# Mode of a Data Set

The mode of a set of data is the value in the set that occurs most often.

Mode is the most commonly occurring data point in the data set or the one with highest frequency.

Consider the data set 12, 17, 21, 31, 35, 17, 37 Here 17 occurs twice. All other numbers occur one time only. So 17 has the maximum frequency of occurrence. Hence, it is the mode of given data set.

A set of data can have one or more modes

Consider the data set 14, 16, 21, 33, 37, 16, 39, 33 Here 16 and 33 each occurs twice. All other numbers occur one time only. So 16 and 33 have the maximum frequency of occurrence which is 2. Hence, there are two modes for given data set, i.e., 16 and 33.

It is also possible to have a set of data with no mode

Consider the data set 10, 15, 24, 34, 38, 16, 41. Here all numbers occur one time only. So no one number has the maximum frequency of occurrence. Hence, there is no mode for this given data set.

## Rules to find the mode of a data set

• Examine all the numbers of the data set and find if one or more numbers are occurring more than once.

• The number with the maximum frequency of occurrence is the mode.

• If more than one number has a maximum frequency, then there is more than one mode for the data set.

• If all the numbers of data set occur only one time, then there is no mode for the data set.

Find the mode of the set of numbers given below −

3, 14, 23, 12, 20, 8, 12, 17, 10

### Solution

Step 1:

The number that occurs most is 12; occurs twice.

Step 2:

So, the mode is given by 12.

Find the mode of the set of numbers given below −

28, 35, 42, 35, 34, 29, 35, 43, 33

### Solution

Step 1:

The number that occurs most is 35; occurs thrice.

Step 2:

So, the mode is given by 35.