(a) If the mean of m, n, s, p and q is 12, calculate the mean of (m + 4), (n – 3), (s + 6), (p – 2) and (q + 8).
(b) In a community of 500 people, the 75th percentile age is 65 years while the 25th percentile age is 15 years. How many of the people are between 15 and 65 years?
Explanation
(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.