Compare the modal ages of two groups of students appearing for an entrance test:

Age (in years):	16-18	18-20	20-22	22-24	24-26
Group A:	50	78	46	28	23
Group B:	54	89	40	25	17

Given:

The ages of two groups of students appearing for an entrance test

To do:

We have to compare the modal ages of the two groups.

Solution:

For Group A:

The frequency of the given data is as given below.

We observe that the class interval of 18-20 has the maximum frequency(78).

Therefore, it is the modal class.

Here,

$l=18, h=2, f=78, f_1=50, f_2=46$

We know that,

Mode $=l+\frac{f-f_1}{2 f-f_1-f_2} \times h$

$=18+\frac{78-50}{2 \times 78-50-46} \times 2$

$=18+\frac{28}{156-96} \times 2$

$=18+\frac{56}{60}$

$=18+0.93$

$=18.93$

The modal age of Group A is 18.93 years.

For Group B:

The frequency of the given data is as given below.

We observe that the class interval of 18-20 has the maximum frequency(89).

Therefore, it is the modal class.

Here,

$l=18, h=2, f=89, f_1=54, f_2=40$

We know that,

Mode $=l+\frac{f-f_1}{2 f-f_1-f_2} \times h$

$=18+\frac{89-54}{2 \times 89-54-40} \times 2$

$=18+\frac{35}{178-94} \times 2$

$=18+\frac{70}{84}$

$=18+0.83$

$=18.83$

The modal age of Group B is 18.83 years.

Hence, the modal ages of groups A and B are 18.93 years and 18.83 years respectively.    

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Updated on: 10-Oct-2022

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