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Year 11 Mathematics · Box plots and bivariate data

Name: ______________________

Date: ____________

1. Find the median of 3, 5, 6, 9, 12, 14, 20.
2. Find the interquartile range of 3, 5, 6, 9, 12, 14, 20.
3. In a box plot, what does the box itself (from Q1 to Q3) represent?
- ☐ (a) All of the data
- ☐ (b) The middle 50% of the data
- ☐ (c) The top 25% of the data
- ☐ (d) Only the outliers
4. Which of these is NOT part of the five-number summary?
- ☐ (a) Minimum
- ☐ (b) Median
- ☐ (c) Mean
- ☐ (d) Upper quartile
5. A data set has Q1 = 20 and Q3 = 32. Using the 1.5 × IQR rule, values above what number are outliers?
6. As the daily temperature rises, a shop sells more cold drinks. What type of correlation is this?
- ☐ (a) Positive
- ☐ (b) Negative
- ☐ (c) No correlation
- ☐ (d) Impossible to say
7. A scatter plot of car age (horizontal axis) against value (vertical axis) shows points falling from left to right, lying very close to a straight line. How is the relationship best described?
- ☐ (a) Weak positive linear
- ☐ (b) Strong negative linear
- ☐ (c) Strong positive non-linear
- ☐ (d) No relationship
8. There is a strong positive correlation between ice-cream sales and the number of sunburn cases. Which conclusion is best?
- ☐ (a) Eating ice-cream causes sunburn.
- ☐ (b) Sunburn causes people to buy ice-cream.
- ☐ (c) Both are likely linked to a third factor, such as hot, sunny weather; correlation alone does not prove causation.
- ☐ (d) The data must be wrong.

Answer sheet

1. 9 — There are 7 values in order, so the median is the 4th value: 9.
2. 9 — Leaving out the median (9): Q1 is the median of 3, 5, 6, which is 5, and Q3 is the median of 12, 14, 20, which is 14. IQR = 14 − 5 = 9.
3. The middle 50% of the data — The box stretches from the lower quartile to the upper quartile, covering the middle half of the data.
4. Mean — The five-number summary is minimum, Q1, median, Q3 and maximum. The mean is not included.
5. 50 — IQR = 32 − 20 = 12. Upper limit = Q3 + 1.5 × 12 = 32 + 18 = 50.
6. Positive — Both variables increase together, which is a positive correlation.
7. Strong negative linear — Value decreases as age increases (negative), and the points are close to a line (strong, linear).
8. Both are likely linked to a third factor, such as hot, sunny weather; correlation alone does not prove causation. — A correlation shows the variables move together, not that one causes the other.