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detailed solution

Correct option is A

For the modal class, let us the consider the class interval with highest frequency

Here, the greatest frequency = 23, so the modal class = 35 – 45,

l = 35,

class width (h) = 10,

fm = 23,

f1 = 21 and f2 = 14

The formula to find the mode is

Mode = l+ [$\frac{\left({f}_{m}-{f}_{1}\right)}{2{f}_{m}-{f}_{1}-{f}_{2}}$]×h

Substitute the values in the formula, we get

Mode = 35+[$\frac{\left(23-21\right)}{46-21-14}$]×10

Mode = 35+($\frac{20}{11}$) = 35+1.8

Mode = 36.8 year

So the mode of the given data = 36.8 year

Calculation of Mean:

First find the midpoint using the formula, xi

The mean formula is

Mean = x̄ =

$\frac{2830}{80}$

= 35.37 years

Therefore, the mean of the given data = 35.37 years

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detailed solution

For the modal class, let us the consider the class interval with highest frequency

Here, the greatest frequency = 23, so the modal class = 35 – 45,

l = 35,

class width (h) = 10,

fm = 23,

f1 = 21 and f2 = 14

The formula to find the mode is

Mode = l+ [$\frac{\left({f}_{m}-{f}_{1}\right)}{2{f}_{m}-{f}_{1}-{f}_{2}}$]×h

Substitute the values in the formula, we get

Mode = 35+[$\frac{\left(23-21\right)}{46-21-14}$]×10

Mode = 35+($\frac{20}{11}$) = 35+1.8

Mode = 36.8 year

So the mode of the given data = 36.8 year

Calculation of Mean:

First find the midpoint using the formula, xi

The mean formula is

Mean = x̄ =

$\frac{2830}{80}$

= 35.37 years

Therefore, the mean of the given data = 35.37 years

+91

Are you a Sri Chaitanya student?