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Book Free DemoThe 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.