Suppose we conduct a survey in which we ask 15 households how many pets they have in their home. The results are as follows:

**1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 6, 7, 8**

One way to summarize these results is to create a **frequency distribution**, which tells us how frequently different values occur in a dataset.

Often we use **grouped frequency distributions**, in which we create groups of values and then summarize how many observations from a dataset fall into those groups.

Here’s an example of a grouped frequency distribution for our survey data:

We first created groups of size 2, then we counted how many individual observations from the dataset fell in each group. For example:

- 7 families had either 1 or 2 pets
- 3 families had either 3 or 4 pets
- 3 families had either 5 or 6 pets
- 2 families had either 7 or 8 pets

Another type of frequency distribution we could create is an **ungrouped frequency distribution**, which displays the frequency of each individual data value rather groups of data values.

Here’s an example of an ungrouped frequency distribution for our survey data:

This type of frequency distribution allows us to directly see how often different values occurred in our dataset. For example:

- 4 families had 1 pet
- 3 families had 2 pets
- 2 families had 3 pets
- 1 family had 4 pets

And so on.

**When to Use Ungrouped Frequency Distributions**

Ungrouped frequency distributions can be useful when you want to see how often each individual value occurs in a dataset.

**Note that ungrouped frequency distributions work best with small datasets in which there are only a few unique values.**

For example, in our survey data from earlier there were only 8 unique values so it made sense to create an ungrouped frequency distribution.

However, if we had a dataset with hundreds or thousands of unique values, an ungrouped frequency distribution would be incredibly long and difficult to gather information from.

**For larger datasets, it makes sense to construct grouped frequency distributions.**

**How to Visualize Ungrouped Frequency Distributions**

The easiest way to visualize the values in an ungrouped frequency distribution is to create a **frequency polygon**, which displays the frequencies of each individual value in a simple chart.

Here’s what a frequency polygon would look like for our sample data:

This helps us quickly gain an understanding of how often each value occurs in the dataset.

Alternatively, we could create a **bar chart** to display the exact same data using bars rather than a single line:

Both charts allow us to quickly understand the distribution of values in our dataset.

23,33,26,40,62,58,37,

21,35,44,26,39,51,67,

25,34,36,43,57,50,20,

38,44,53,60,27,65,

51,43.

This is ungrouped data.

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