## Cumulative Frequency Curves

Cumulative frequency curves are useful statistical tools that provide a visual summarry of data and enable an easy calculation of the interquartile range. Suppose we have a data set comprising the lengths of a selection of fish, summarised in the table below.

mm) | |

2 | |

4 | |

8 | |

14 | |

6 | |

4 | |

2 |

We find the cumulative frequencies by adding up the frequencies as we go down the table.

mm) | |

2 | |

6 | |

14 | |

28 | |

34 | |

38 | |

40 |

From this table we can plot the cumulative frequency curve.

From the cumulative frquency curve we can find the lowe quartile, median and upper quartile. Go one quarter, half and three quarters of the way up the cumulative frequency axis respectively, across then down to the length axis.

From the diagram above the lower quartile is about 22 cm, the median is about 27 cm and the upper quartile is about 32 cm.