# StudySquare

# Graphs and plots for AQA A-level Maths

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.

# 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

# 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<a≤8, 7; 8<a≤12, 14; 12<a≤16, 9; 16<a≤20, 18.

image

# 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

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