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The term **univariate analysis **refers to the analysis of one variable. You can remember this because the prefix “uni” means “one.”

The purpose of univariate analysis is to understand the distribution of values for a single variable. You can contrast this type of analysis with the following:

**Bivariate Analysis:**The analysis of two variables.**Multivariate Analysis:**The analysis of two or more variables.

For example, suppose we have the following dataset:

We could choose to perform univariate analysis on any of the individual variables in the dataset to gain a better understanding of its distribution of values.

For example, we may choose to perform univariate analysis on the variable **Household Size**:

There are three common ways to perform univariate analysis:

**1. Summary Statistics**

The most common way to perform univariate analysis is to describe a variable using summary statistics.

There are two popular types of summary statistics:

**Measures of central tendency:**these numbers describe where the center of a dataset is located. Examples include the*mean*and the*median*.**Measures of dispersion:**these numbers describe how spread out the values are in the dataset. Examples include the*range*,*interquartile range*,*standard deviation*, and*variance*.

**2. Frequency Distributions**

Another way to perform univariate analysis is to create a frequency distribution, which describes how often different values occur in a dataset.

**3. Charts**

Yet another way to perform univariate analysis is to create charts to visualize the distribution of values for a certain variable.

Common examples include:

- Boxplots
- Histograms
- Density Curves
- Pie Charts

The following examples show how to perform each type of univariate analysis using the **Household Size** variable from our dataset mentioned earlier:

**Summary Statistics**

We can calculate the following measures of central tendency for Household Size:

**Mean (the average value):**3.8**Median (the middle value):**4

These values give us an idea of where the “center” value is located.

We can also calculate the following measures of dispersion:

**Range (the difference between the max and min):**6**Interquartile Range (the spread of the middle 50% of values):**2.5**Standard Deviation (an average measure of spread):**1.87

These values give us an idea of how spread out the values are for this variable.

**Frequency Distributions**

We can also create the following frequency distribution table to summarize how often different values occur:

This allows us to quickly see that the most frequent household size is **4**.

**Resource:** You can use this Frequency Calculator to automatically produce a frequency distribution for any variable.

**Charts**

We can create the following charts to help us visualize the distribution of values for Household Size:

**1. Boxplot**

A boxplot is a plot that shows the five-number summary of a dataset.

The five-number summary includes:

- The minimum value
- The first quartile
- The median value
- The third quartile
- The maximum value

Here’s what a boxplot would look like for the variable Household Size:

**Resource:** You can use this Boxplot Generator to automatically produce a boxplot for any variable.

**2. Histogram**

A histogram is a type of chart that uses vertical bars to display frequencies. This type of chart is a useful way to visualize the distribution of values in a dataset.

Here’s what a histogram would look like for the variable Household Size:

**3. Density Curve**

A density curve is a curve on a graph that represents the distribution of values in a dataset.

It’s particularly useful for visualizing the “shape” of a distribution, including whether or not a distribution has one or more “peaks” of frequently occurring values and whether or not the distribution is skewed to the left or the right.

Here’s what a density curve would look like for the variable Household Size:

**4. Pie Chart**

A pie chart is a type of chart that is shaped like a circle and uses slices to represent proportions of a whole.

Here’s what a pie chart would look like for the variable Household Size:

Depending on the type of data, one of these charts may be more useful for visualizing the distribution of values than the others.