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GCSE Maths · Statistics
Time series graphs GCSE Questions and Worked Answers
A time series graph shows measurements in chronological order, usually with time on the horizontal axis. Plot values at their correct times and join consecutive observations when appropriate. Describe overall trend, repeated seasonal patterns and unusual values separately.
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Start with the meaning
What you need to know about time series graphs
Suppose a shop records its number of orders every month. January has 20, February 24 and March 22. A time series keeps these observations in the order they happened. Put the months along the bottom of a graph and orders up the side, then plot one point for each month. This lets you see changes over time.
See the idea first
Keep time order and read changes, not just heights
The plotted points use two coordinates: time across and the measured value up. Joining neighbouring observations helps show the sequence. The overall direction is called the trend. A pattern repeating at similar times each year is seasonal variation; one isolated peak is not enough to establish it.
From problem to method
Typical problems you need to be able to solve
These are the main kinds of question in this topic. Each card first states the problem, then explains how to solve it.
Read and compare values
What the problem asks: Orders rise from 22 in March to 30 in April. Find the change.
How to solve it: Subtract the earlier value from the later: 30 − 22 = 8 more orders. State the units and the direction.
Describe a trend
What the problem asks: Over six months orders are 20, 24, 22, 30, 28, 34. Describe the pattern.
How to solve it: There is an overall increase from 20 to 34, with falls in March and May. Do not claim it rises every month.
Identify seasonality and limits
What the problem asks: Sales peak every December for four years. What does that suggest about next December?
How to solve it: It suggests an annual seasonal peak, but not a guaranteed value. Other changes could alter the pattern; use several cycles as evidence.
A reliable routine
Plot and interpret a time series
Use this for values recorded at successive times. The horizontal spacing must represent elapsed time; interpreting the ordered sequence can reveal trend and repetition that a list of unordered values would hide.
- Label time horizontally and the measured quantity and units vertically.
- Choose consistent scales; unequal time gaps need unequal spacing.
- Plot the observations accurately and join consecutive points if the task calls for a line graph.
- Describe trend with values, then repeated patterns and unusual observations; qualify any forecast.
Check: A straight segment between monthly readings is not evidence that change was constant during the month. A forecast beyond the observed time range is an extrapolation, so its reliability depends on the pattern continuing.
Fully worked
Time series graphs GCSE worked examples
Each solution explains the clue, why the method fits and how to check the result.
Example 1
Plot a short series
Question
A shop records 12, 18, 15 and 21 orders in January, February, March and April. Describe how to draw a time series graph.
Put January–April in order at equal monthly intervals on the horizontal axis. Label the vertical axis 'Orders' with an even scale covering 0–25, for example steps of 5. Plot Jan 12, Feb 18, Mar 15, Apr 21 and join consecutive points with straight segments. Do not reorder months by sales size.
Example 2
Find a change
Question
A time series shows 45 visits in May and 62 in June. Find the increase.
The increase is 17 visits. This is a difference, not a percentage increase unless requested.
Example 3
Percentage change
Question
A monthly total rises from 80 to 100. Find its percentage increase.
Use the earlier value as the base.
Example 4
Trend with fluctuations
Question
Annual totals are 120, 135, 128, 150 and 160. Describe the overall pattern with evidence.
The series rises overall from 120 to 160, a net increase of 40, but falls from 135 to 128 in the third year. Say 'overall upward trend with a temporary fall', not 'increases every year'.
Example 5
Seasonal pattern
Question
Quarterly sales are: Year 1 — Q1: 20, Q2: 30, Q3: 50, Q4: 25; Year 2 — Q1: 24, Q2: 34, Q3: 55, Q4: 29; Year 3 — Q1: 28, Q2: 38, Q3: 60, Q4: 33. Identify a seasonal feature and an overall trend.
Quarter 3 is the highest in all three years, suggesting a repeated seasonal peak. Comparing the same quarter across years also shows growth, for example Q1 rises 20 → 24 → 28 and Q3 rises 50 → 55 → 60. The series has both seasonality and an upward trend.
Example 6
A cautious forecast
Question
Annual counts are 100, 110, 120 and 130. Use the continuing linear pattern to predict the next count, and state a limitation.
Successive increases are 10.
A prediction is 140 if the pattern continues. This extrapolates beyond the data; a change in circumstances could make it inaccurate.
10 original questions · total 21 marks
Time series graphs GCSE exam-style questions
Try each question before opening its fully worked answer. The difficulty rises through the set.
Before you startAllow about 26 minutes · Show your working. Give exact answers unless a question asks you to round, and include units where needed. · answers start collapsed
Choose the horizontal axis
You record water usage each day. What belongs on the horizontal axis of a time series graph?
Show worked answer
The days in chronological order, with spacing representing elapsed time. Water usage belongs on the vertical axis with units.
Difference
Visits fall from 72 on Monday to 59 on Tuesday. Find the decrease.
Show worked answer
A decrease of 13 visits.
Greatest change
Monthly totals are Jan 15, Feb 24, Mar 20, Apr 33. Between which consecutive months is the greatest increase?
Show worked answer
Changes are +9, −4, +13. The greatest increase is March to April, by 13.
Net change
Values are 50, 65, 55 and 70 in order. Find the net change from first to last.
Show worked answer
Net increase 20; intermediate rises and falls do not change that endpoint difference.
Percentage fall
A value falls from 150 to 120 over one month. Find the percentage decrease.
Show worked answer
Overall description
Annual values are 90, 84, 88, 75. Describe the pattern.
Show worked answer
An overall decrease from 90 to 75, with a temporary rise from 84 to 88. It does not decrease every year.
Seasonality evidence
A graph has just one summer peak in a single year. Is this enough to establish a repeating annual seasonal pattern?
Show worked answer
No. It may be seasonal, but several years of similar timing would give stronger evidence that the peak repeats annually.
Unequal time intervals
Measurements occur at 09:00, 09:30 and 11:00. Should all three points be equally spaced horizontally? Explain.
Show worked answer
No. The second gap is 90 minutes, three times the first 30-minute gap, so it needs three times the horizontal spacing on a time scale.
Interpolate
A straight segment joins 10:00 at 40 litres to 12:00 at 60 litres. Estimate the value at 11:00 from that segment and state the assumption.
Show worked answer
11:00 is halfway, so
This line-based estimate assumes a constant rate between the readings; the actual unseen value might differ.
Extrapolate
A series has annual values 200, 190, 180, 170. Predict the next value if the pattern continues and explain why it is uncertain.
Show worked answer
The pattern subtracts 10 per year.
Predicted value 160. It is beyond the observed range, and the decline may not continue.
Examiner-style feedback
Common time series graphs mistakes
Keep observations in chronological order.
Seasonality requires evidence of a repeating time-related pattern.
State the continuation assumption and uncertainty.
30-second recap
Choose, carry out, check
Translate the wording before you reach for a rule.
- Time order and correct spacing.
- Read values and units.
- Separate trend from seasonal repetition.
- Qualify interpolation and forecasts.
Quick answers
Time series graphs FAQ
How is this different from a scatter graph?
A time series specifically tracks values against time and often joins them in order. A scatter graph usually compares two variables without a chronological joining rule.
Must a time-series vertical axis start at zero?
Not always, but any shortened scale must be clear. Check the axis values before judging how dramatic a change looks.
Content standards
Curriculum and rights review
S2 time-series graphs across tiers. No moving-average method is presented as required GCSE Mathematics content; this guide focuses on plotting, interpretation and cautious prediction. Questions, suggested marks, solutions and diagrams are original practice material, not official past-paper questions.
Official specification references