If mean of 14, 13, 18, 16, k, (k + 3) is 13, then what will be the mean of k, 8, 9, 11, 5, 10, 6?

Question: If mean of 14, 13, 18, 16, k, (k + 3) is 13, then what will be the mean of k, 8, 9, 11, 5, 10, 6?

Solution:
The mean of 14, 13, 18, 16, k, (k + 3) = 13 which means
{14 + 13 + 18 + 16 + k + (k + 3)}/6 = 13
⇒ 2k + 64 = 78
⇒ 2k = 78 - 64
⇒ 2k = 14
⇒ k = 14/2
∴ k = 7

Then, the mean of k, 8, 9, 11, 5, 10, 6 is
= (k + 8 + 9 + 11 + 5 + 10 + 6)/7
= (7 + 8 + 9 + 11 + 5 + 10 + 6)/7
= 56/7
= 8