Here you will learn what is the formula for mode of grouped and ungrouped data and how to find mode with examples.

Let’s begin –

## What is Mode ?

Mode is the size of the variable which occurs most frequently.

## Formula for Mode :

**(i) For ungrouped distribution : **The value of that variate which is repeated maximum number of times.

**Example** : Find the mode of the following data 1, 2, 3, 1, 5, 6, 2, 8, 2, 9.

**Solution** : Here, 2 is repeated maximum number of times.

Hence, Mode is 2.

**(ii) For ungrouped frequency distribution : **The value of that variate which have maximum frequency.

Example : Find the mean of the following freq. dist.

Size of the shoes | 4 | 5 | 6 | 7 | 8 |

Number of pairs sold | 10 | 15 | 20 | 35 | 16 |

Solution : In the above table we notice that the size 7 has the maximum frequency i.e. 35

Therefore, 7 is the mode of distribution.

**(iii) For grouped frequency distribution : **First we find the class which have maximum frequency, this is model class.

\(\therefore\) Mode = (\(l\) + \(f_0 – f_1\over {2f_0 – f_1 – f_2}\))\(\times\)h

where \(l\) = lower limit of model class

\(f_0\) = freq. of model class

\(f_1\) = freq. of the class preceding model class

\(f_2\) = freq. of the class succeeding model class

h = class interval of model class

Example : Find the mean of the following freq. dist.

Size of the shoes | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |

Number of pairs sold | 2 | 18 | 30 | 45 | 35 | 20 | 6 | 3 |

Solution : Here the class 30-40 has maximum frequency, so this is the modal class

\(l\) = 30, \(f_0\) = 45, \(f_1\) = 30, \(f_2\) = 35, h = 10

\(\therefore\) Mode = (\(l\) + \(f_0 – f_1\over {2f_0 – f_1 – f_2}\))\(\times\)h = \(45 – 30\over 2\times 45 – 30 – 35\)\(\times\) 10 = 36