Histograms Lesson | GCSE Maths Edexcel IGCSE Higher

Histograms

This lesson covers:

What a histogram is
How to calculate frequency density
Interpreting histograms

Introduction to histograms

Histograms plot frequency density on their vertical axis to show how data is spread over various ranges, known as classes.

Histogram showing frequency density by age in years with three bars representing different age ranges.

Class width

Class width is the width of the bars on the histogram.

It can be calculated using the formula:

class width = highest value in class - lowest value in class

Frequency Density

Frequency density is the frequency per unit for the data in each class.

It can be calculated using the formula:

$\text{frequency density = }\frac{\text{frequency}} {\text{class width}}$

Frequency

The number of times a value occurs.

Frequency can be calculated using the rearranged formula:

frequency = frequency density x class width

Worked example 1: Sunflower height survey

The following dataset records the height and frequency of sunflowers in a field. Find the missing frequency.

height (cm)	Frequency
0 < x ≤ 40	40
40 < x ≤ 120
120 < x ≤ 160	280
160 < x ≤ 200	40

Histogram showing the frequency density of sunflower heights in a field.

Worked example 2: Histogram of resale value.

Use the table below to plot a histogram of the resale value of some second hand cars.

resale value	frequency	frequency density
0 < p $\leq$ 5,000	4
5000 < p $\leq$ 15,000	9
15,000 < p $\leq$ 20,000	4
20,000 < p $\leq$ 30,000	1

Calculate the missing frequency density in the table below.

Number of points	Frequency	Frequency density
0 < p $\leq$ 5	5	1
5 < p $\leq$ 12	6	0.86
12 < p $\leq$ 19	4	0.57
12 < p $\leq$ 25	2	?

0.08

0.15

12.5

13

0

/

1

Calculate the missing frequency in the table below.

Age (months)	Frequency	Frequency density
0 < p $\leq$ 6	?	1.5
6 < p $\leq$ 12	7	1.17
12 < p $\leq$ 24	12	1
24 < p $\leq$ 36	9	0.75

9

7

6

5

0

/

1

The table shows information about the time, in seconds, taken for some people to complete a puzzle.

Time (seconds)	Frequency	Frequency density
10 < t $\leq$ 20	12	0.8
25 < t $\leq$ 35	28
35 < a $\leq$ 40	42	8.4
40 < a $\leq$ 45	30	6.0
45 < a $\leq$ 60	9	0.6

Use the information in the table to complete the histogram.

Blank histogram template with time in seconds on the x-axis and frequency density on the y-axis.

0

/

3

Worked example 2: Histogram of resale value.

Use the table below to plot a histogram of the resale value of some second hand cars.

resale value	frequency	frequency density
0 < p $\leq$ 5,000	4
5000 < p $\leq$ 15,000	9
15,000 < p $\leq$ 20,000	4
20,000 < p $\leq$ 30,000	1