Let sets A and B have 5 elements each. Let the mean of the elements in sets A and B be 5 and 8 respectively and the variance of the elements in sets A and B be 12 and 20 respectively. A new set C of 10 elements is formed by subtracting 3 from each element of A and adding 2 to each element of B . Then the sum of the mean and variance of the elements of C is

Step-by-step solution

Let the elements in set A be x 1 , x 2 , x 3 , x 4 , x 5 Now given mean is = 5 Now subtracting 3 from each term we get, New mean as x 1 - 3 , x 2 - 3 … , x 5 - 3 = 5 - 3 = 2 So, sum of elements will be 2 × 5 = 10 Also given variance, Var X = 12 Now we know that subtracting 3 from each term will not change the variance, So, Var x 1 - 3 , x 2 - 3 , … x 5 - 3 = 12 ⇒ ∑ x i - 3 2 5 - 4 = 12 ⇒ ∑ x i - 3 2 = 80 Now let elements in set B be y 1 , y 2 … y 5 Given mean y 1 , y 2