Exams › JEE Advanced › Maths

Two data sets are given: the first has 6 terms with mean 11 and variance 24; the second has 3 terms with mean 14 and variance 36. Find the variance of the combined set of 9 terms.

1. (A) 40
2. (B) 30
3. (C) 50
4. (D) 35

Correct answer: (B) 30

Solution

Combined mean = 12. Total sum of squared deviations = 6*24 + 6*(11-12)² + 3*36 + 3*(14-12)² = 144 + 6 + 108 + 12 = 270. Combined variance = 270/9 = 30.

Related JEE Advanced Maths questions

• The standard deviation of a set containing 25 values is 40. If 5 is added to each value in the set, what will the updated standard deviation be?
• Given Σ(xi − 5) = 9 and Σ(xi − 5)² = 45 for a dataset of 9 values x1, x2,..., x9, what is the standard deviation of the data?
• The variables X and U are connected by the equation X = 5 + 2U. If the mean of X is 10 and its coefficient of variation is 2.6, what is the coefficient of variation for U?
• What is the average absolute deviation from the mean for the arithmetic progression a, a + d, a + 2d,..., a + 2nd?
• What is the variance of the first n positive integers?
• Seven real numbers 9 = x1 < x2 <... < x7 form an arithmetic progression with common difference d. If their standard deviation is 4 and their mean is x_bar, find the value of x_bar + x6.

⚔️ Practice JEE Advanced Maths free + battle 1v1 →