In these lessons, we will learn how to draw a cumulative frequency graph (cumulative frequency curve) and how to find the median, quartiles and inter-quartile range.

**Related Pages**

Frequency Table

Cumulative Frequency Table

More Statistics Lessons

A Cumulative Frequency Graph is a graph plotted from a cumulative
frequency table. A cumulative frequency graph is also called an **ogive**
or cumulative frequency curve. The following examples show how to
draw a cumulative frequency curve for grouped data.

**Example:**

Draw a cumulative frequency graph for the frequency table below.

Length (x mm) | Frequency |

11 – 15 | 2 |

16 – 20 | 4 |

21 – 25 | 8 |

25 – 30 | 14 |

31 – 35 | 6 |

36 – 40 | 4 |

41 – 45 | 2 |

**Solution:**

We need to add a class with 0 frequency before the first class and then find the upper boundary
for each class interval.

Length (x mm) | Frequency | Upper Class Boundary | Length (x mm) | Cumulative Frequency |

6 – 10 | 0 | 10.5 | x ≤ 10.5 | 0 |

11 – 15 | 2 | 15.5 | x ≤ 15.5 | 2 |

16 – 20 | 4 | 20.5 | x ≤ 20.5 | 6 |

21 – 25 | 8 | 25.5 | x ≤ 25.5 | 14 |

25 – 30 | 14 | 30.5 | x ≤ 30.5 | 28 |

31 – 35 | 6 | 35.5 | x ≤ 35.5 | 34 |

36 – 40 | 4 | 40.5 | x ≤ 40.5 | 38 |

41 – 45 | 2 | 45.5 | x ≤ 45.5 | 40 |

And then plot the cumulative frequency against the upper class boundary of each interval and join the points with a smooth curve.

**How To Obtain A Cumulative Frequency Graph From A Cumulative Frequency Table?**

Calculate the cumulative frequency. Write down the upper class boundaries. Plot the cumulative frequency curve. Find the median values. Find the upper and lower quartiles. Find the inter-quartile range.

**How To Draw A Cumulative Frequency Curve From A Cumulative Frequency Table?**

How to draw a cumulative frequency curve from a cumulative frequency table and how to estimate the median, quartiles and interquartile range.

**What Are Cumulative Frequency Diagrams?**

Investigating cumulative frequencies and cumulative frequencies diagrams.

**Cumulative Frequency - Median and Quartiles**

Investigating how cumulative frequency diagrams are used to estimate the median and quartiles of a frequency distribution.

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