Mode and choosing an average

The mode is the value that occurs most often. The word comes from the French 'la Mode', meaning the fashion: the most popular. Data may have one mode (unimodal), two (bimodal), several (multimodal), or none at all.

In a continuous series, the class with the largest frequency is the modal class, and:

Mode = L + [D1 ÷ (D1 + D2)] × h

where L is the lower limit of the modal class, D1 = (its frequency – the frequency of the class before), D2 = (its frequency – the frequency of the class after), and h is the class width. The classes must be equal and exclusive.

A note on the book: in its Example 11, the working 25 + (12 ÷ 22) × 5 actually gives 27.727 thousand rupees; the book prints 27.273, which is a slip.

The three averages are related. The median always lies between the mean and the mode: either mean > median > mode, or mean < median < mode.

Which average to choose?

• The mean uses all the values, so it is best for data without extreme values, and when a total matters.
• The median is best for skewed data (with extremes) and for open-ended classes (such as '60 and above'), whose mid-points cannot be found.
• The mode is best for finding the most popular item, such as the shoe size a shoe company should make most of; it can also be used for qualitative data.