Exams › JEE Advanced › Maths

Two data sets, each of size 10, have variances 4 and k, and corresponding means 2 and 4 respectively. If the variance of the combined data set (of size 20) is 5.5, find k.

1. 5
2. 6
3. 4
4. 3

Correct answer: 5

Solution

Combined mean = (10*2+10*4)/20 = 60/20 = 3. d1 = 2-3 = -1, d2 = 4-3 = 1. Combined variance = [10*(4) + 10*k + 10*(1) + 10*(1)]/20 = [40+10k+10+10]/20 = (60+10k)/20 = 5.5. So 60+10k = 110 => 10k = 50 => k = 5.

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 →