__6.5 Cumulative Frequency__**Cumulative Frequency**of a data or a class interval in a frequency table is obtained by determining the sum of its frequency with the total frequencies of all its previous data or class interval.

**(A) Ogive**

Ogive is a cumulative frequency graph which is obtained by plotting the cumulative frequency against the upper boundaries of each class.

**Example:**

Books |
Frequency |

6-10 |
3 |

11-15 |
7 |

16-20 |
11 |

21-25 |
16 |

26-30 |
11 |

31-35 |
8 |

36-40 |
4 |

**(a)**Construct a cumulative frequency table for the given data.

**(b)**By using the scales of 2cm to 5 books on the horizontal axis and 2cm to 10 students on the vertical axis, draw an ogive for the data.

*Solution:***(a)**

- Add a class with frequency 0 before the first class.
- Find the upper boundary of each class interval.

Books |
Frequency |
Cumulative Frequency |
Upper Boundary |

1-5 |
0 |
0 |
5.5 |

6-10 |
3 |
0 + 3 = 3 |
10.5 |

11-15 |
7 |
3 + 7 = 10 |
15.5 |

16-20 |
11 |
10 + 11 = 21 |
20.5 |

21-25 |
16 |
21 + 16 = 37 |
25.5 |

26-30 |
11 |
37 + 11 = 48 |
30.5 |

31-35 |
8 |
48 + 8 = 56 |
35.5 |

36-40 |
4 |
56 + 4 = 60 |
40.5 |