The age distribution of 40 children is as follows

Age (in yr.)	5 - 6	6 - 7	7 - 8	8 - 9	9 - 10	10 - 11
No. of children	4	7	9	12	6	2

Consider the following statements in respect of the above frequency distribution.

(A) The median of the age distribution is 7 yr.

(B) 70% of the children are in the age group 6-9 yr.

(C) The modal class of the children is 8-9 yr.

Which of the above statements are true?

Choose the correct answer from the options given below:

The age distribution has 40 children total.

Age Group	Children	Running Total
5-6	4	4
6-7	7	11
7-8	9	20
8-9	12	32
9-10	6	38
10-11	2	40

---

For Statement A, the median position with 40 children is at the average of the 20th and 21st child.

From the running totals, the first 20 children end at age group 7-8, and the 21st child is in age group 8-9.

The median class is 8-9 years.

Using the median formula for grouped data:

Median $= L + \dfrac{(n/2 - CF)}{f} \times h$

Where:

$L = 8$ (lower limit of median class)

$n/2 = 40/2 = 20$

$CF = 20$ (cumulative frequency before median class)

$f = 12$ (frequency of median class)

$h = 1$ (class width)

Median $= 8 + \dfrac{(20 - 20)}{12} \times 1$

Median $= 8 + 0$

Median $= 8$ years

Statement A is false since the median is 8 years, not 7 years.

---

For Statement B, counting children in the age group 6-9 years:

Age 6-7: 7 children

Age 7-8: 9 children

Age 8-9: 12 children

Total $= 7 + 9 + 12 = 28$ children

Percentage $= \dfrac{28}{40} \times 100$

Percentage $= 70\%$

Statement B is true.

---

For Statement C, the modal class is the age group with the highest frequency.

Frequencies: 5-6 has 4, 6-7 has 7, 7-8 has 9, 8-9 has 12, 9-10 has 6, 10-11 has 2

The highest frequency is 12 in the age group 8-9 years.

Statement C is true.

---

Only statements B and C are true.

The correct answer is option 2.