Plotting a cumulative-frequency graph Revision Card

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Plotting a cumulative-frequency graph.

Cumulative frequency is a running total. Plot it at the upper class boundary.
Read the median at N/2, Q₁ at N/4 and Q₃ at 3N/4.
The interquartile range is Q₃ − Q₁. Graph readings are estimates.

Example 1

Draw a cumulative frequency graph.

Given information

Class	Frequency
	3
	5
	7
	2

Add a running total

Class	Frequency	Cumulative frequency
	3	3
	5	8
	7	15
	2	17

Black: given data. Blue: working we add.

Plot cumulative frequency at each upper class boundary. Begin at the lowest boundary with frequency zero.

Join the points with a smooth non-decreasing curve. Read estimates from your curve.

Example 2

Draw a cumulative frequency graph.

Given information

Class	Frequency
	4
	5
	8
	2

Add a running total

Class	Frequency	Cumulative frequency
	4	4
	5	9
	8	17
	2	19

Black: given data. Blue: working we add.

Plot cumulative frequency at each upper class boundary. Begin at the lowest boundary with frequency zero.

Join the points with a smooth non-decreasing curve. Read estimates from your curve.

Your turn

Question 1

Draw a cumulative frequency graph.

Given information

Class	Frequency
	5
	5
	9
	2

Check answer

Add a running total

Class	Frequency	Cumulative frequency
	5	5
	5	10
	9	19
	2	21

Black: given data. Blue: working we add.

Plot cumulative frequency at each upper class boundary. Begin at the lowest boundary with frequency zero.

Join the points with a smooth non-decreasing curve. Read estimates from your curve.

Question 2

Draw a cumulative frequency graph.

Given information

Class	Frequency
	6
	5
	10
	2

Check answer

Add a running total

Class	Frequency	Cumulative frequency
	6	6
	5	11
	10	21
	2	23

Black: given data. Blue: working we add.

Plot cumulative frequency at each upper class boundary. Begin at the lowest boundary with frequency zero.

Join the points with a smooth non-decreasing curve. Read estimates from your curve.

Question 3

Draw a cumulative frequency graph.

Given information

Class	Frequency
	7
	5
	7
	2

Check answer

Add a running total

Class	Frequency	Cumulative frequency
	7	7
	5	12
	7	19
	2	21

Black: given data. Blue: working we add.

Plot cumulative frequency at each upper class boundary. Begin at the lowest boundary with frequency zero.

Join the points with a smooth non-decreasing curve. Read estimates from your curve.

Question 4

Draw a cumulative frequency graph.

Given information

Class	Frequency
	3
	6
	8
	2

Check answer

Add a running total

Class	Frequency	Cumulative frequency
	3	3
	6	9
	8	17
	2	19

Black: given data. Blue: working we add.

Plot cumulative frequency at each upper class boundary. Begin at the lowest boundary with frequency zero.

Join the points with a smooth non-decreasing curve. Read estimates from your curve.

Question 5

Draw a cumulative frequency graph.

Given information

Class	Frequency
	4
	6
	9
	2

Check answer

Add a running total

Class	Frequency	Cumulative frequency
	4	4
	6	10
	9	19
	2	21

Black: given data. Blue: working we add.

Plot cumulative frequency at each upper class boundary. Begin at the lowest boundary with frequency zero.

Join the points with a smooth non-decreasing curve. Read estimates from your curve.