Mode for Grouped Data

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A mode is that value among the observations which occurs most often, that is, the value of the observation having the maximum frequency.
↪ The data is said to be multimodal if more than one value may have the same maximum frequency.
↪ In a grouped frequency distribution, it is not possible to determine the mode by looking at the frequencies. Here, we can only locate a class with the maximum frequency, called the modal class.
↪ The mode is a value inside the modal class, and is given by the formula:

Mode

=

where, l = lower limit of the modal class,
h = class size (assuming all class sizes to be equal),
f₁ = frequency of the modal class,
f₀ = frequency of the class preceding the modal class,
f₂ = frequency of the class succeeding the modal class.
↪ This formula can be applied only when class intervals are continuous.

Example: The following data gives the information on the observed lifetimes (in hours) of 225 electrical components :

Determine the modal lifetimes of the components.

Solution:
Modal class is (60 - 80)
Lower limit (l ) of the modal class = 60,
The class size (h) = 20,
Frequency ( f₁ ) of modal class = 61,
Frequency ( f₀ ) of the class preceding the modal class = 52,
Frequency ( f₃) of the class succeeding the modal class = 38.

∴ Mode

=

Mean for Grouped Data
	Cumulative frequency & Ogive ➤