Lesson Worksheet: Cumulative Frequency Graphs Mathematics • 9th Grade

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In this worksheet, we will practice drawing a cumulative frequency diagram and using it to make estimations about the data.

Q1:

The table shows the number of hours that 100 students spent revising for an exam.

Number of Hours	0–	2–	4–	6–	8–	10–
Frequency	0	10	19	37	24	10
Cumulative Frequency

Determine the missing cumulative frequency results.

A0, 10, 29, 66, 90, 100
B0, 10, 29, 56, 90, 100
C0, 10, 29, 66, 80, 100
D0, 10, 29, 66, 90, 91
E10, 10, 29, 66, 90, 100

Q2:

The following table shows the ages of people applying to a company.

Age	19–	22–	25–	28–	31–	34–	37–	40–	Total
Number of Applicants	2	5	10	14	12	11	8	7	69
Cumulative Frequency		7		31		54	62

What are the missing values from the cumulative frequency table respectively?

A7, 22, 48, 74
B2, 17, 69, 43
C7, 22, 74, 48
D2, 17, 43, 69
E2, 16, 42, 68

Q3:

If a cumulative histogram were drawn from the data given in the table, what would the highest cumulative frequency be?

Time (Minutes)
Frequency	4	12	34	32	26

Q4:

A manufacturer samples the mass, in grams, of 30 pencils from the production line. Their masses are recorded in the table. No pencil has a mass greater than 60 g.

Mass (g)	10–	20–	30–	40–	50–
Frequency	3	6	11	7	3

Which cumulative frequency graph correctly shows this information?

Q5:

The following table shows the ages of people applying for a job, knowing that no one is older than 50 years.

Age	19–	22–	25–	28–	31–	34–	37–	40–	Total
Number of Applicants	2	5	10	14	12	11	8	7	69

Which of the following is the cumulative frequency graph?

Q6:

The following table shows the heights of students in a high school. No student is taller than 175 cm.

Height (cm)	150–	155–	160–	165–	170–
Frequency	4	22	56	30	8

Which cumulative frequency graph correctly represents this data?

Q7:

Mason took a sample of 100 balls from a box. He weighed each ball and recorded its weight in the table.

Weight (g)	0–	40–	80–	120–	160–
Frequency	9	17	46	17	11

He used the data to draw the cumulative frequency graph shown on the grid.

Estimate how many balls had a weight of less than 80 g.

Estimate how many balls had a weight of 130 g or more.

A78 balls
B12 balls
C11 balls
D22 balls
E32 balls

Q8:

A botanist records the height in centimeters of 120 tomato plants in an experiment testing different growing conditions. By drawing a cumulative frequency curve to represent the data, estimate the number of plants with a height less than 116 cm.

Height (cm)	100–	110–	120–	130–	140–
Frequency	12	21	52	30	5

A98 plants
B22 plants
C11 plants
D90 plants
E30 plants

Q9:

The following table shows different weights of boxes in a warehouse. Note that no box is heavier than 210 kg.

Weight (kg)	150–	160–	170–	180–	190–	200–	Total
Frequency	4	6	7	10	9	1	37

Which of the following is the cumulative frequency graph?

Find the number of boxes that have a greater than 180 kg.

Q10:

In order to compare the heights of players in two teams, A and B, the following cumulative frequency graph has been drawn as given.

Determine which team has the most players that are taller than 170 cm.

ATeam A
BTeam B

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