OxfordAQA International GCSE Mathematics: Interpreting graphs, comparing distributions and correlation (9260) – Revision Notes

These revision notes are for OxfordAQA International GCSE Mathematics (9260), specification Version 5.1 (for exams May/June 2018 onwards). They cover references S6, S7 and S8 in section 3.4.2, Interpretation, all Core content that can also be assessed on the Extension papers. For full explanations and longer worked examples, read the study guide.

Related pages: the practice set, the course hub, the printable checklist and the free diagnostics.

Coverage at a glance

Ref	Skill	Tier
S6	Read and interpret graphs and diagrams; draw conclusions	Core
S7	Compare distributions; make inferences	Core
S8	Recognise correlation; lines of best fit by eye and what they represent	Core

S6: Reading graphs and diagrams

Method in steps:

1. Read the title, axis labels, units and key.
2. Find the value of one small square on each scale.
3. Read the exact values needed.
4. Describe the trend in context.
5. State a conclusion the data supports.

Diagram	Key reminder
Line graph	Steeper means faster change; flat means no change
Dual bar chart	Compare the same category in each group
Composite bar chart	Read the size of each part as the difference between the tops of the sections
Pie chart	Frequency = (angle ÷ 360) × total
Stem-and-leaf	Check the key; count leaves for the total
Scatter graph	Direction, strength, outliers

Percentage change = (change ÷ original) × 100. Always divide by the starting value.

Worked reminder: a pie chart for 240 people has a sector of 120°. Frequency = 120/360 × 240 = 80 people (one third of 240).

Worked reminder: a line graph shows a plant’s height as 8 cm in week 2 and 20 cm in week 6. The mean growth is (20 - 8) ÷ (6 - 2) = 3 cm per week. The line is steeper where growth is faster, so a flat section would mean no growth in those weeks. Say “grew about 3 cm each week between weeks 2 and 6”, not “grows 3 cm every week forever”.

Reading between the lines of a graph: a straight segment between two plotted points is an assumption. If the graph shows readings at 10:00 and 11:00 only, an estimate for 10:30 assumes steady change. Say so when you estimate.

Signs a graph may mislead:

• the vertical axis does not start at zero
• the scale is uneven or the bars have different widths
• the diagram is 3-D or has a stretched image
• there is a very small sample or no source

S7: Comparing distributions

Recipe for a full comparison, with all four parts:

1. An average for each set, with its value.
2. A spread for each set (range), with its value.
3. A sentence saying which is higher, lower or more consistent, in context.
4. A reason or a caution (an extreme value, a small sample, unequal group sizes).

Measure	Use	Weakness
Mean	Uses every value; good for balanced data	Pulled by extreme values
Median	Middle value; good when there are extremes	Ignores how far the other values lie
Mode, modal class	Most common; works for categories	May not exist or may not be unique
Range	Easy spread measure	Depends only on the two end values

For grouped data, the mean is only an estimate (use class midpoints) and you can give the modal class but not an exact mode.

Pattern for the sentence: “On average, [group] had a higher [quantity] (median 14 against 11), but its results were less consistent (range 20 against 8).”

Worked reminder: two players’ scores in five games are P: 6, 8, 9, 10, 12 and Q: 2, 9, 9, 10, 15.

P: mean 45 ÷ 5 = 9, median 9, range 12 - 6 = 6
Q: mean 45 ÷ 5 = 9, median 9, range 15 - 2 = 13

“Both players have the same mean and median score (9), so their typical performance is equal. P is more consistent, with a range of 6 against 13 for Q.”

Making inferences: say what the data suggests about the wider group or the situation, then give a limit. Useful limits are a small sample, groups chosen in different ways, a difference that is small compared with the spread, and a trend that may not continue.

Do not write “A is better” without saying which measure and what the larger value means. A higher time is worse; a higher score is better.

Words to use precisely:

Term	Meaning
Outlier	A point well away from the general pattern
Trend	The general direction of the data over time
Interpolate	Estimate inside the range of the data
Extrapolate	Estimate outside the range of the data
Consistent	Little spread, so values are similar to each other
Modal class	The class with the highest frequency in grouped data

S8: Correlation and lines of best fit

Type	Description
Positive	Points rise left to right
Negative	Points fall left to right
None	No pattern
Strong	Points close to a straight line
Weak	Points scattered round the trend

Say both parts: “weak positive correlation”.

Method to draw a line of best fit by eye:

1. If the data are given, find the mean point (mean of x, mean of y).
2. Follow the trend with a ruler, aiming for balanced points above and below.
3. Let the line pass through or very close to the mean point.
4. Draw one straight line across the whole data range.
5. Leave out any outlier when placing it.

Using the line:

• To find the equation, read two points far apart on the line. Gradient = (y₂ - y₁) ÷ (x₂ - x₁). Substitute one point to find c in y = mx + c.
• Interpolation (estimates inside the data range) is fairly reliable.
• Extrapolation (outside the range) is not. Check that the answer makes sense.
• The gradient is the change in y for each 1 unit increase in x, in the units of the question.
• The y-intercept is the predicted y when x = 0. Only treat it as meaningful if x = 0 makes sense.

Must-know distinction: correlation shows a relationship, not that one variable causes the other. A third factor may affect both.

Worked reminder: a line passes through (0, 10) and (5, 35). Gradient = 25 ÷ 5 = 5, intercept 10, so y = 5x + 10. At x = 3, y = 5(3) + 10 = 25.

Quick self-test

1. A pie chart shows 200 people. One sector has angle 54°. How many people is that?
2. Find the mean, median and range of 3, 5, 5, 8, 14.
3. Which average is best for the data in question 2, and why?
4. Set A has mean 12 and range 4. Set B has mean 12 and range 9. Compare them.
5. A bar chart axis starts at 40, not 0. Why can this mislead?
6. x-values are 2, 4, 6, 8 and the y-values are 5, 9, 10, 16. Find the mean point.
7. A line of best fit passes through (0, 10) and (5, 35). Find its equation and estimate y when x = 3.
8. A graph shows values of 20, 26 and 35 in three successive months. Find the percentage increase from the first to the third.
9. State the type of correlation you expect between the age of a phone and its resale value.
10. A line of best fit for heights of children aged 4 to 10 is used to predict height at age 40. What is wrong?

Answers

1. 54/360 × 200 = 30 people.
2. Mean = 35 ÷ 5 = 7. Median = 5. Range = 14 - 3 = 11.
3. The median (5). The value 14 is much larger than the rest, so it pulls the mean up to 7, which is bigger than three of the five values.
4. Both sets have the same average, but B is more spread out. A is more consistent.
5. The part of each bar above 40 is shown, so differences between bars look bigger than they are.
6. Mean x = 20 ÷ 4 = 5. Mean y = 40 ÷ 4 = 10. The mean point is (5, 10).
7. Gradient = 25 ÷ 5 = 5, intercept 10: y = 5x + 10. When x = 3, y = 25.
8. (35 - 20) ÷ 20 × 100 = 75%.
9. Negative correlation: older phones tend to be worth less.
10. Age 40 is far outside the data range 4 to 10 (extrapolation), and children stop growing, so the straight-line trend does not continue.

Where marks are usually lost

• Reading the wrong scale: counting a small square as 1 when it is worth 2 or 5.
• Giving a pie chart angle as the frequency instead of converting it.
• Comparing averages but not spread, or the reverse.
• Quoting numbers for one set only.
• Not using the context, such as “Class B was slower” instead of just “B is higher”.
• Dividing by the new value rather than the original in a percentage change.
• Describing correlation with one word (“positive”) when the question needs both direction and strength.
• Drawing a line of best fit that bends, joins the first and last point, or ignores the trend.
• Trusting an extrapolated estimate without comment.
• Claiming that correlation proves cause.

Official syllabus

OxfordAQA International GCSE Mathematics (9260), specification Version 5.1 (for exams May/June 2018 onwards), published by OxfordAQA, section 3.4.2 Interpretation, references S6, S7 and S8.