Graphs and plots for OCR GCSE Maths

Graphs and plots

This page covers the following topics:

1. Time series
2. Scatter graphs
3. Box plots
4. Pictograms
5. Histograms

Time series graphs are used to represent data collected over time.

Time series

Scatter graphs use a line of best fit, drawn centrally through the points, to show correlations between variables; extend the line to extrapolate (estimate) values outside the range of data given.

Scatter graphs

Box plots visually display the median, quartiles and interquartile range of a data set against a scale.

Box plots

Pictograms display data using symbols that makes information visually easier to understand and uses a key to show what each symbol presents. Below is an example displaying the number of cupcakes sold each day at a cafe.

Pictograms

Histograms are used when class intervals are unequal. Frequency is represented by the area of the bar; the height of each bar is called the frequency density and there are no gaps between the bars.

Histograms

1

Ben constructs this box plot to display the 400m and 600 run times of his classmates. State 2 comparisons you can make between the two sets of data.

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Possible answers include: the class takes longer to run 500m; the range of times for running 500m is larger than for 400m; the interquartile range for running 500m is larger than for 400m so the times are more spread out for 500m.

Ben constructs this box plot to display the 400m and 600 run times of his classmates. State 2 comparisons you can make between the two sets of data.

2

A study surveys some families and constructs a histogram of how much they each spend on food in a week. 20 families spend between £20-£30. Estimate how many families spend over £40.

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From the information in the question the frequency density scale is marked with increments of 0.5 (since the frequency density of £20-£30 = 2) so 35 families spend over £40.

A study surveys some families and constructs a histogram of how much they each spend on food in a week. 20 families spend between £20-£30. Estimate how many families spend over £40.

3

This list shows the number of hours per day Aaron spends on his homework over 10 days: 3, 2.5, 0.5, 2, 2.75, 2, 3.5, 1, 2, 2.5. Construct a box plot of the data.

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image

This list shows the number of hours per day Aaron spends on his homework over 10 days: 3, 2.5, 0.5, 2, 2.75, 2, 3.5, 1, 2, 2.5. Construct a box plot of the data.

4

This pictogram shows the number of fish in different tanks in an aquarium; what is the average number of fish in a tank?

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32 fish

This pictogram shows the number of fish in different tanks in an aquarium; what is the average number of fish in a tank?

5

This table below shows the distance (d) a group of students has walked on a particular day. Use it to draw a histogram.

Distance (km), Frequency;
0 < d ≤ 0.5, 5;
0.5 < d ≤ 1.5, 15;
1.5 < d ≤ 2.5, 20;
2.5 < d ≤ 4, 11.

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image

This table below shows the distance (d) a group of students has walked on a particular day. Use it to draw a histogram. Distance (km), Frequency; 0 < d ≤ 0.5, 5; 0.5 < d ≤ 1.5, 15; 1.5 < d ≤ 2.5, 20; 2.5 < d ≤ 4, 11.

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