In ten observations, the mean of all 10 numbers is 15 , the mean of the first six observations is 16 and the mean of the last five observations is 12 . The sixth number is

Step-by-step solution

Let the mean of the last four observations be A 2 . Then, by the formula for combined mean, we get, 15 = 6 × 16 + 4 × A 2 6 + 4 or 150 = 96 + 4 A 2 ∴ A 2 = 54 4 Let the sixth number is x , then taking the sixth number as a collection, the combined mean of this collection and the collection of the last four is 12 . ∴ By the definition of combined mean 12 = 1 × x + 4 × 54 4 1 + 4 ∴ 60 = x + 54 ∴ x = 6 Hence, the sixth number = 6