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Draw Histograms

In this worksheet, students practice drawing histograms.

'Draw Histograms' worksheet

Key stage:  KS 4

Curriculum topic:  

Curriculum subtopic:  

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

At the higher level in GCSE maths, you have to be able to make the leap from using a bar chart to represent data to a histogram.

When do I use a histogram? 

Histograms are used when you have continuous data that is grouped.

 

What is the difference between histograms and bar charts.

Both Histograms and Bar Charts are drawn with rectangular bars bu there is one main difference.

In a bar chart, the height is used to represent frequency and in a histogram area is used to represent the frequency.

 

Example: The table gives the heights of a group of boys.

 

Height, h (cm) 151 < h ≤ 153 153 < h ≤ 154 154 < h ≤ 155 155 < h ≤ 159 159 < h ≤ 160
Frequency 120 90 150 240 40

 

Step 1: Find the widths of the bars you need to draw.

This is also called the class width. This can easily be found by subtracting the lowest value of the class from the largest value.

Height, h (cm) 151 < h ≤ 153 153 < h ≤ 154 154 < h ≤ 155 155 < h ≤ 159 159 < h ≤ 160
Frequency 120 90 150 240 40
Class Width 2 1 1 4 1

 

Step 2: Find out how high we need to draw the bars.

We have already said that in a histogram, the area of the bar represents the frquency.

We can say that Frequency = Class Width x Height of the bar

And this can be rearranged into the equation.

Height =
Frequency
Class Width

The correct name of the hight of the bar in a histogram is the Frequency Density, this makes our formula...

Frequency Density =
Frequency
Class Width
Height, h (cm) 151 < h ≤ 153 153 < h ≤ 154 154 < h ≤ 155 155 < h ≤ 159 159 < h ≤ 160
Frequency 120 90 150 240 40
Class Width 2 1 1 4 1
Frequency Density 60 90 150 60 40

 

Step 3: Draw your histogram.

To draw the histogram, we plot the class on the bottom (don't forget to use a continuous scale) and the frequency density up the side.

Dividing frequency by class width will give...

The heights of 400 tulips are shown in a grouped frequency table.

Height, h (cm) 24 < h ≤ 26 26 < h ≤ 27 27 < h ≤ 28 28 < h ≤ 31 31 < h ≤ 37
Frequency 50 50 60 120 120

 

Match the groups with the correct class width.

Column A

Column B

24 < h ≤ 26
1
26 < h ≤ 27
1
27 < h ≤ 28
3
28 < h ≤ 31
2
31 < h ≤ 37
6

The heights of 400 tulips are shown in a grouped frequency table.

Height, h (cm) 24 < h ≤ 26 26 < h ≤ 27 27 < h ≤ 28 28 < h ≤ 31 31 < h ≤ 37
Frequency 50 50 60 120 120
Class Width 2 1 1 3 6

 

What are the frequency densities for each group?

 Frequency Density
24 < h ≤ 26
26 < h ≤ 27
27 < h ≤ 28
28 < h ≤ 31
31 < h ≤ 37

The heights of 400 tulips are shown in a grouped frequency table.

Height, h (cm) 24 < h ≤ 26 26 < h ≤ 27 27 < h ≤ 28 28 < h ≤ 31 31 < h ≤ 37
Frequency 50 50 60 120 120
Class Width 2 1 1 3 6
Freq Density 25 50 60 40 20

 

Which of the two histograms have been drawn correctly?

 

A

B

The ages of a groups pf children are shown in the grouped frequency table.

Age (Years) 11 < x ≤ 14 14 < x ≤ 16 16 < x ≤ 17 17 < x ≤ 21
Frequency 21 24 10 20

 

Match the groups with the correct class width.

Column A

Column B

11 < x ≤ 14
4
14 < x ≤ 16
3
16 < x ≤ 17
2
17 < x ≤ 21
1

The ages of a groups pf children are shown in the grouped frequency table.

Age (Years) 11 < x ≤ 14 14 < x ≤ 16 16 < x ≤ 17 17 < x ≤ 21
Frequency 21 24 10 20
Class Width 3 2 1 4

 

What are the frequency densities for each group?

 Frequency Density
11 < x ≤ 14
14 < x ≤ 16
16 < x ≤ 17
17 < x ≤ 21

The ages of a groups pf children are shown in the grouped frequency table.

Age (Years) 11 < x ≤ 14 14 < x ≤ 16 16 < x ≤ 17 17 < x ≤ 21
Frequency 21 24 10 20
Class Width 3 2 1 4
Frequency Density 7 12 10 5

 

Which of these two histograms have been drawn correctly?

 

A

B

The ages of a groups pf children are shown in the grouped frequency table.

Time (minutes) 0 < x ≤ 8 8 < x ≤ 12 12 < x ≤ 16 16 < x ≤ 20
Frequency 72 48 54 36

 

Match the groups with the correct class width.

Column A

Column B

0 < x ≤ 8
4
8 < x ≤ 12
4
12 < x ≤ 16
4
16 < x ≤ 20
8

The ages of a groups pf children are shown in the grouped frequency table.

Time (minutes) 0 < x ≤ 8 8 < x ≤ 12 12 < x ≤ 16 16 < x ≤ 20
Frequency 72 48 54 36
Class Width 8 4 4 4

 

What are the frequency densities for each group?

 Frequency Density
0 < x ≤ 8
8 < x ≤ 12
12 < x ≤ 16
16 < x ≤ 20

The ages of a groups pf children are shown in the grouped frequency table.

Time (minutes) 0 < x ≤ 8 8 < x ≤ 12 12 < x ≤ 16 16 < x ≤ 20
Frequency 72 48 54 36

Has this histogram been drawn completely correctly?

 

Yes

No

  • Question 1

Dividing frequency by class width will give...

CORRECT ANSWER
EDDIE SAYS
It's vital that you get the language here, there is a mark in the exam for labelling the histogram axes correctly
  • Question 2

The heights of 400 tulips are shown in a grouped frequency table.

Height, h (cm) 24 < h ≤ 26 26 < h ≤ 27 27 < h ≤ 28 28 < h ≤ 31 31 < h ≤ 37
Frequency 50 50 60 120 120

 

Match the groups with the correct class width.

CORRECT ANSWER

Column A

Column B

24 < h ≤ 26
2
26 < h ≤ 27
1
27 < h ≤ 28
1
28 < h ≤ 31
3
31 < h ≤ 37
6
EDDIE SAYS
All we have to do to find the class width is subract the lowest number from the higher number for the group
  • Question 3

The heights of 400 tulips are shown in a grouped frequency table.

Height, h (cm) 24 < h ≤ 26 26 < h ≤ 27 27 < h ≤ 28 28 < h ≤ 31 31 < h ≤ 37
Frequency 50 50 60 120 120
Class Width 2 1 1 3 6

 

What are the frequency densities for each group?

CORRECT ANSWER
 Frequency Density
24 < h ≤ 26
26 < h ≤ 27
27 < h ≤ 28
28 < h ≤ 31
31 < h ≤ 37
EDDIE SAYS
Remember the formula for frequency density? fd = freq / class wirth
  • Question 4

The heights of 400 tulips are shown in a grouped frequency table.

Height, h (cm) 24 < h ≤ 26 26 < h ≤ 27 27 < h ≤ 28 28 < h ≤ 31 31 < h ≤ 37
Frequency 50 50 60 120 120
Class Width 2 1 1 3 6
Freq Density 25 50 60 40 20

 

Which of the two histograms have been drawn correctly?

 

CORRECT ANSWER
B
EDDIE SAYS
One of the biggest mistakes people make when they draw histograms is that they draw they frequency instead of the frequency density
  • Question 5

The ages of a groups pf children are shown in the grouped frequency table.

Age (Years) 11 < x ≤ 14 14 < x ≤ 16 16 < x ≤ 17 17 < x ≤ 21
Frequency 21 24 10 20

 

Match the groups with the correct class width.

CORRECT ANSWER

Column A

Column B

11 < x ≤ 14
3
14 < x ≤ 16
2
16 < x ≤ 17
1
17 < x ≤ 21
4
EDDIE SAYS
All we have to do to find the class width is subract the lowest number from the higher number for the group
  • Question 6

The ages of a groups pf children are shown in the grouped frequency table.

Age (Years) 11 < x ≤ 14 14 < x ≤ 16 16 < x ≤ 17 17 < x ≤ 21
Frequency 21 24 10 20
Class Width 3 2 1 4

 

What are the frequency densities for each group?

CORRECT ANSWER
 Frequency Density
11 < x ≤ 14
14 < x ≤ 16
16 < x ≤ 17
17 < x ≤ 21
EDDIE SAYS
Remember the formula for frequency density? fd = freq / class wirth
  • Question 7

The ages of a groups pf children are shown in the grouped frequency table.

Age (Years) 11 < x ≤ 14 14 < x ≤ 16 16 < x ≤ 17 17 < x ≤ 21
Frequency 21 24 10 20
Class Width 3 2 1 4
Frequency Density 7 12 10 5

 

Which of these two histograms have been drawn correctly?

 

CORRECT ANSWER
A
EDDIE SAYS
We need to take care with is where the bars are drawn. Option A has the first bar starting at 11 Option B has the first bar starting at 10. Which one does the table tell us we should be using?
  • Question 8

The ages of a groups pf children are shown in the grouped frequency table.

Time (minutes) 0 < x ≤ 8 8 < x ≤ 12 12 < x ≤ 16 16 < x ≤ 20
Frequency 72 48 54 36

 

Match the groups with the correct class width.

CORRECT ANSWER

Column A

Column B

0 < x ≤ 8
8
8 < x ≤ 12
4
12 < x ≤ 16
4
16 < x ≤ 20
4
EDDIE SAYS
All we have to do to find the class width is subract the lowest number from the higher number for the group
  • Question 9

The ages of a groups pf children are shown in the grouped frequency table.

Time (minutes) 0 < x ≤ 8 8 < x ≤ 12 12 < x ≤ 16 16 < x ≤ 20
Frequency 72 48 54 36
Class Width 8 4 4 4

 

What are the frequency densities for each group?

CORRECT ANSWER
 Frequency Density
0 < x ≤ 8
8 < x ≤ 12
12 < x ≤ 16
16 < x ≤ 20
EDDIE SAYS
Remember the formula for frequency density? fd = freq / class wirth
  • Question 10

The ages of a groups pf children are shown in the grouped frequency table.

Time (minutes) 0 < x ≤ 8 8 < x ≤ 12 12 < x ≤ 16 16 < x ≤ 20
Frequency 72 48 54 36

Has this histogram been drawn completely correctly?

 

CORRECT ANSWER
No
EDDIE SAYS
This is very nearly correct. The only thing that is incorrect is that the top of the third bar has not been drawn fully across the bar. While this may seem like a small thing, it would be enough to lose a mark in the exam.
---- OR ----

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