Calculate the mode for the following frequency distribution:

# Calculate the mode for the following frequency distribution:

1. A
32
2. B
34.65
3. C
32.23
4. D
33.33

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### Solution:

The following frequency distribution is given:
Here, the maximum frequency is 45 and the class interval corresponding to this frequency is $30-40$.
So, the modal class is $30-40$.
Therefore, .
We know that mode is said to be the value of data which appears most in the given data.

In the formula, l will be the lower limit of  modal class. h will be the size of  class intervals. ${f}_{0}$ will be frequency of modal class, ${f}_{1}$  will be frequency of preceding modal class, ${f}_{2}$  will be the frequency of succeeding modal class.

$⇒\mathit{Mode}=30+\left(\frac{10}{30}\right)×10$
$⇒\mathit{Mode}=30+3.33$
$⇒\mathit{Mode}=33.33$
Considering the circumstances stated above, the mode of the frequency is 33.33.
Hence, option 4 is correct.

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