## The table shows the distribution of ages of a number of children in a school. If the mean of the distribution is 7, find the; (a) value of x, (b) standard deviation of their ages.

Age 3 4 5 6 7 8 9 10

No. of children 2 6 5 4 6 9 8 5

The table shows the distribution of ages of a number of children in a school. If the mean of the distribution is 7, find the;

(a) value of x, (b) standard deviation of their ages.

Solution & Explanation

Mean = (3Ã—2 +4Ã—6 + 5Ã—5 + 6x + 7Ã—6 + 8Ã—9 + 9Ã—8 + 10Ã—5) Ã· (2 + 6 + 5 + x + 6 + 9 + 8 + 5)

7 = (291 + 6x) Ã· (41+x)

7(41+x) = 291 + 6x

287 + 7x = 291 + 6x

x = 4

(b)

Age(x in yrs) No.of child Fx2

3 2 18

4 6 96

5 5 125

6 4 144

7 6 294

8 9 576

9 8 648

10 5 500

Î£f = 45 Î£fx2 = 2401

Standard deviation = âˆš196/45 = âˆš4.3555

= 2.087