# 8.3.2. Ascending and Descending Cumulative Frequency Tables and Their Graphical Representation

The table below shows the frequency distribution of the grades of 60 students in an exam. Find the number of failed students, given that the minimum success grade is 30 marks.

Sets | 0– | 10– | 20– | 30– | 40– | 50– | Total |
---|---|---|---|---|---|---|---|

Frequency | 3 | 18 | 10 | 8 | 15 | 6 | 60 |

- A31 students
- B10 students
- C39 students
- D21 students

The following table shows the frequency distribution of the heights of 100 students in a school:

Height (cm) | 115– | 120– | 125– | 130– | 135– | 140– | 145– | Total |
---|---|---|---|---|---|---|---|---|

Number of Students | 12 | 12 | 20 | 16 | 12 | 10 | 18 | 100 |

How many students' heights are greater than or equal to cm?

Show SolutionThe following table shows the frequency distribution of the grades of 100 students in a science exam:

Sets | 0– | 10– | 20– | 30– | 40– | 50– | Total |
---|---|---|---|---|---|---|---|

Frequency | 6 | 15 | 12 | 26 | 23 | 18 | 100 |

How many students got 40 marks or more?

Show SolutionThe following table shows the frequency distribution of the grades of 100 students in an exam:

Sets | 0– | 10– | 20– | 30– | 40– | 50– | Total |
---|---|---|---|---|---|---|---|

Frequency | 5 | 25 | 21 | 16 | 19 | 14 | 100 |

Find the percentage of success given that the minimum grade for success is 20 marks.

- A
- B
- C
- D

The following table shows the frequency distribution for the ages of 50 workers:

Sets | 20– | 25– | 30– | 35– | 40– | 45– | 50– | Total |
---|---|---|---|---|---|---|---|---|

Frequency | 5 | 6 | 8 | 10 | 8 | 6 | 7 | 50 |

Draw the ascending cumulative frequency curve then determine the number of workers whose ages are less than 43.

Show SolutionThe following table shows the distribution of 1000 students’ scores in an exam:

Scores | 20– | 30– | 40– | 50– | 60– | 70– | 80– | 90– | Total |
---|---|---|---|---|---|---|---|---|---|

Frequency | 123 | 127 | 127 | 131 | 129 | 127 | 133 | 103 | 1000 |

Draw the ascending cumulative frequency curve, then determine the number of students whose scores are less than 85.

Show SolutionThe table below shows the scores of 73 students in an English exam. Find the value of .

Scores | 0– | 5– | 10– | 15– | 20– | 25– | 30– | Total |
---|---|---|---|---|---|---|---|---|

Frequency | 6 | 5 | 6 | 15 | 11 | 12 | 73 |

The years of experience of 100 workers in a factory ranges from 5 to 35 years. The table below shows the descending cumulative frequency distribution for the workers according to the years of experience. Fill in the frequency table below.

Lower Boundaries of Sets | 5 and more | 10 and more | 15 and more | 20 and more | 25 and more | 30 and more | 35 and more |
---|---|---|---|---|---|---|---|

Descending Cumulative Frequency | 100 | 89 | 77 | 61 | 42 | 28 | 0 |

Years | 5– | 10– | 15– | 20– | 25– | 30– | Total |
---|---|---|---|---|---|---|---|

Frequency |

- A100, 89,77, 61, 42, 28, 397
- B11, 28, 16, 19, 14, 28, 116
- C11, 12, 16, 19, 14, 28, 100
- D23,12, 16, 19, 14, 28, 112