# Lesson Worksheet: Descending Cumulative Frequency Graphs Mathematics

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

Q1:

As a part of a childcare course, students recorded the age, in months, at which a group of babies and toddlers began to walk. The data is recorded in the grouped frequency table below.

 Age (Months) Frequency 8– 10– 12– 14– 16– 18– Total 2 15 40 51 35 7 150

Complete the descending cumulative frequency table.

 Age (Months) Descending Cumulative Frequency 8 or more 10 or more 12 or more 14 or more 16 or more 18 or more 20 or more ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯
• A150, 148, 133, 93, 42, 7, 150
• B2, 148, 133, 93, 42, 7, 150
• C150, 150, 133, 93, 42, 7, 0
• D150, 148, 133, 93, 42, 7, 0
• E0, 2, 17, 57, 108, 143, 150

Q2:

Complete the following descending cumulative frequency table. Note that no player is taller than 200 cm.

 Height (cm) Number of Players CF 140– 150– 160– 170– 180– 190– Total 4 6 9 3 7 1 30 30 26 ⋯ ⋯ ⋯ ⋯
• A20, 11, 1, 8
• B11, 20, 8, 1
• C20, 11, 8, 1
• D32, 41, 44, 51
• E20, 8, 11, 1

Q3:

Consider the frequency distribution shown.

 Grade (𝑔) Number of Students 0– 10– 20– 30– 40– 8 10 6 6 2

Which of the following is the descending cumulative frequency diagram that represents these data?

• A
• B
• C
• D
• E

Q4:

The following table shows the amount of money customers put in a donation box. Note that no customer donated more than \$100.

 Donation (\$) Number of Customers 10– 20– 30– 40– 50– 60– 70– 90– Total 3 7 10 12 13 9 7 4 65

Which of the following is the descending cumulative frequency graph?

• A
• B
• C
• D
• E

Q5:

The following table shows the heights of players in a basketball game. Note that no player is taller than 200 cm.

 Height (cm) Number of Players 140– 150– 160– 170– 180– 190– Total 4 6 9 3 7 1 30

Which of the following is the descending cumulative frequency graph?

• A
• B
• C
• D
• E

Q6:

The times, in seconds, for adults to complete a puzzle were recorded. The results are given in the table below.

 Time (s) Frequency 0– 30– 60– 90– 120– 3 17 35 43 2

Which of the following is the descending cumulative frequency diagram that represents these data?

• A
• B
• C
• D
• E

Q7:

Consider the given descending cumulative frequency graph, which represents the age, in years, of people enrolled in a certain online course.

What is the total number of people in the course?

Q8:

Consider the descending cumulative frequency graph shown, which represents the weights of 200 people.

How many people weigh more than 60 kg?

Q9:

The table shows the times of runners who completed a 5 km race.

 Time (Minutes) Number of Runners 15– 17– 19– 21– 23– 5 21 18 12 4

Which of the following is the descending cumulative frequency diagram representing these data?

• A
• B
• C
• D
• E

How many runners had a race time of 21 minutes or more?

Q10:

Descending cumulative frequency diagrams have been drawn to represent the grades achieved in a test by students in two classes, class A and class B.

Determine which class has more students achieving a grade of 40 or higher.

• AClass B
• BClass A