Question

In the following frequency distribution, height of 20 students of a class is given. From the given data find the mean. 160 161 162 163 Height (cm) Number of boys 4, 6 ,5 ,5,​

Answer 1

Answer:

Heights No. of students

159.5−162.5 15

162.5−165.5 118

165.5−168.5 142

168.5−171.5 127

171.5−174.5 18

Here, the maximum frequency is 142, then the corresponding class 165.5−168.5 is the modal class.

We know,

Mode=l+

2f−f

1

−f

2

f−f

1

×h

l= lower limit of the modal class

h= size of the class intervals

f= frequency of the modal class

f

1

= frequency of the class preceding the modal class

f

2

= frequency of the class succeed in the modal class.

⇒ l=165.5,h=168.5−165.5=3,f=142,f

1

=118,f

2

=127

⇒ Mode=165.5+

2×142−118−127

142−118

×3

⇒ Mode=165.5+

39

72

⇒ Mode=165.5+1.85=167.35cm