Ogives, also known as cumulative frequency curves, depict the cumulative frequency of a dataset.

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They are useful in visualizing the distribution of values and identifying patterns. To construct an ogive, follow these steps:

**Prepare your data:**

- Arrange your data in ascending order.
- Create a table with columns for the data values and their corresponding frequencies.

**Calculate cumulative frequencies:**

- Add up the frequencies as you go down the list. The last entry in the cumulative frequency column should be the total frequency.

**Construct the ogive:**

- Use a graphing tool or paper to create a set of axes. Label the horizontal axis with your data values and the vertical axis with cumulative frequencies.
- Plot points corresponding to each data value and its cumulative frequency.

**Connect the points:**

- Use a line or a smooth curve to connect the plotted points. This line represents the ogive.

Here’s a simple example:

Data Value | Frequency |
---|---|

10 | 4 |

15 | 6 |

20 | 8 |

25 | 12 |

30 | 15 |

- Calculate cumulative frequencies:

Data Value | Frequency | Cumulative Frequency |
---|---|---|

10 | 4 | 4 |

15 | 6 | 10 |

20 | 8 | 18 |

25 | 12 | 30 |

30 | 15 | 45 |

- Plot the points (10, 4), (15, 10), (20, 18), (25, 30), and (30, 45) on the graph and connect them to form the ogive.