In the data set $3, 3, 4, 5, 5, 5, 6$, the mode is $5$.

In statistics, the mode refers to the value that occurs most frequently within a data set. To determine the mode, one must count the frequency of each number in the data set. In our example, the numbers present are $3$, $3$, $4$, $5$, $5$, $5$, and $6$. Let’s analyze the occurrences of each number:

• The number $3$ appears $2$ times.
• The number $4$ appears $1$ time.
• The number $5$ appears $3$ times.
• The number $6$ appears $1$ time.

Since the number $5$ occurs more frequently than any other number in this data set, it is identified as the mode.

Understanding the mode is valuable as it provides insight into the most common value within a collection of data. This can be particularly useful in various real-life scenarios, such as identifying the most popular product in a store or determining the most common score on a test.

It is important to note that a data set can have more than one mode if multiple values share the same highest frequency; in such instances, the data set is referred to as multimodal. However, in the specific data set we are examining, $5$ is the sole mode.