# Statistics - Frequency Distribution

Frequency distribution is a table that displays the frequency of various outcomes in a sample. Each entry in the table contains the frequency or count of the occurrences of values within a particular group or interval, and in this way, the table summarizes the distribution of values in the sample.

### Example

**Problem Statement:**

Constructing a frequency distribution table of a survey was taken on Maple Avenue. In each of 20 homes, people were asked how many cars were registered to their households. The results were recorded as follows:

1 | 2 | 1 | 0 | 3 | 4 | 0 | 1 | 1 | 1 | 2 | 2 | 3 | 2 | 3 | 2 | 1 | 4 | 0 | 0 |

**Solution:**

Steps to be followed for present this data in a frequency distribution table.

Divide the results (x) into intervals, and then count the number of results in each interval. In this case, the intervals would be the number of households with no car (0), one car (1), two cars (2) and so forth.

Make a table with separate columns for the interval numbers (the number of cars per household), the tallied results, and the frequency of results in each interval. Label these columns Number of cars, Tally and Frequency.

Read the list of data from left to right and place a tally mark in the appropriate row. For example, the first result is a 1, so place a tally mark in the row beside where 1 appears in the interval column (Number of cars). The next result is a 2, so place a tally mark in the row beside the 2, and so on. When you reach your fifth tally mark, draw a tally line through the preceding four marks to make your final frequency calculations easier to read.

Add up the number of tally marks in each row and record them in the final column entitled Frequency.

Your frequency distribution table for this exercise should look like this:

Frequency table for the number of cars registered in each household | ||
---|---|---|

Number of cars (x) | Tally | Frequency (f) |

0 | ${\lvert\lvert\lvert\lvert}$ | 4 |

1 | ${\require{cancel} \cancel{\lvert\lvert\lvert\lvert} \lvert}$ | 6 |

2 | ${\cancel{\lvert\lvert\lvert\lvert}}$ | 5 |

3 | ${\lvert\lvert\lvert}$ | 3 |

4 | ${\lvert\lvert}$ | 3 |

By looking at this frequency distribution table quickly, we can see that out of 20 households surveyed, 4 households had no cars, 6 households had 1 car.