Mode - Grouped frequency distribution — lesson. Mathematics CBSE, Class 10.

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The mode of the grouped frequency distribution can be determined using the formula:

Mode

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

The class interval with maximum frequency is called the modal class.

Where

$l$ is the lower limit of the modal class,

$f_1$ is the frequency of the modal class,

$f_0$ is the frequency of the class preceding the modal class,

$f_2$ is the frequency of the class succeeding the modal class, and

$h$ is the width of the class interval.

Example:

Find the mode of the following data:

Class interval	$130 - 140$	$140 - 150$	$150 - 160$	$160 - 170$	$170 - 180$
Frequency	$5$	$36$	$14$	$28$	$1$

Solution:

The maximum frequency is

$36$ , and the modal class is

$140 - 150$ .

The mode of the grouped frequency distribution can be determined using the formula:

Mode

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

Here,

$l = 140$ ,

$f_1 = 36$ ,

$f_0 = 5$ ,

$f_2 = 14$ ,

$h = 10$

Substituting the known values in the above formula, we have;

Mode

$= 140 + \left(\frac{36 - 5}{2(36) - 5 - 14} \right) \times 10$

$= 140 + \left(\frac{36 - 5}{72 - 5 - 14} \right) \times 10$

$= 140 + (\frac{31}{53}) \times 10$

$= 140 + 0.585 \times 10$

$= 140 + 5.85$

$= 145.85$

Therefore, the mode of the given data is

$145.85$ .

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2. Mode - Grouped frequency distribution