Theory question 105
Measures of Dispersion(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?
Show the model answer
Model answer
(a) m + n + s + p + q = 60
New total = 60 − 4 − 3 + 6 − 2 − 8 = 49; new mean = 49/5 = 9.8
(b) 75% − 25% = 50% of the people: 0.5 × 500 = 250 people
Explanation
Find the total first; adding or subtracting from each value changes the total by the sum of the changes.