In statistics, we use **skewness **and **kurtosis **to measure the shape of a distribution.

**Skewness** measures the asymmetry of a distribution. This value can be positive or negative.

- A negative skew indicates that the tail is on the left side of the distribution, which extends towards more negative values.
- A positive skew indicates that the tail is on the right side of the distribution, which extends towards more positive values.
- A value of zero indicates that there is no skewness in the distribution at all, meaning the distribution is perfectly symmetrical.

**Kurtosis **is a measure of whether or not a distribution is heavy-tailed or light-tailed relative to a normal distribution.

- The kurtosis of a normal distribution is 0.
- If a given distribution has a kurtosis less than 0, then it tends to produce fewer and less extreme outliers than the normal distribution.
- If a given distribution has a kurtosis greater than 0, then it tends to produce more outliers than the normal distribution.

The following example shows how to calculate skewness and kurtosis for a given dataset in SPSS.

**Example: How to Calculate Skewness & Kurtosis in SPSS**

Suppose we have the following dataset in SPSS that shows the exam scores received by various students in some class:

To calculate the skewness and kurtosis for the distribution of exam scores, click the **Analyze** tab, then click **Descriptive Statistics**, then click **Descriptives**:

In the new window that appears, drag **Exam_Score** to the **Variables** panel:

Then click the **Options** button. In the new window that appears, check the boxes next to **Kurtosis** and **Skewness**:

Then click **Continue**. Then click **OK**.

The following output will appear:

From the output we can see the values for the skewness and kurtosis of the distribution:

- The skewness is
**-1.551**. Since this value is negative, it indicates that the distribution is left-skewed. - The kurtosis is
**2.230**. Since this value is greater than zero, it indicates that the distribution has heavier “tails” than a normal distribution.

In addition to calculating these metrics, it can be helpful to create a histogram to visualize the distribution.

To do so, click the **Graphs** tab, then click **Histogram**:

In the new window that appears, drag **Exam_Score** into the **Variable** panel:

Once you click **OK**, a histogram will be generated that shows the distribution of exam scores:

We can see that the distribution is indeed left-skewed (the “tail” extends to the left side of the distribution), which matches the fact that we calculated the skewness to be negative.

**Related:** Left Skewed vs. Right Skewed Distributions

By calculating the skewness and kurtosis along with creating a histogram, we now have a pretty good understanding of the distribution of exam scores in this dataset.

**Additional Resources**

The following tutorials explain how to perform other common tasks in SPSS:

How to Calculate a Five Number Summary in SPSS

How to Create a Frequency Table in SPSS

How to Calculate Percentiles in SPSS