Three averages, two kinds of chart and one probability formula. The questions are short, so the marks here are the cheapest in the paper.
Study Zone is free for our students — you just need to log in with your WhatsApp number first.
Log in with WhatsApp →The first two chapters of every book are free once you're logged in. To open this one, request an unlock and we'll get back to you on WhatsApp.
Different questions want different averages. Read carefully which one is asked for.
📈 Which is which
| Average | How to find it |
|---|---|
| Mean | add everything, divide by how many |
| Median | put in order first, then take the middle one |
| Mode | the value that appears most often |
| Range | largest minus smallest |
Order the data before finding the median. For 7, 2, 9, 4, 6 the median is not 9. Sorted, the list is 2, 4, 6, 7, 9, so the median is 6.
An even number of values? Take the mean of the two middle ones. For 3, 5, 7, 9 the median is (5 + 7) ÷ 2 = 6 — a value that is not in the list at all.
The reverse question. "The mean of five numbers is 12. Four of them are 8, 10, 14 and 16. Find the fifth." The total must be 60, and the four add to 48, so the fifth is 12.
A pie chart shares out 360°; a bar graph shares out a scale.
🥧 Reading a pie chart
The whole circle is 360° and stands for the total.
Angle for a part = (part ÷ total) × 360°.
To go the other way: part = (angle ÷ 360) × total.
Worked example. In a survey of 720 people, 180 chose cricket. Its slice is (180 ÷ 720) × 360 = 90° — a quarter of the circle, which you could have seen at a glance.
Bar graphs are for comparing; pie charts are for shares of a whole. A question asking "what fraction of the total…" is nearly always a pie-chart question.
Probability = favourable outcomes ÷ total outcomes. It is always between 0 and 1.
🎲 Standard results
| Experiment | Event | Probability |
|---|---|---|
| One coin | a head | 1/2 |
| One die | an even number | 3/6 = 1/2 |
| One die | a prime number | 3/6 = 1/2 (2, 3, 5) |
| One die | a number over 4 | 2/6 = 1/3 |
| Two coins | exactly one head | 2/4 = 1/2 |
1 is not a prime number. On a die the primes are 2, 3 and 5 — three of them, not four. This is the most common slip in the probability question.
The probability of an event not happening is 1 minus the probability that it does. If P(rain) = 0.3 then P(no rain) = 0.7.
12 Olympiad questions on averages, charts and probability. 🍀
