WAEC 2018 · Paper 2 · Q5

(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?

Worked solution (try it first)

(a)

Turn the mean into a total: $m + n + s + p + q = 5 \times 12 = 60$ .
The new numbers add up to $(m + n + s + p + q) + 4 - 3 + 6 - 2 + 8 = 60 + 13$
$= 73$ , so their mean is $\frac{73}{5} = 14.6$ .

(b)

A quarter of the people are below the 25th percentile (15 years) and three quarters below the 75th percentile (65 years).
So between 15 and 65 years there are $75\% - 25\% = 50\%$ of the people: $0.5 \times 500 = 250$ .
(That's $375 - 125 = 250$ .)

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