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 Hours0–2–4–6–8–10–
Frequency01019372410
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.

Age19–22–25–28–31–34–37–40–Total
Number of Applicants25101412118769
Cumulative Frequency7315462

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)708090100110
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?

  • 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.

Age19–22–25–28–31–34–37–40–Total
Number of Applicants25101412118769

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)150–155–160–165–170–
Frequency42256308

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)0–40–80–120–160–
Frequency917461711

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–
Frequency122152305
  • 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
Frequency467109137

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

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