We will learn here to find one of the measures of Central tendency for Grouped Data called Mode.
Prerequisite / Revise this:
What is Mode
A mode is that value among the observations which occurs most often, that is, value of the observation having 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:
where, l = lower limit of the modal class,
h = class size (assuming all class sizes to be equal),
f_{1}= 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.
↪ 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 (f_{1}) of modal class = 61,
Frequency (f_{0}) of the class preceding the modal class = 52,
Frequency (f_{2}) of the class succeeding the modal class = 38,
Then,
⏪ Mean for Grouped Data | Cumulative frequency & Ogive ⏩ |