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.