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Graphs and plots for AQA A-level Maths

Graphs and plots

This page covers the following topics:

1. Histograms

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

A study surveys some families and constructs a histogram of how much they each spend on food in a week. 20 families spend between ยฃ20-ยฃ30. Estimate how many families spend over ยฃ40.

From the information in the question the frequency density scale is marked with increments of 0.5 (since the frequency density of ยฃ20-ยฃ30 = 2) so 35 families spend over ยฃ40.

A study surveys some families and constructs a histogram of how much they each spend on food in a week. 20 families spend between ยฃ20-ยฃ30. Estimate how many families spend over ยฃ40.

2

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 โ‰ค 0.5, 5;
0.5 < d โ‰ค 1.5, 15;
1.5 < d โ‰ค 2.5, 20;
2.5 < d โ‰ค 4, 11.

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 โ‰ค 0.5, 5; 
0.5 < d โ‰ค 1.5, 15; 
1.5 < d โ‰ค 2.5, 20; 
2.5 < d โ‰ค 4, 11.

3

Adam has surveyed the distance travelled to school by his classmates with the results provided below. Use the results to construct a histogram.

Distance (km), Frequency;
0.5 < d โ‰ค 1, 9;
1 < d โ‰ค 1.8, 15;
1.8 < d โ‰ค 2, 6;
2 < d โ‰ค 2.5, 5.

image

Adam has surveyed the distance travelled to school by his classmates with the results provided below. Use the results to construct a histogram. 

Distance (km), Frequency; 
0.5 < d โ‰ค 1, 9; 
1 < d โ‰ค 1.8, 15; 
1.8 < d โ‰ค 2, 6; 
2 < d โ‰ค 2.5, 5.

4

This is a table representing the ages, a, of people who visit a park, use it to construct a histogram: Age (years), Frequency; 5<aโ‰ค8, 7; 8<aโ‰ค12, 14; 12<aโ‰ค16, 9; 16<aโ‰ค20, 18.

image

This is a table representing the ages, a, of people who visit a park, use it to construct a histogram: Age (years), Frequency; 5<aโ‰ค8, 7; 8<aโ‰ค12, 14; 12<aโ‰ค16, 9; 16<aโ‰ค20, 18.

5

The number of cars parked per day in a month in a parking lot, with space for 50 cars, is shown in this histogram; estimate on how many days the parking lot was 80% full or more.

Frequency of 40-50 cars parked = 12 days

The number of cars parked per day in a month in a parking lot, with space for 50 cars, is shown in this histogram; estimate on how many days the parking lot was 80% full or more.

End of page

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