Exams › JEE Advanced › Maths
Two data sets, each of size 5, have variances 4 and 5 and means 2 and 4 respectively. What is the variance of the combined data set of 10 values?
- 5/2
- 11/2
- sqrt(11)/2
- 13/2
Correct answer: 11/2
Solution
The combined variance accounts for both within-group variance and the spread of group means from the combined mean. With equal group sizes n=5, combined mean = 3, and the formula yields (5*5 + 5*6)/10 = 55/10 = 11/2.
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 →