*23*

A frequency distribution table is a table that displays the frequencies of different data classes.

For example, the following frequency distribution table shows the frequency for five different classes:

Class | Frequency |
---|---|

1 â€“ 10 | 20 |

11 â€“ 20 | 21 |

21 â€“ 30 | 16 |

31 â€“ 40 | 5 |

41 â€“ 50 | 4 |

You can find the midpointÂ of each class by adding the lower class limit and the upper class limit, then dividing by two:

**Class midpointÂ ** = (lower class limit + upper class limit) / 2

The following table shows how to calculate the midpoint of each class:

Class | Frequency | Midpoint |
---|---|---|

1 â€“ 10 | 20 | (1+10) / 2 |

11 â€“ 20 | 21 | (11+20) / 2 |

21 â€“ 30 | 16 | (21+30) / 2 |

31 â€“ 40 | 5 | (31+40) / 2 |

41 â€“ 50 | 4 | (41+50) / 2 |

Thus, weâ€™re left with the following midpoints:

Class | Frequency | Midpoint |
---|---|---|

1 â€“ 10 | 20 | 5.5 |

11 â€“ 20 | 21 | 15.5 |

21 â€“ 30 | 16 | 25.5 |

31 â€“ 40 | 5 | 35.5 |

41 â€“ 50 | 4 | 45.5 |

**When Are Class Midpoints Used?**

Class midpoints are often used when you want to create a histogram to visualize the values in a frequency table.

A histogram lists the classes along the x-axis of a graph and uses bars to represent the frequency of each class along the y-axis. Each bar is centered at itsÂ **class midpoint**.Â

The following histogram provides a visual representation of the data in the previous frequency table:

Notice how each bar is centered at its class midpoint:

When youâ€™re creating a histogram by hand, itâ€™s especially useful to know the class midpoints so that you know where to place the bars.

However, most statistical softwares are able to automatically center the bars of a histogram around the class midpoints, so you typically wonâ€™t have to manually find these midpoints yourself.

**Additional Resources**

How to Find Class Boundaries

How to Find Class Limits

How to Find Class Intervals

Class Width Calculator

Histogram Generator