Question

Statement (1): The mean of 100 observations is 50 and one of these observations is increased by 150, the sum of resulting observations is 100 × 50 + 150.

Statement (2): The sum of resulting observations = 100 × 50 + 100.

Options

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true, and statement 2 is false.

• Statement 1 is false, and statement 2 is true.

Answer 1

Statement 1 is true, and statement 2 is false.

Explanation:

The original sum of the 100 observations is 100 × 50. When a single observation is increased by 150, the total sum increases by that exact amount, making the new sum 100 × 50 + 150. Thus, Statement 1 is correct while Statement 2 is incorrect.