Time-Series Graphs — GCSE Maths Tutorial, Worked Examples & Practice

Revise Time-Series Graphs (plotting, reading and comparing trends and seasonal variation on time-series line graphs) within Statistics — Data Representation, aligned to Edexcel, AQA & OCR GCSE (9–1) and International GCSE Maths. The interactive practice tool at the top of this page includes 8 self-marking practice questions across 3 structured skill steps, with instant diagnostic feedback and full worked solutions.

Step 1 of 34 interactive practice questions

Reading & Comparing Time-Series Graphs

Reading values at equal time intervals, finding steepest changes and comparing two series

Key Method & Revision Notes

A time-series graph is a line graph that shows how a quantity changes over equal intervals of time (such as days, months, or quarters Q1–Q4, where each year is split into $4$ three-month quarters).
Time always goes on the horizontal axis ($x$-axis) in chronological order, and the measured quantity goes on the vertical axis ($y$-axis).
Steepest upward segment $=$ greatest increase between consecutive periods; steepest downward segment $=$ greatest decrease.
Comparing two series: Use the key (solid vs dashed line) and check where one graph crosses above or below the other.

Worked Example

Question:

The time-series graph shows quarterly cinema admissions (in thousands) in $2024$ and $2025$. (a) Write down the admissions in Q3 $2024$. (b) Work out the decrease from Q3 $2025$ to Q4 $2025$.

Step-by-Step Solution:

1. Read Q3 $2024$: Move up from Q3 $2024$ to the cross at $30 \implies 30{,}000$ admissions.

2. Find the decrease: Q3 $2025 = 34$ thousand and Q4 $2025 = 26$ thousand ($1\text{ small square} = 2$ thousand).

3. $34{,}000 - 26{,}000 = 8{,}000$ admissions.

Ready to test this skill? Use the interactive tool at the top of the page to practise 4 self-marking exam-style questions (8 questions loaded in this topic module).

Step 2 of 32 interactive practice questions

Plotting & Completing a Time-Series Graph

Plotting neat crosses on vertical gridlines and joining consecutive points with ruled segments

Key Method & Revision Notes

To complete a time-series graph accurately under GCSE exam conditions:
Check the vertical scale first: Count how many small squares make one major step (e.g. $5$ squares for $10$ units $\implies 1\text{ square} = 2$ units).
Plot directly on each vertical time line: Mark each point with a neat cross ($\times$) directly above its month or quarter label.
Join consecutive points in time order using a sharp pencil and straight ruler. Do not draw a smooth curve or a line of best fit!

Worked Example

Question:

Quarterly bike hires (in hundreds) were $10, 24, 32, 14$ in $2024$ and $12, 28, 36, 16$ in $2025$. The first $6$ points are plotted. Complete the time-series graph for Q3 $2025$ ($36$) and Q4 $2025$ ($16$).

Step-by-Step Solution:

1. Each small vertical square represents $10 \div 5 = 2$ hundred hires.

2. Plot $(\text{Q3 2025}, 36)$ ($3$ squares above $30$) and $(\text{Q4 2025}, 16)$ ($3$ squares above $10$), then join Q2 → Q3 → Q4 with ruled straight segments:

Ready to test this skill? Use the interactive tool at the top of the page to practise 2 self-marking exam-style questions (8 questions loaded in this topic module).

Step 3 of 32 interactive practice questions

Trends & Seasonal Variation

Describing overall long-term trends, repeating seasonal peaks/troughs and reliability of predictions

Key Method & Revision Notes

When a GCSE question asks you to "describe what the time-series graph shows" or "make two comments" ($2$ marks), always comment on both features:
1. Seasonal Variation (short-term repeating cycle): Identify which quarter or season peaks every year and which is lowest every year (e.g. "Sales peak every Q3 in summer and are lowest every Q1 in winter").
2. General / Overall Trend (long-term direction): Compare matching quarters from year to year — state whether there is an upward (increasing) trend, a downward (decreasing) trend, or whether figures stay roughly constant.
Reliability of predictions: Extrapolating into future years is only an estimate because it assumes the current trend continues unchanged.

Worked Example

Question:

The graph shows a household's quarterly gas bills (£) from $2023$ to $2025$. Make two comments describing the seasonal variation and the overall trend.

Step-by-Step Solution:

1. Seasonal variation: Gas bills follow a repeating yearly pattern, peaking every Q1 (winter heating) and dropping to a trough every Q3 (summer).

2. Overall trend: There is an upward (increasing) overall trend from $2023$ to $2025$ — each quarter's bill is higher than the same quarter in the previous year (e.g. Q1 rises £$400 \to \text{£}425 \to \text{£}475$).

Ready to test this skill? Use the interactive tool at the top of the page to practise 2 self-marking exam-style questions (8 questions loaded in this topic module).

Time-Series Graphs — GCSE Maths Tutorial, Worked Examples & Practice

Reading & Comparing Time-Series Graphs

Key Method & Revision Notes

Worked Example

Plotting & Completing a Time-Series Graph

Key Method & Revision Notes

Worked Example

Trends & Seasonal Variation

Key Method & Revision Notes

Worked Example

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