Line Graphs and Time Series

A line graph shows how an amount changes over time, such as the temperature during a day or the number of tickets sold each day. Time goes along the horizontal axis. Each value is plotted as a point, and the points are joined in order with straight lines.

A time series graph is a line graph of data recorded at regular times: every hour, every month, every quarter or every year. It shows how something changes as time goes on.

In the exam you are usually asked to read a value from the graph, work out a difference or a total, or describe the trend, for 1 or 2 marks. Harder questions ask you to say what is wrong with a graph someone has drawn, or to use the trend to make a prediction and say whether it is reliable, for up to 4 marks.

Read the title and the labels on both axes first. Then work out what one small square is worth. If the labels go up in 20s with 5 small squares between them, each small square is worth 20\div5=4

To read a value, go up from the time on the horizontal axis to the line, then across to the vertical axis. Check the units in the axis label too: if it says “Number of visitors (thousands)”, a reading of 4 means 4000 visitors.

The lines between the points let you estimate a value at a time in between. The temperature on this graph was measured every 3 hours. At 07:30, halfway between 06:00 and 09:00, the line is at 8, so an estimate of the temperature at 07:30 is 8^\circC.

It is only an estimate, because the temperature was not measured at 07:30. Joining the points with a straight line assumes the temperature rose steadily between the two readings.

A line going up shows an increase. A line going down shows a decrease. A flat line shows no change.

When the times are equally spaced, the steeper the line, the bigger the change. To find a change, read the values at both ends and subtract the smaller from the larger.

Once you have read the values, use them like any other numbers. Add them for a total. For a mean, divide the total by how many values there are: readings of 12, 15 and 18 have a mean of 45\div3=15

Put time on the horizontal axis, with the times equally spaced and in order. Give the vertical axis a scale that goes up in equal steps, and label both axes.

Plot each value as a small cross. Then join each point to the next one with a straight line drawn with a ruler. Don't draw a curve, and don't join the last point back to the first.

You may be asked what is wrong with a graph someone has drawn. Check that the scale goes up in equal steps, that both axes are labelled, that every time is shown, and that the points are joined with straight lines. This graph has two faults.

Say exactly what is wrong: “the scale is wrong” is not enough. Write “the vertical scale jumps from 10 to 20, but every other step is 5” and “the points are joined with a curve, not straight lines”.

Look at where the vertical scale starts, too. If it starts at 500 instead of 0, a small rise looks like a big one, so the graph is misleading.

The trend is the general direction of a time series over the whole time, ignoring the small ups and downs. It may be going up, going down, or staying about the same.

Describe a trend in words, using the context: “the number of visitors is going up” or “the percentage of people who walk to work is going down”. Don't just list the values.

Some data change with the seasons. Ice cream sales are high every summer and low every winter. This is a pattern that repeats every year.

Data are often given for each quarter of a year: Q1 is January to March, Q2 is April to June, Q3 is July to September and Q4 is October to December. To see the trend in data like this, compare each quarter with the same quarter a year before.

To make a prediction, carry the trend on past the last point. Lay a ruler through the middle of the points, draw a straight trend line, and continue it to the time you want. A prediction just after the data is more reliable than one far into the future, because the trend may not carry on. A trend can't go on for ever: a percentage that keeps falling would in the end go below 0, which is impossible.

Two time series can be drawn on the same axes so you can compare them. The key tells you which line is which, for example a solid line with dots and a dashed line with crosses. In the exam, tell your lines apart by their style, not by colour, because answers are scanned and marked in grey.

To compare them at one time, read both lines at that time and subtract. The bigger the gap between the lines, the bigger the difference.

Where the lines cross, the two amounts are about the same. After that, the other line is higher.

• Taking each small square to be worth 1. Work out what one small square is worth from the labels before you read or plot a value.
• Writing “the scale is wrong” without saying how. Name the axis and say exactly what is wrong, such as one step of 10 where the others are 5
• Joining the points with a curve, or not joining them. Join each point to the next with a straight line drawn with a ruler.
• Listing values instead of describing the trend. Give the general direction in words, using the context, such as “the number of bookings is going up”.
• Leaving the vertical axis without a label. Label both axes, so the reader knows what the numbers count.
• Trusting a prediction far beyond the data. Only carry a trend a short way past the last point.