CIE iGCSE Maths C9.1 Classifying statistical data Exam Style Practice Questions- Paper 1
Given the sets:
$$ \begin{aligned} & \mathscr{E}=\{\mathrm{a}, \mathrm{~b}, \mathrm{c}, \mathrm{~d}, \mathrm{e}, \mathrm{f}, \mathrm{~g}, \mathrm{~h}, \mathrm{i}, \mathrm{j}, \mathrm{k}\} \\ & F=\{\mathrm{f}, \mathrm{a}, \mathrm{c}, \mathrm{e}\} \\ & B=\{\mathrm{b}, \mathrm{a}, \mathrm{c}, \mathrm{k}\} \end{aligned} $$
(a) Complete the Venn diagram.
(b) Find $\mathrm{n}(F \cup B)$.
▶️ Answer/Explanation
(a)
The Venn diagram is completed by placing:
- $\{\mathrm{a}, \mathrm{c}\}$ in the intersection of $F$ and $B$ (common elements).
- $\{\mathrm{f}, \mathrm{e}\}$ in $F$ only.
- $\{\mathrm{b}, \mathrm{k}\}$ in $B$ only.
- Remaining elements $\{\mathrm{d}, \mathrm{g}, \mathrm{h}, \mathrm{i}, \mathrm{j}\}$ outside both sets.
(b) Ans: 6
$F \cup B = \{\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{e}, \mathrm{f}, \mathrm{k}\}$.
Count the elements: $\mathrm{n}(F \cup B) = 6$.
(a) Mei writes down five integers.
- The lowest integer is 8.
- The range is 9.
- The median is 15.
- The total of the five integers is 66.
- There is no mode.
Write down the five integers.
(b) Huan writes down four numbers.
- The mean of these four numbers is 17.
- He writes down a fifth number.
- The mean of these five numbers is 20.
Find the fifth number.
▶️ Answer/Explanation
(a) Ans: 8, 10, 15, 16, 17
Given the lowest number is 8 and range is 9, the highest number is 17. With median 15, the third number must be 15. The remaining two numbers must be between 8-15, distinct (no mode), and sum to 66-(8+15+17)=26. The only pair satisfying these conditions is 10 and 16.
(b) Ans: 32
Total of first four numbers = 4 × 17 = 68. Total of five numbers = 5 × 20 = 100. Therefore, the fifth number = 100 – 68 = 32.