**Definition:**

A frequency distribution table is a tabulated form of data consisting of two columns- class intervals and frequency. The class intervals tell us the range of values that the data takes and the frequency tells us the number of times these values occur in the data given to us.

**How to make Frequency Distribution Table:**

- Given the data in raw form, decide how many classes you want to have.
- Calculate the class width using the formula, Class width=(Largest value-Smallest value)/Number of Intervals.
- Now that class intervals have been constructed, count the number of data occurring in each interval and note it down as the frequency in the second column.

**What are the advantages of a Frequency Distribution Table?**

It happens that many times data is given to us in raw form. The data in the raw form may consist of hundreds or thousands of data points. In that case, it is very hard to make sense of the data because of the sheer volume of data.

Here the advantage of constructing a frequency distribution table is that we can get an idea about how the data is distributed at a glance. Another advantage is that we can use it to construct histograms and bar graphs which help in data visualization.

**Frequency Distribution Table for Grouped Data**:

In a grouped frequency table the data is divided into classes. This makes the data much more compact in terms of presentation. We can use a grouped frequency table to draw a histogram which can help us in visualizing the data. Consider the following frequency distribution about the heights of a group of 20 people.

The frequency histogram looks like,

Also, by using the frequency distribution we can construct the cumulative frequency table and relative frequency table. Using these we can draw ogives and relative frequency histograms that help us further in data visualization.

**Ungrouped Frequency Distribution Table:**

If the data is not divided into classes but the frequencies are noted down for each data point then such a tabular presentation of data is known as an ungrouped frequency distribution table. As an example consider the following ungrouped distribution table. It shows the heights of a group of 40 people along with the corresponding frequency:

Height(in cm) | Frequencies(Number of people) |

167 | 3 |

168 | 7 |

169 | 12 |

170 | 8 |

171 | 7 |

172 | 8 |

173 | 5 |

N = 40 |

So we can see from the above table, that 8 out of 40 people have a height of exactly 170cm. Here we have not divided the data into classes because the range of values for the height is very small. We should use grouped distribution when the range of data values is so high that there is no choice but to divide the data into class intervals in order to make the data compact and easy to understand.

##### What is n in a frequency distribution table?

The ‘n’ in the frequency distribution table refers to the total number of data points in the given data. For example in the above frequency table, N=40 meaning that we are dealing with the data for a total of 40 people.