(a) \(\frac{m + n + s + p + q}{5} = 12 \)
\(\implies m + n + s + p + q = 12 \times 5 = 60\)
\(\frac{(m + 4) + (n - 3) + (s + 6) + (p - 2) + (q + 8)}{5} = \frac{m + n + s + p + q + 4 - 3 + 6 - 2 + 8}{5}\)
= \(\frac{60 + 13}{5} = \frac{73}{5}\)
= 14.6.
(b) In the community, there are 500 people.
The 75th percentile age = 65 years
Number of people in the 75th percentile = \(\frac{75 \times 500}{100} = 375\)
The 25th percentile = 15 years
Number of people in the 25th percentile = \(\frac{25 \times 500}{100} = 125\)
Number of people between 15 years and 65 years = 375 - 125 = 250 people.