# 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) | 8– | 10– | 12– | 14– | 16– | 18– | Total |
---|---|---|---|---|---|---|---|

Frequency | 2 | 15 | 40 | 51 | 35 | 7 | 150 |

Complete the descending cumulative frequency table.

Age (Months) | 8 or more | 10 or more | 12 or more | 14 or more | 16 or more | 18 or more | 20 or more |
---|---|---|---|---|---|---|---|

Descending Cumulative Frequency |

- 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) | 140– | 150– | 160– | 170– | 180– | 190– | Total |
---|---|---|---|---|---|---|---|

Number of Players | 4 | 6 | 9 | 3 | 7 | 1 | 30 |

CF | 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 () | 0– | 10– | 20– | 30– | 40– |
---|---|---|---|---|---|

Number of Students | 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 ($) | 10– | 20– | 30– | 40– | 50– | 60– | 70– | 90– | Total |
---|---|---|---|---|---|---|---|---|---|

Number of Customers | 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) | 140– | 150– | 160– | 170– | 180– | 190– | Total |
---|---|---|---|---|---|---|---|

Number of Players | 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) | 0– | 30– | 60– | 90– | 120– |
---|---|---|---|---|---|

Frequency | 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) | 15– | 17– | 19– | 21– | 23– |
---|---|---|---|---|---|

Number of Runners | 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