EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Time series
Interpreting and representing data · Lesson 2 of 6
Last Lesson and Before
Answer each one, then check.
1. Last lesson: a sector of 90° on a pie chart of 200 people - how many people?
50
2. Last lesson: is time discrete or continuous?
Continuous
3. Work out the mean of 2, 4 and 6.
4
4. What are the coordinates of a point 3 across and 5 up?
(3, 5)
Learning Objectives
1. Plot a time series graph.
2. Read values from a time series graph.
3. Describe the trend of a time series.
4. Recognise seasonal variation.
5. Make predictions, and say how reliable they are.
What Is a Time Series?
A time series is a set of data recorded at regular intervals of time.
▸ The axes. Time always goes on the horizontal axis, in equal steps. The data goes on the vertical axis.
▸ Plotting. Plot each value above its time.
▸ Joining. Join the points with straight lines. The lines only show the pattern - they do not give real values between the points.
▸ Examples. Monthly rainfall, quarterly sales, a city's population every ten years.
Ice Cream Sales
A seaside ice cream shop's sales, in thousands of pounds, each quarter (three months) for two years.
|
Year |
Q1 (Jan to Mar) |
Q2 (Apr to Jun) |
Q3 (Jul to Sep) |
Q4 (Oct to Dec) |
|---|---|---|---|---|
|
Year 1 |
12 |
20 |
26 |
10 |
|
Year 2 |
14 |
23 |
29 |
12 |
The Time Series Graph
|
Two things show at once. Sales peak in Q3 (summer) and fall in Q4 every year - that is seasonal variation. And each quarter is a little higher than the same quarter a year earlier - that is the trend, which is increasing. |
Up every summer, down every winter - and a little higher each year. |
Trend and Seasonal Variation
Describe a time series in two parts.
▸ The trend. The general direction over the whole time: increasing, decreasing or staying about the same. Ignore the ups and downs.
▸ Seasonal variation. A pattern that repeats at the same time each year, like higher ice cream sales every summer.
▸ Compare like with like. Compare Q3 with the Q3 before it, not with Q4: 29 against 26 shows the growth.
▸ Use the context. Say what the numbers mean: "sales increased", not just "the line goes up".
Reading a Time Series
|
Using the ice cream sales, (a) how much higher were sales in Q3 of Year 2 than in Q3 of Year 1? (b) Describe the trend. (c) Describe the seasonal pattern. |
1. (a) Read the two values
Year 1 Q3 = 26, Year 2 Q3 = 29
2. Subtract, and remember the units
29 − 26 = 3 thousand pounds
3. (b) Compare each quarter with the same quarter a year earlier
Every quarter is higher in Year 2
4. (c) Look for the repeating pattern
Highest in Q3, lowest in Q4, every year
Answer: (a) £3000 higher. (b) Sales are increasing. (c) Sales are highest in summer (Q3) and lowest in Q4.
Making Predictions
A time series can be used to predict what will happen next - with care.
▸ Follow both patterns. Continue the trend AND the seasonal pattern: Year 3 Q3 might be about 32.
▸ Near is better. A prediction for next quarter is more reliable than one for five years' time.
▸ Things change. A new competitor, a wet summer or a price rise could break the pattern.
▸ Say so. In an exam, a comment on reliability usually mentions how far ahead the prediction is.
A Good Time Series Graph
|
Equal time steps Each quarter, month or year takes the same space on the axis. |
Labelled axes With units, such as "Sales (£ thousands)". |
|
Accurate points Each point plotted exactly above its time. |
Straight lines Points joined with a ruler, in order. |
Case Study
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CASE STUDY The Central England Temperature Record The Central England Temperature series is the longest record of measured temperatures in the world. It gives the average temperature of a triangle of central England for every month since 1659, built from old diaries and weather records for the earliest years. Plotted as a time series, it shows a strong seasonal pattern - warm summers and cold winters, every year - and, over the last century, a clear upward trend in temperature. |
|
1659 The year the monthly record begins |
360+ Years of monthly temperatures in one time series |
Key Terms
|
Time series Data recorded at regular intervals of time. |
Trend The general direction of the data over time. |
|
Seasonal variation A pattern that repeats at the same time each year. |
Quarter A three-month period of the year. |
|
Prediction An estimate of a future value based on the pattern so far. |
|
Your Task: Make Your Own Time Series
15 minutes
|
A cinema's visitors, in thousands, each quarter for two years were: Year 1: 18, 15, 22, 30. Year 2: 20, 16, 25, 34. Draw a time series graph. Describe the trend and the seasonal variation, and predict Year 3 Q4 with a comment on how reliable your prediction is. 1. Draw and label the axes. 2. Plot and join the points. 3. Describe the trend and seasonal pattern. 4. Predict, and comment. |
A good answer shows: A graph with equal quarters on the horizontal axis and points joined with straight lines. Trend: increasing (every quarter higher in Year 2). Seasonal: busiest in Q4 (the Christmas holidays), quietest in Q2. Prediction around 37 to 38 thousand, reasonably reliable as it is only one year ahead - but new films or prices could change it.
Can I...?
☐ Plot a time series graph.
☐ Read values from a time series.
☐ Describe the trend.
☐ Describe seasonal variation.
☐ Compare values a year apart.
☐ Make a prediction.
☐ Comment on how reliable a prediction is.
☐ Answer in the context of the data.
Summary
✓ Time goes on the horizontal axis in equal steps; points are joined with straight lines.
✓ The trend is the overall direction; seasonal variation is the pattern that repeats each year.
✓ Compare each quarter with the same quarter in the year before.
✓ Predictions are less reliable the further ahead they go.
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EXAM FOCUS Describe the trend in the number of visitors to the museum. (1 mark) Always answer in context: "the number of visitors increased" earns the mark; "it goes up" often does not. |