On the sports day of a school, 300 students participated. Their ages are given in the following distribution:Find the mean and mode of the data.

# On the sports day of a school, 300 students participated. Their ages are given in the following distribution:Find the mean and mode of the data.

1. A
11.72 years and 11.25 years
2. B
10.66 years and 11.95 years
3. C
10.95 years and 11.66 years
4. D
11.66 years and 10.95 years

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### Solution:

The following data is given:
We know that the mean is given as,

In the formula, A is the  assumed mean, is the frequency of class, is the deviation of class, ${x}_{i}$ = class mark = , ${u}_{i}=\frac{{x}_{i}-A}{h}$  , Total number of observations.
And the mode is given as,

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.
Consider the following table:
The mean of the data with and maximum frequency 95 will be,

$⇒\mathit{Mean}=12+\left(\frac{-201}{300}\right)×2$

Now, from the above table modal class $=11-13$ as the maximum frequency is 95.
So,

The mean and mode of the data is 10.66 years and 11.96 years respectively.
Hence, option 2 is correct.

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