top of page

3.4 Time Series

GCSE Maths Foundation · Edexcel · Chapter 3: Graphs, tables and charts

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: drawing and reading time series graphs, trends and seasonal patterns. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Plot a time series graph from a table of data
  • Read values and changes from a time series graph
  • Describe the trend and any seasonal pattern
  • Compare two time series and make sensible estimates

Key words

  • Time series: Data collected at regular intervals of time, e.g. every hour, month or quarter.
  • Trend: The general direction of the data over time: going up, going down or staying level.
  • Seasonal pattern: A pattern that repeats at the same time each year (or each day or week).
  • Quarter: A three-month period. Q1 = Jan–Mar, Q2 = Apr–Jun, Q3 = Jul–Sep, Q4 = Oct–Dec.

Drawing a time series graph

Time always goes on the horizontal axis, with equal steps. Plot each value with a small cross or dot, then join the points with straight lines. The lines help you see changes; they do not give exact values between the points.

  • Temp (°C); 06:00 4; 08:00 7; 10:00 10; 12:00 15; 14:00 17; 16:00 14; 18:00 10

Worked example: reading the graph

(a) What was the highest temperature, and when? 17 °C at 14:00
(b) Between which two readings did the temperature rise the most?
Rises: 3, 3, 5, 2. The biggest is 10 → 15, from 10:00 to 12:00.
(c) Estimate the temperature at 13:00. Halfway between 15 and 17, so about 16 °C.

Answer: (a) 17 °C at 14:00 (b) 10:00 to 12:00 (5 °C) (c) about 16 °C

Trends and seasonal patterns

To describe a time series, say what the trend is (look past the ups and downs at the overall direction) and describe any repeating pattern. Always use the context.

Worked example: describing a time series

Pattern: every year sales are lowest in Q1, rise to a peak in Q3 (summer), then fall in Q4.
Trend: each quarter is higher than the same quarter the year before, e.g. Q3: 41, 45, 48.
Yearly totals: 98, 109, 118 hundred bottles.

Answer: sales peak every summer, and the overall trend is upwards

Key fact: Compare like with like: Q3 with Q3, not Q3 with the next Q4. Seasonal ups and downs are not the trend.

Comparing two time series

Two time series on the same axes let you compare them. Look at where the lines cross and at how quickly each one is changing.

Worked example: comparing

Gym A is rising overall, Gym B is falling steadily.
April: A 128, B 138. May: A 140, B 132. So A first had more members in May.
Change Jan to Jun: A + 26, B − 21.

Answer: Gym A overtook Gym B in May

Predictions and estimates

You can use a trend to make a prediction for the next time period, but it is only an estimate. Trends can change, and predictions far into the future are less reliable.

Worked example: predicting

Yearly sales: 2023 98, 2024 109, 2025 118 (hundreds of bottles). Predict 2026.
Increases: 11 then 9, roughly 10 a year. 118 + 10 = 128.

Answer: about 12 800 bottles (an estimate, e.g. weather may change it)

Common mistakes

  • Putting time on the vertical axis, or using uneven time steps.
  • Treating a value read between two plotted points as exact. It is only an estimate.
  • Describing the seasonal ups and downs instead of the overall trend.
  • Forgetting to use the context when describing a pattern (say "sales", "temperature", not just "it").

Revision questions

Try these, then check your answers below each one.

Question 1. Temperatures at a weather station one day: 8 am 6 °C, 10 am 9 °C, 12 noon 14 °C, 2 pm 16 °C, 4 pm 13 °C, 6 pm 9 °C. The points are plotted on a time series graph and joined with straight lines. What was the highest temperature recorded?

Answer: 16 °C

Working: The highest reading is 16 °C at 2 pm.

Question 2. Temperatures at a weather station one day: 8 am 6 °C, 10 am 9 °C, 12 noon 14 °C, 2 pm 16 °C, 4 pm 13 °C, 6 pm 9 °C. The points are plotted on a time series graph and joined with straight lines. Between which two readings did the temperature rise the most? (Choose from: 8 am and 10 am, 10 am and 12 noon, 12 noon and 2 pm, 2 pm and 4 pm.)

Answer: 10 am and 12 noon

Working: Rises: 3, 5, 2. The biggest rise is 5 °C, from 10 am to 12 noon.

Question 3. Temperatures at a weather station one day: 8 am 6 °C, 10 am 9 °C, 12 noon 14 °C, 2 pm 16 °C, 4 pm 13 °C, 6 pm 9 °C. The points are plotted on a time series graph and joined with straight lines. Use the graph to estimate the temperature at 11 am.

Answer: 11.5 °C

Working: Halfway between 9 °C and 14 °C is 11.5 °C (an estimate).

Related lessons

Continue in the full course

This lesson is section 3.4 (EGCMF0304) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

bottom of page