Mode is the value of a variable which occurs most frequently in a set of observations.

For simple frequency distribution the mode is the value of a variable corresponding to the maximum frequency. For grouped frequency distribution the mode is obtained as follows.

where,

L = Lower limit or boundary of the modal class

*h *= Width of the modal class

*f1*= Frequency of the modal class

*f 0= *Frequency of the class preceding the modal class

*f*2 = Frequency of the class succeeding the modal class.

**Note.** 1. If 2f_{1}- f_{0} -f_{2} = 0, then the mode is obtained as follows :

2. lf the maximum frequency is repeated then the above technique is not practicable.

3. For symmetrical distribution,

Mean = Median = Mode. (Mean = *x).*

However, for moderately skewed distribution there is an empirical relationship due to Karl Pearson *i.e.,*

Mean - Mode = 3 (Mean - Median).

** **

**Example **5 : *Find the mode of the problem as given in example 4.*** **

**Solution. **Here maximum frequency is 25, so the modal class is 61-70.

L = 61, *h *= 9, *f1* = 25, *f0 *= 15, *f2 *= 10