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# Graphs and plots for OCR A-level Maths

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.

# 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 £20-£30. Estimate how many families spend over £40.

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.

# 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 ≤ 0.5, 5;
0.5 < d ≤ 1.5, 15;
1.5 < d ≤ 2.5, 20;
2.5 < d ≤ 4, 11.

image

# 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 ≤ 1, 9;
1 < d ≤ 1.8, 15;
1.8 < d ≤ 2, 6;
2 < d ≤ 2.5, 5.

image

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