Mode

What is a mode?

A mode of a set of observations is defined as the value which occurs most frequently and around which other values cluster densely.

Mode for an ungrouped data:

For an ungrouped data, mode is the frequently occurring value, i.e., a value occurring more than once.

Mode for a discrete frequency distribution:

In the case of discrete frequency distribution, mode is the value of x standing for the maximum frequency.

Mode can be calculated by using the method of grouping in the following cases:

• If the maximum frequency is repeated more than once.
• If the maximum frequency occurs either in the beginning or at the end of the distribution.
• If there are irregularities in the distribution.

Mode for a continuous frequency distribution:

In the case of continuous frequency distribution, mode is estimated using the formula:

Mode = l + [h (f₁-f₀)] / [2f₁ -f₀ -f₂]

Where l = lower limit

h = magnitude

f₁ = frequency of the modal class

f₀ and f₂ = frequencies of the classes preceding and succeeding the modal class.

Mode can be calculated by using the method of grouping in the following cases:

• If the maximum frequency is repeated more than once.
• If the maximum frequency occurs either in the beginning or at the end of the distribution.
• If there are irregularities in the distribution.

Sometimes, mode can be evaluated from the mean and the median, i.e.,

Mode = 3 Median - 2 Mean

Merits of a Mode:

The merits of mode are as follows:

• Mode is easy to understand and easy to estimate. Just like median, mode can also be obtained by mere inspection (in few cases only)
• The extreme values does not affect mode.
• Open end classes do not pose any problem in the location of mode.