GATE Probability and Statistics: Mean, median, mode, standard deviation, correlation and covariance – Previous Year Questions

6 GATE previous year questions on Mean, median, mode, standard deviation, correlation and covariance (Probability and Statistics, Data Science and Artificial Intelligence) with answers and explanations, from every paper.

1. GATE 2024 DA Q34 (1 mark, Numerical answer) – The sample average of 50 data points is 40. The updated sample average after including a new data point taking the value of 142 is .
2. GATE 2024 DA Q65 (2 marks, Numerical answer) – Two fair coins are tossed independently. X is a random variable that takes a value of 1 if both tosses are heads and 0 otherwise. Y is a random…
3. GATE 2025 DA Q20 (1 mark, Multiple choice) – Let X = aZ + b, where Z is a standard normal random variable, and a, b are two unknown constants. It is given that E[X] = 1, E[(X - E[X])Z] = -2, E[(X…
4. GATE 2025 DA Q54 (2 marks, Multiple select) – Consider a coin-toss experiment where the probability of head showing up is p. In the ith coin toss, let X i = 1 if head appears, and X i = 0 if tail…
5. GATE 2026 DA Q62 (2 marks, Numerical answer) – For a given data set \x 1, x 2, , x n\, where n = 100, it is known that 12000 i=1n j=1n(x i - x j)2 = 99 Let us denote x = 1n i=1n x i. The value of…
6. GATE 2026 DA Q63 (2 marks, Numerical answer) – Let X be a random variable that follows Uniform(-1, 1) distribution. The conditional distribution of the random variable Y given X = x is the…