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Data & Statistics · Lesson 5 of 14

Line Graphs

A line graph joins readings taken over time. Rising lines show increases, falling lines show decreases, and steep lines show fast change.

What you will learn

  • Read values from a line graph.
  • Describe rises and falls and find the change.
  • Draw a line graph and know when to use one.

Before you start: you should be able to read a bar chart and use a scale. See Bar Charts.

The idea

A line graph shows how something changes, usually over time. The horizontal axis shows time (hours, days or weeks). The vertical axis shows the quantity. Each reading is a dot, and straight lines join the dots in order.

Line graph: 6am 8, 9am 12, noon 18, 3pm 20, 6pm 15, 9pm 10Line graph: 6am 8, 9am 12, noon 18, 3pm 20, 6pm 15, 9pm 10. The scale goes from 0 to 20 in steps of 5.051015206am9amnoon3pm6pm9pmTimeTemp (°C)
Temperature through a day. It rises until 3 pm and then falls. The steepest rise is between 9 am and noon.

Reading a line graph

  • Go straight up from the time on the horizontal axis to the dot, then across to the scale.
  • A line going up means an increase, going down means a decrease and flat means no change.
  • A steeper line means faster change.

Estimating between readings

The line between two dots is a guide. If the line is straight, the value half way between two times is half way between the two readings. This is only an estimate. The real temperature may not have changed steadily.

Line graph: Wk1 2, Wk2 5, Wk3 9, Wk4 14, Wk5 16Line graph: Wk1 2, Wk2 5, Wk3 9, Wk4 14, Wk5 16. The scale goes from 0 to 16 in steps of 2.0246810121416Wk1Wk2Wk3Wk4Wk5WeekHeight (cm)
A plant's height each week. It grows fastest in week 4, then slows down.

Scales that go below zero

A scale can start below zero, for example for winter temperatures. Always check where zero is.

Line graph: Mon -1, Tue 5, Wed 3, Thu 8Line graph: Mon -1, Tue 5, Wed 3, Thu 8. The scale goes from -4 to 8 in steps of 2.-4-202468MonTueWedThuDayTemp (°C)
Midday temperature on four days. Monday was below freezing at -1 degrees.

Worked examples

Example 1: Finding a rise

Use the plant graph. How much did it grow in week 4?

  1. Height at the end of week 3 is 99 cm and at the end of week 4 is 1414 cm.
  2. 14−9=514 - 9 = 5.

Answer: 55 cm

Example 2: Estimating

Use the plant graph. Estimate the height half way between week 1 and week 2.

  1. Week 1 is 22 and week 2 is 55.
  2. Half way is (2+5)÷2=3.5(2 + 5) \div 2 = 3.5.

Answer: about 3.53.5 cm

Example 3: Describing a trend

Describe the temperature graph from 33 pm to 99 pm.

  1. The line goes down from 2020 to 1515 to 1010.

Answer: the temperature falls by 10∘C10^\circ\text{C} over 66 hours.

Tip: only join the dots with a line when the quantity can change smoothly over time. For separate categories use bars.

Why it matters

Line graphs show weather, prices, heart rates, populations and growth. They help you see patterns and spot sudden changes. You can use them to predict what might happen next, though predictions are only estimates.

Practice

Your turn. Type or choose an answer, then press Check. Getting one wrong is fine, that is what practice is for. You can try as many times as you like.

Question 1 of 8

A line graph shows temperatures: 66 am 88, 99 am 1212, noon 1818, 33 pm 2020, 66 pm 1515, 99 pm 1010 (in ∘C^\circ\text{C}). What was the temperature at noon?

Question 2 of 8

Using the same readings, by how many degrees did it rise from 66 am to 33 pm?

Question 3 of 8

Using the same readings, by how many degrees did it fall from 33 pm to 99 pm?

Question 4 of 8

Using the same readings, at what time was it warmest?

Choose one answer

Question 5 of 8

Using the same readings, estimate the temperature half way between 99 am and noon if the line is straight.

Question 6 of 8

Using the same readings, what was the biggest rise between two neighbouring readings, in degrees?

Question 7 of 8

When is a line graph the best choice?

Choose one answer

Question 8 of 8

Using the same readings, how many readings are above 12∘C12^\circ\text{C}?