# Lesson Worksheet: Cumulative Frequency Graphs Mathematics • 9th Grade

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 Frequency Cumulative Frequency 0– 2– 4– 6– 8– 10– 0 10 19 37 24 10 ⋯ ⋯ ⋯ ⋯ ⋯ ⋯

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 Number of Applicants Cumulative Frequency 19– 22– 25– 28– 31– 34– 37– 40– Total 2 5 10 14 12 11 8 7 69 ⋯ 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 70− 80− 90− 100− 110− 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) Frequency 10– 20– 30– 40– 50– 3 6 11 7 3

Which cumulative frequency graph correctly shows this information?

• A • B • C • D • E Q5:

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

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

Which of the following is the cumulative frequency graph?

• A • B • C • D • E Q6:

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

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

Which cumulative frequency graph correctly represents this data?

• A • B • C • D • E Q7:

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

 Weight (g) Frequency 0– 40– 80– 120– 160– 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) Frequency 100– 110– 120– 130– 140– 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) Frequency 150– 160– 170– 180– 190– 200– Total 4 6 7 10 9 1 37

Which of the following is the cumulative frequency graph?

• A • B • C • D • E Find the number of boxes that have a greater than 180 kg.

• A20
• B12
• C1
• D37
• E17

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