Age
3
4
5
6
7
8
9
10
No. of children
2
6
5
x
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.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
Mean = \(\frac{\sum fx}{ \sum f}\) = (3x2) +(4x6) + (5x5) + (6x) + (7x6) + (8x9) + (9x8) + (10x5) \div (2 + 6 + 5 + x + 6 + 9 + 8 + 5)
7 = (291 + 6x) \div (41+x)
7(41+x) = 291 + 6x
287 + 7x = 291 + 6x
x = 4
(b)
Age(x in yrs)
No.of child
Fx\(^2\)
3
2
18
4
6
96
5
5
125
6
4
144
7
6
294
8
9
576
9
8
648
10
5
500
Σf = 45
Σfx\(^2\) = 2401
Standard deviation = \(\sqrt \frac{196}{45} = \sqrt 4.3555\)
= 2.087
Source: Myschool Past Questions Archive (Record #65868)