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),
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.
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 (f2) of the class succeeding the modal class = 38,
|⏪ Mean for Grouped Data||Cumulative frequency & Ogive ⏩|