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Find the mode of the following distribution.
Class-interval: | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 | 35-40 |
Frequency: | 30 | 45 | 75 | 35 | 25 | 15 |
To do:
We have to find the mode of the given distribution.
Solution:
The frequency of the given data is as given below:
Class-interval($x_i$): | Frequency$(f_i$): |
10-15 | 30 |
15-20 | 45 |
20-25 | 75 |
25-30 | 35 |
30-35 | 25 |
35-40 | 15 |
We observe that the class interval of 20-25 has the maximum frequency(75).
Therefore, it is the modal class.
Here,
$l=20, h=5, f=75, f_1=45, f_2=35$
We know that,
Mode $=l+\frac{f-f_1}{2 f-f_1-f_2} \times h$
$=20+\frac{75-45}{2 \times 75-45-35} \times 5$
$=20+\frac{30}{150-80} \times 5$
$=20+\frac{150}{70}$
$=20+2.14$
$=22.14$
Hence, the mode of the given distribution is 22.14.
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