Calculate the value of mode for the following frequency distribution:

# Calculate the value of mode for the following frequency distribution:

1. A
24.4
2. B
24.5
3. C
24.6
4. D
24.7

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### Solution:

Here, the classes are not in the inclusive form. So, we first convert them in inclusive form by subtracting $\frac{h}{2}$ from the lower limit and adding $\frac{h}{2}$ to the upper limit of each class, where h is the difference between the lower limit of a class and the upper limit of the preceding class.
To find the modal class, we use the grouping method:
Since 24.5−28.5 has the maximum numbers of bars. So, 24.5−28.5 is the modal class.

l=24.5,h=4,f=14,${f}_{1}$​=14,${f}_{2}$​=15
Then, Mode=$\left(l+\frac{f-{f}_{1}}{2f-{f}_{1}-{f}_{2}}\right)×h$
Putting the values, $\left(24.5+\frac{14-14}{28-14-15}\right)×4$
Mode=24.5+0 = 24.5
Hence (2) is the correct option.

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