The age distribution of 40 children is as follows Age in years 5 6 6 7 7 8 8 9 9 10 10 11 Number of ...........

Quantitative Aptitude (CDS) Average

The age distribution of 40 children is as follows

Age(in years)	5-6	6-7	7-8	8-9	9-10	10-11
Number of children	4	7	9	12	6	2

Consider the following statements in respect of the above frequency distribution

1. The median of the age distribution is 7 yr.

2. 70% of the children are in the age group 6-9 yr.

3. The modal age of the children is 8 yr.

Which of the above statements are correct?

1 and 2

2 and 3

1 and 3

1,2 and 3

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Explanation:

1. Here, N = 40/2= 20
Thus, 7-8 is the median class.
l = 7,f = 9 ,cf= 11,N/2 = 20 and h = 1
Median = $l+\frac{\frac{N}{2}-cf}{f}\times h=7+\frac{20-11}{9}\times 1$
=7+1=8 yr
Hence, Statement 1 is incorrect.
2. Total number of children (N) = 40
Number of children in the age group 6-9
= 7 + 9 + 12 = 28
Required percentage = 28/40×100%= 70%
Hence, Statement 2 is correct.
3. Modal group = 8-9
Modal age = 8 yr
Since, 9 is not included in this group.
Hence, Statement 3 is correct.