The mean of 5 numbers is 20. If one number is excluded their mean is 15. Then the excluded number is

Given that, Total number of observations = 5

Mean = 20

So, Sum of observations can be given as

Sum of observations = Mean × Total number of observations [∵ ]

⇒ Sum of observations = 20 × 5

⇒ Sum of observations = 100

Let the excluded number be x.

New Sum of observations = 100 – x

New Mean = 15

New total number of observations = 4

Mean is given by

⇒

⇒ 100 – x = 15 × 4

⇒ 100 – x = 60

⇒ x = 100 – 60 = 40

⇒ The excluded number is 40.

Thus, option (B) is correct.