The average of the numbers 5, 3, 9, 11, 29 and (p+1) is 12. The average increases by 2 when the numbers (q-5) and (q+11) are also included. Find the value of q.

17

We know that,

Average = \(\frac{Sum \; of \; observation}{Number \; of \; observation}\)

No need to find the value of p,

The sum of given 6 numbers = 12 × 6 = 72

Now, according to the question,

72 + q - 5 + q + 11 = (12 + 2 ) × 8

78 + 2q = 112

2q = 34

q = 17