Take timed practice tests on Statistics for JEE Main and JEE Advanced with session-wise drills, score review, and explanation-led revision.
Six 20-question timed sessions plus one 60-question module test. Each question is original and calibrated from the uploaded material pattern without copying PDF wording.
Ready
1. The mean of {2, 4, 6, 8, 10} is:
Explanation: Mean = (2+4+6+8+10)/5 = 30/5 = 6.
2. The median of {3, 1, 4, 1, 5, 9, 2} (sorted: 1,1,2,3,4,5,9) is:
Explanation: After sorting: 1, 1, 2, 3, 4, 5, 9. n = 7 (odd). Median = middle value = (7+1)/2 = 4th value = 3.
3. The mode of {2, 3, 3, 4, 5, 3, 6} is:
Explanation: Mode = most frequently occurring value. 3 appears 3 times — more than any other value → mode = 3.
4. The variance of a dataset is the:
Explanation: Variance σ² = (1/n)Σ(xᵢ − x̄)². Standard deviation σ = √(variance).
5. If all values in a dataset are increased by a constant k, the standard deviation:
Explanation: Adding a constant to all values shifts the mean by k but doesn't change the spread. Variance and SD are unchanged. However, multiplying all values by k multiplies SD by |k|.
6. The coefficient of variation (CV) is:
Explanation: CV = (σ/x̄) × 100%. It is a relative measure of dispersion, useful for comparing variability across datasets with different units or means. Lower CV = less relative variability.
7. The interquartile range (IQR) is:
Explanation: IQR = Q₃ − Q₁, where Q₁ = 25th percentile and Q₃ = 75th percentile. It measures the spread of the middle 50% of data.
8. If the mean of 10 observations is 15 and each observation is increased by 5, the new mean is:
Explanation: Adding 5 to each observation adds 5 to the mean: new mean = 15 + 5 = 20. The mean shifts by the same constant.
9. Variance = (Σx²/n) − (x̄)². This formula shows:
Explanation: Alternative variance formula: σ² = (Σxᵢ²/n) − (x̄)². This is computationally easier than finding deviations from mean. Derived by expanding Σ(xᵢ−x̄)²/n.
10. If Σxᵢ = 60, Σxᵢ² = 480, n = 10, then the standard deviation is:
Explanation: σ² = Σxᵢ²/n − (Σxᵢ/n)² = 480/10 − (6)² = 48 − 36 = 12. σ = √12 = 2√3 ≈ 3.46. All three expressions represent the same value.
11. For a symmetric distribution, which relationship holds?
Explanation: In a perfectly symmetric distribution (e.g., normal distribution), the mean, median, and mode all coincide at the centre of the distribution.
12. The range of the dataset {5, 3, 8, 1, 9} is:
Explanation: Range = Maximum − Minimum = 9 − 1 = 8.
13. If variance of n observations xᵢ is σ², then variance of axᵢ + b is:
Explanation: Shifting by b (adding constant) doesn't change variance. Scaling by a: Var(aX+b) = a²Var(X) = a²σ². Standard deviation becomes |a|σ.