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 \(1\), with a frequency of \(3\).

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.