Choose the correct option. The A.M. of the first ten odd numbers is

(1) 10 (2) 100 (3) 1000 (4) 1

The arithmetic mean is nothing but an average of the values in the data set.

Answer: The A.M. of the first ten odd numbers is 10, that is option(1).

Let's understand the formula of the arithmetic mean and thereby find the solution to a given problem.

Explanation:

The first ten odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19.

The sum of the first ten odd numbers are 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100 = 10²

The arithmetic mean is given by the formula: A.M = Sum of the observations / Number of observations

A.M = Sum of first 10 odd numbers / 10 = (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19) / 10 = 100/10 = 10.

The arithmetic mean of the first ten odd numbers is 10.

Trick:

• Sum of first n odd numbers = n²
• Average or Mean or A.M of first n odd numbers = n     [∵ n² / n = n]

Thus, A.M. of the first ten odd numbers is 10, that is option(1).