Sheet № 239 · Foundation + Higher · AQA · Edexcel · OCR
Time Series Graphs –
Time series graphs appear on GCSE Maths papers at both Foundation and Higher tier, particularly on AQA and Edexcel. They show how a variable changes over time — for example, quarterly sales, monthly temperatures or yearly population figures. Exam questions ask you to plot data, describe trends, identify seasonal patterns and calculate mov
§Key definitions
Question:
The table shows the number of visitors (thousands) to a museum each quarter for two years.
Answer:
There is a seasonal pattern with a peak in Q3 each year. The overall trend is slightly increasing — each year's values are slightly higher than the previous year's.
Q1 (Foundation):
Monthly ice cream sales (units) from January to June are: 120, 150, 210, 340, 480, 520. Plot these on a time series graph and describe the trend.
Q2 (Foundation):
Looking at the graph in Q1, which month shows the biggest increase from the previous month?
Q3 (Higher):
Quarterly electricity usage (kWh) for a house is: Q1: 800, Q2: 500, Q3: 400, Q4: 750, Q1: 850, Q2: 520. Calculate the first three 4-point moving averages.
§Formulas to memorise
n-point moving average = sum of n consecutive values ÷ n
Trend — the overall direction of the data (increasing, decreasing or staying roughly constant) over a long period.
Seasonal variation — a regular repeating pattern within a fixed time period (e.g. ice cream sales peak every summer).
Moving average — a calculated average of consecutive data points that smooths out short-term fluctuations and reveals the underlying trend.
Plot the data — put time on the horizontal axis and the variable on the vertical axis. Use a consistent scale with no gaps.
Join the points — with straight lines.
Describe the trend — look at the overall direction, ignoring short-term ups and downs.
Identify seasonal variation — look for a repeating pattern with the same period (e.g. every 4 quarters).
Calculate moving averages — add the appropriate number of consecutive values and divide. Plot each moving average at the midpoint of the values used.
Draw a trend line — through the moving averages to make predictions.
Worked example
The table shows the number of visitors (thousands) to a museum each quarter for two years. | Quarter | Q1 Y1 | Q2 Y1 | Q3 Y1 | Q4 Y1 | Q1 Y2 | Q2 Y2 | Q3 Y2 | Q4 Y2 | |---|---|---|---|---|---|---|---|---| | Visitors (000s) | 12 | 18 | 24 |
Working:
⚠ Common mistakes
- ✗Using the wrong number of points in a moving average. For quarterly data, always use a 4-point moving average unless told otherwise.
- ✗Plotting the moving average at the wrong position. A 4-point moving average should be plotted at the midpoint of the four values used, not at the start or end.
- ✗Confusing trend with seasonal variation. The trend is the long-term direction; seasonal variation is the short-term repeating pattern within each cycle.
✦ Exam tips
- →When describing a trend, use phrases like "overall increasing trend" or "general downward trend" — avoid just listing individual rises and falls.
- →Moving average questions often ask you to plot the values on the same graph as the original data — use a different symbol (e.g. crosses vs dots).
- →Predictions based on the trend line are only reliable if the trend continues — always state this limitation.
- →For related data representation topics, see bar charts, pie charts and pictograms.