Two dice thrown; P(sum = 7), P(doublet), P(sum > 10)
• Bag with coloured marbles; P(drawing specific colour)

CBSE Exam Tips

• Draw ogive on graph paper with uniform scale; locate median and quartiles
• For probability: always list sample space if it is small (less than 20 outcomes)
• Mode formula: memorise carefully — f₀, f₁, f₂ definitions must be correct