## Exam-Style Questions on Cumulative frequency## Problems on Cumulative frequency adapted from questions set in previous exams. |

## 1. | GCSE Higher |

This Cumulative Frequency graph shows the heights of 58 Scouts. Work out an estimate for the number of these Scouts with a height greater than 160cm.

## 2. | GCSE Higher |

The table shows the test marks for 31 students.

Percentage (p) | Frequency |

5 ≤ p < 15 | 2 |

15 ≤ p < 25 | 3 |

25 ≤ p < 35 | 4 |

35 ≤ p < 45 | 3 |

45 ≤ p < 55 | 8 |

55 ≤ p < 65 | 8 |

65 ≤ p < 75 | 2 |

75 ≤ p < 85 | 1 |

Marco drew this cumulative frequency graph using the data.

Make three criticisms of Marco’s graph.

## 3. | IB Standard |

The weights in grams of 98 mice are shown in the cumulative frequency diagram. The heaviest mouse weighted 160g.

(a) Write down the median weight of the mice.

(b) Find the percentage of mice that weigh 70 grams or less.

The same data is presented in the following table.

Weights w grams | 0 < w ≤ 40 | 40 < w ≤ 80 | 80 < w ≤ 120 | 120 < w ≤ 160 |
---|---|---|---|---|

Freequency | p | 63 | q | 3 |

(c) Find the value of p.

(d) Find the value of q.

(e) Use the values from the table to estimate the mean and standard deviation of the weights.

A second batch of mice are normally distributed with the same mean and standard deviation as those of the first group mentioned above.

(f) Find the percentage of the second batch of mice that weigh 70 grams or less.

(g) A sample of five mice is chosen at random from the second batch. Find the probability that at most three mice weigh 70 grams or less.

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

The solutions to the questions on this website are only available to those who have a Transum Subscription.

Exam-Style Questions Main Page

To search the **entire Transum website** use the search box in the grey area below.

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

Kausar Begum Khan, Kenya

Friday, January 26, 2018

"This is a fabulous website! I cannot thank you enough."

Aruna Upadhyayula, Bahrain

Tuesday, November 6, 2018

"Transum is so resourceful. The resources are so child-friendly that my students love its usage.It has a wide range of topics and caters to most of my needs. 'Thankyou" will be too small a word to express my gratitude to the content developers of this site."

Ahmed Jaja, Ghana

Thursday, November 22, 2018

"It was very useful for me.I recommend it to every math student.Thank you."

Madiwa Otieno, Kenya

Tuesday, February 5, 2019

"A very great site.Nice questions."