Mode for Grouped Data

mode of data

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:

Mode=l+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h

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 (f2) of the class succeeding the modal class = 38,

Then,

Mode=l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h

=60+\left(\frac{61-52}{2\times61-52-38}\right)\times 20

=60+\left(\frac{9}{32}\right)\times 20

=65.62

⏪ Mean for Grouped Data Cumulative frequency & Ogive ⏩

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