Probability & Statistics

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The Mode

The mode is a method of finding the average, and represents the most commonly found number.

One way of analyzing and describing the average of a set of data is by looking at the mode. The mode or modal group is the data that appears the most frequently, or, in other words, is most popular.

Here is a set of data collected on the shoe sizes of 10 students. $5, \space 5, \space 6, \space 6, \space 7, \space 7, \space 7, \space 7, \space 8, \space 8$

Which is the most common number here? $5, \space 5, \space 6, \space 6, \space 7, \space 7, \space 7, \space 7, \space 8, \space 8$

$7$ is the most common number in the set of data. Therefore, $7$ can be said to be the mode.

Here is another set of data collected on the height of 10 students. What is the mode? $1.67, \space 1.35 ,\space 1.49 ,\space 1.56 ,\space 1.78 ,\space 1.7 , \space 1.62 ,\space 1.69 ,\space 1.68 ,\space 1.58$

We can put the heights into a grouped frequency table

This gives intervals within which individual values can fall.

Instead of a mode, we now have a modal class interval

The modal class interval is the group with the most frequency, which in this case is: $1.6 < x \leq 1.7$