Definition

Mode: the most frequent value, and it need not be unique

Statistics • Mode

Statement

The mode of a data set is the value that occurs with the greatest frequency. Unlike the mean and the median it need not be unique: a set with two values tied at the highest frequency is bimodal, more ties make it multimodal, and a set in which every value occurs equally often is usually said to have no mode at all. For grouped data the modal class is the class of greatest frequency.

How to use it

1Tally the values and read off whichever has the largest count; stop only after checking whether anything else ties it.
2For grouped data with equal class widths, take the class with the greatest frequency as the modal class.
3Being a count rather than an arithmetic combination, the mode is the one average that applies to purely qualitative data such as colours or brands.
4A claim that 'the mode is unique' is refuted by a single bimodal example such as $1, 1, 2, 2, 3$ .

Worked example

Find the mode of

4, 7, 7, 9, 9, 11

Step-by-step

1
Frequencies: $4$ once, $7$ twice, $9$ twice, $11$ once
Why: Tally each distinct value.
2
Both $7$ and $9$ reach the highest frequency $2$
Why: The greatest frequency is attained twice, so the set is bimodal.

Answer

Two modes,

7

and

9

Watch out

The mode is the VALUE that occurs most often, not the frequency itself: for

4, 7, 7, 9

the mode is

7

, not

2

. And it carries none of the mean's or median's uniqueness, so any statement asserting a single mode is false in general.

Also known as

mode, most frequent value, modal value, modal class, bimodal, multimodal

Appears in past papers

2020 (II)

Q93

2019 (II)

2019 (I)

Q69

2017 (II)

Q95