A frequency distribution is given as follows: x_i 1 2 4 f_i a b 2 If the mean and variance of this distribution are 2.1 and 1.09 respectively, then the value of 2a + 3b is equal to

Step-by-step solution

Let the total frequency be N = a + b + 2 . The mean is given by: x = f_i x_i N 2.1 = a(1) + b(2) + 2(4) a + b + 2 2.1(a + b + 2) = a + 2b + 8 2.1a + 2.1b + 4.2 = a + 2b + 8 1.1a + 0.1b = 3.8 11a + b = 38 (1) The variance is given by: ^2 = f_i x_i^2 N - ( x )^2 1.09 = a(1)^2 + b(2)^2 + 2(4)^2 a + b + 2 - (2.1)^2 1.09 = a + 4b + 32 a + b + 2 - 4.41 5.5 = a + 4b + 32 a + b + 2 5.5(a + b + 2) = a + 4b + 32 5.5a + 5.5b + 11 = a + 4b + 32 4.5a + 1.5b = 21 3a + b = 14 (2) Subtracting equation (2) from equation (1) : (11a