## 1.3 Mode

The mode is the most commonly occurring value in a given set of values. For example, suppose $$n=10$$ randomly selected students were asked the question, how many siblings do you have?, with responses as follows: $2, 0, 1, 1, 3, 1, 2, 3, 4, 0$

Arranging these responses into a frequency table allows us to more easily see what the mode is:

Table 1.2: Frequency table detailing number of siblings students had
Number of Siblings Frequency
0 2
1 3
2 2
3 2
4 1

Since the most commonly occurring response was $$1$$ sibling, with $$3$$ responses, we can say that the mode is $$3$$.

The mode does not always exist. Consider again, for example, the five income values from our previous example: $$1740, 6940, 25000, 1170, 66300$$. Since every value is unique, the mode does not exist for this data set.

Another way to determine the mode is to view a histogram. For example, now suppose $$n=100$$ randomly selected students were asked the question, how many siblings do you have?, with responses represented in the below histogram: As we can see, the mode is now $$2$$ siblings, with a frequency of $$33$$.

Sometimes, there is more than one mode, which can lead to either a bi-modal or multi-modal distribution. We will consider these concepts shortly.