Data
Graphs
Some graphs help us spot how data changes or whether two things are linked. In this section we read and interpret frequency diagrams, line graphs and scatter graphs. Scatter graphs are new at this stage - they show whether there might be a link between two sets of data.
Frequency diagrams
A frequency diagram groups measurements into equal intervals, such as 40-60 km/h, and the height of each bar shows how many are in that group. If a measurement is exactly on a group boundary it is recorded in the group above, so 40 km/h goes in the 40-60 group. Add groups together to answer 'less than' or 'in total' questions.
Line graphs
A line graph is used for data collected over time, such as a temperature or a pulse rate. The points are joined with straight lines, so you can read a value at any time and even estimate a value between two points. Read up from the time axis to the line, then across to the other axis.
Scatter graphs and lines of best fit
A scatter graph plots two measurements for each item, one on each axis, to show whether there is a link. If the points rise from left to right, more of one thing links with more of the other. A line of best fit is a straight line drawn through the middle, with about the same number of points above and below, that you can use to estimate values.
Choosing the right graph
Use a line graph for something changing over time, a frequency diagram for finding the most common group of a measurement, and a scatter graph to see if two measured quantities are linked.
Worked examples
Reading a frequency diagram
- A frequency diagram shows vehicle speeds: 20-40 km/h (6), 40-60 km/h (12), 60-80 km/h (8), 80-100 km/h (4).
- For 'less than 60 km/h', add the groups below 60: 6 + 12.
- For the total, add every group: 6 + 12 + 8 + 4.
Answer: 18 vehicles travelled less than 60 km/h, and 30 vehicles passed in total.
Reading a line graph
- Dee's pulse line graph reads: 0 to 66, 10 to 102, 20 to 102, 30 to 118, 40 to 106, 50 to 130, 60 to 130, 70 to 88, 80 to 68 beats per minute.
- To find when her pulse was 118, find 118 on the pulse axis and read across to the point, then down to the time.
- The highest point on the line is 130 beats per minute.
Answer: Her pulse was 118 at 30 minutes, and her highest pulse rate was 130 beats per minute.
Reading a scatter graph
- A scatter graph plots plant height (cm) against number of leaves, including the points (6, 2) and (18, 9).
- For the 18 cm plant, find 18 on the height axis, go up to the point and read across to 9 leaves.
- The points rise from left to right, so taller plants tend to have more leaves.
Answer: The 18 cm plant has 9 leaves, and there is a link: the more leaves, the taller the plant tends to be.
Choosing the right graph
- To show how quickly hot water cools, the data changes over time, so use a line graph.
- To see if height and science test score are linked, plot two measurements together on a scatter graph.
Answer: Use a line graph for change over time and a scatter graph to look for a link.
Where you see this in real life
- Reading a line graph of a runner's pulse rate during and after exercise.
- Using a scatter graph to see if taller people tend to have longer arms.
- Reading a frequency diagram of the speeds of vehicles passing a school.
Key words
- Frequency diagram
- A chart that groups measurements into equal intervals and shows the frequency of each group.
- Line graph
- A graph of data over time, with the points joined by straight lines.
- Scatter graph
- A graph that plots two measurements for each item to show whether they are linked.
- Line of best fit
- A straight line through the middle of the points, with about the same number above and below, used to estimate values.
- Link
- A relationship where one measurement changing tends to go with another measurement changing.
- Group boundary
- The edge value between two groups; a measurement on the boundary is recorded in the group above.