(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 ...
Question 1 Report
(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?
Answer Details
(a) The mean of five numbers is their sum divided by 5.
Since the mean of \(m, n, s, p, q\) is 12, the sum is \(5 \times 12 = 60\).
Adding the constants changes the sum by \(+4 - 3 + 6 - 2 + 8 = +13\).
New sum \(= 60 + 13 = 73\), so new mean \(= \dfrac{73}{5} = 14.6\).
(b) The 25th percentile (15 years) and the 75th percentile (65 years) enclose the middle 50% of the data.
Number of people between 15 and 65 years \(= 50\% \times 500 = 250\).
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