Statistics and Probability – JEE Mains Mathematics

• by Zenith LMS
• Updated April 2025

1. Measures of Dispersion

• Range: Difference between the highest and lowest values.
• Mean Deviation:
  • For ungrouped data: Mean deviation from mean/median is calculated using absolute differences.
  • For grouped data: Apply class-wise deviations and frequencies.
• Standard Deviation (σ):
  • For ungrouped data:

    σ = √[(1/n) × Σ(xᵢ - x̄)²]

  • For grouped data: Use midpoints and frequency for calculation.
• Variance: Square of the standard deviation.

2. Measures of Central Tendency

• Mean: Average of all data values.
• Median: Middle value when data is arranged in order.
• Mode: Most frequent value in the dataset.
• For grouped data: Apply appropriate formulae using class intervals and frequencies.

3. Probability

• Probability of an Event:

  P(E) = Number of favorable outcomes / Total number of outcomes

• Addition Theorem:

  P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

• Multiplication Theorem:

  P(A ∩ B) = P(A) × P(B|A)

• Bayes' Theorem:

  P(A|B) = [P(B|A) × P(A)] / P(B)

  Useful for finding conditional probabilities.

4. Probability Distribution

• Random Variable: A variable whose possible values are numerical outcomes of a random phenomenon.
• Probability Distribution: A table or function that gives the probabilities of outcomes of a random variable.
• Expected Value:

  E(X) = Σ xᵢ P(xᵢ)