Question

The mean of six numbers: x − 5, x − 1, x, x + 2, x + 4 and x + 12 is 15. Find the mean of first four numbers.

Answer 1

The mean of six numbers are x – 5, x – 1, x, x + 2, x + 4 and x + 12 is 15

∴ Mean =`(("x"-5)+("x"-1)+("x")+("x"+2)+("x"+4)+("x"+12))/6`

= `("x"-5+"x"-1+"x"+"x"+2+"x"+4+"x"+12)/6`

= `(12+6"x")/6=15`

⇒ 12 + 6x = 90

⇒ 6x = 90 − 12

⇒ 6x = 78

⇒ x = `78/6=13`

x = 13

∴ The six numbers are (13 − 5), (13 − 1), 13, (13 + 2), (13 + 4), (13 + 12) i.e. 8, 12, 13, 15, 17, 25

Now, mean of first four numbers =`(8+12+13+15)/4=48/4=12`