This **frequency distribution calculator** is used to organize and summarize data by grouping values into categories and counting their occurrences. This method provides a clear picture of how often different values or ranges appear within a dataset.

**For example, imagine you’re analyzing the ages of students in a university:**

```
Ages: 18, 19, 20, 18, 21, 19, 20, 22, 18, 20, 19, 21, 18, 20, 19
```

Age | Frequency |
---|---|

18 | 4 |

19 | 4 |

20 | 4 |

21 | 2 |

22 | 1 |

**This representation table quickly reveals that ages 18, 19, and 20 are the most common, each occurring four times.**

## Frequency Distribution Calculator

`Grades: A, B, C, A, B, D, C, B, A, F, C, B, A, C, B, A, D, C, B, A`

Grade | Frequency | Relative Frequency | Cumulative Frequency |
---|---|---|---|

A | 6 | 0.30 | 0.30 |

B | 6 | 0.30 | 0.60 |

C | 5 | 0.25 | 0.85 |

D | 2 | 0.10 | 0.95 |

F | 1 | 0.05 | 1.00 |

From this table, we can derive several insights:

- The
**mode**(most frequent grade) is tied between A and B. - 60% of students received a grade of B or higher.
- Only 5% of students failed the course.
- The
**median**grade falls in the B category (as the 50th percentile is at 0.60).

## Frequency Distribution Formula

**Frequency = Number of occurrences of a value / Total number of values**

Let’s examine a more complex example using test scores:

`Scores: 65, 70, 75, 80, 85, 90, 95, 65, 70, 75, 80, 85, 90, 95, 70, 75, 80, 85, 90, 95`

We can group these scores into intervals:

Score Range | Frequency | Relative Frequency |
---|---|---|

60-69 | 2 | 0.10 |

70-79 | 5 | 0.25 |

80-89 | 6 | 0.30 |

90-99 | 7 | 0.35 |

The **relative frequency** is calculated by dividing each frequency by the total number of scores (20 in this case).

## How do I calculate frequency distribution?

**Collect and organize data**: Gather your dataset and arrange it in ascending order.**Determine categories or intervals**: For continuous data, decide on appropriate intervals.**Count occurrences**: Tally how many times each value or interval appears.**Calculate frequencies**: Divide the count by the total number of observations.**Create a table or graph**: Present your results in a clear, visual format.

Let’s walk through an example using daily temperatures for a week:

```
Temperatures (°F): 72, 75, 68, 70, 73, 71, 69
```

- Organize the data: 68, 69, 70, 71, 72, 73, 75
- Count occurrences:
- 68: 1
- 69: 1
- 70: 1
- 71: 1
- 72: 1
- 73: 1
- 75: 1

- Calculate frequencies (divide by 7):
- 68: 1/7 ≈ 0.14
- 69: 1/7 ≈ 0.14
- 70: 1/7 ≈ 0.14
- 71: 1/7 ≈ 0.14
- 72: 1/7 ≈ 0.14
- 73: 1/7 ≈ 0.14
- 75: 1/7 ≈ 0.14

Temperature (°F) | Frequency | Relative Frequency |
---|---|---|

68 | 1 | 0.14 |

69 | 1 | 0.14 |

70 | 1 | 0.14 |

71 | 1 | 0.14 |

72 | 1 | 0.14 |

73 | 1 | 0.14 |

75 | 1 | 0.14 |

This distribution shows an even spread of temperatures throughout the week.

Related Tools