Frequency distributions display data in a table. They are constructed by counting the observations of a variable belonging to a distinct group or having a given value.

To construct a frequency distribution of a categorical variable, you first count the number of observations of each unique value of the variable. Then you create a table listing each unique value and the corresponding count. Finally, you sort the records in either ascending or descending order.

The table below is a frequency distribution of the companies in the Dow Jones Industrial Average by sector. The first column describes the sector, the second is the absolute frequency (the number of companies in that sector), and the last column is the relative frequency (the percentage of the total companies that are in that sector). It is easy to see that information technology is the largest sector.

Information Technology | 7 | 23% |

Industrials | 4 | 13% |

Healthcare | 4 | 13% |

Financials | 4 | 13% |

Consumer Staples | 4 | 13% |

Consumer Discretionary | 3 | 10% |

Communication Services | 2 | 7% |

Materials | 1 | 3% |

Energy | 1 | 3% |

When creating a frequency distribution for numerical values they must first be grouped into ranges. The next frequency distribution is the same companies sorted by market capitalization. Here we see that the vast majority are smaller than 250 billion, there are none at all between 500 billion and 1 trillion, and there are 2 that are larger than 1 trillion.

< 250 Billion | 20 |

250-500 Billion | 8 |

500-750 Billion | 0 |

750 Billion – 1 Trillion | 0 |

> 1 Trillion | 2 |

When creating a frequency distribution, if a large number of the bins have a value of zero the ranges are probably too narrow.