(a) \(P = x : x \leq 2 = {..., -1, 0, 1, 2}\)
\(Q = x : -7 < x < 15 = {-6, -5, -4, -3, -2, -1, 0, ..., 13, 14}\)
\(R = x : -2 \leq x < 19 = {-2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18}\)
(i) \(P \cap Q = {-6, -5, -4, -3, -2, -1, 0, 1, 2}\)
(ii) \(R' = {..., -5, -4, -3, 19, 20, ...}\)
\(Q \cup R' = {..., -1, 0, 1, 2, 3, ...}\)
\(\therefore P \cap (Q \cup R') = {..., -1, 0, 1, 2}\)
(b)(i)
Class intervals | Midpoint (x) | Freq (f) | \(fx\) |
20 - 29 | 24.5 | 3 | 73.5 |
30 - 39 | 34.5 | 5 | 172.5 |
40 - 49 | 44.5 | 10 | 445 |
50 - 59 | 54.5 | 13 | 708.5 |
60 - 69 | 64.5 | 6 | 387 |
70 - 79 | 74.5 | 3 | 223.5 |
\(\sum \) | | 40 | 2010 |
(ii) \(Mean = \frac{\sum fx}{\sum f} = \frac{2010}{40}\)
= \(50.25\)