Question

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

Answer 1

SOLUTION :  

For Group A :  

Here the maximum frequency is 78, and the class corresponding to this frequency is 18 – 20.  So the  modal class is 18 – 20.

Here, l = 18, h = 20 – 18 = 2, f1 = 78, f0 = 50, f2 = 46

Mode = l + [(f1- f0) / (2f1- f0 - f2)] ×h

= 18 + [(78–50) / (2 × 78–50–46)] ×2

= 18 + [(28) / (156 - 96)]× 2  

= 18 + 56/ 60

= 18 + 0.93

= 18.93 years

For group B :  

Here the maximum frequency is 89, and the class corresponding to this frequency is 18 – 20 So the  modal class is 18 - 20 .

Here, l = 18, h = 20 – 18 = 2, f1 = 89, f0 = 54, f2 = 40

Mode = l + [(f1- f0) / (2f1- f0 - f2)] ×h

= 18 + [(89–54)/(2 × 89–54–40)]×2

= 18 + [(35)/(178 - 94)] × 2

= 18 + [ (35 × 2)/ 84]  

= 18 + 70/ 84

= 18+ 0.83

= 18.83 years

Hence , the modal age for the Group A is 18.93 years and that for Group B is 18.83 years . The modal age of group A is higher than of group B.

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Answer 2

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