AGE
5
6
7
8
9
10
FREQUENCY
2
2x - 1
y + 2
4
2
y - 1
The table shows the ages of 20 children in a household.
Given that x: y = 1: 2
(a) values of x and y
(b) mean ages of the children.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a)
Age
Frequency
5
2
6
2x - 1
7
y + 2
8
4
9
2
10
y - 1
\(\sum\)f = 20
2 + 2x - 1 + y + 2 + 4 +2 + y - 1 = 20
2x + 2y + 8 = 20
2x + 2y = 20 - 8 = 12
divide through by 2
x + y = 6 - - - - - - - - - - - - - -(i)
Also, \(\frac{\text{x}}{\text{y}}\) = \(\frac{1}{2}\)
y = 2x - - - - - - - - - - - - (ii)
put y = 2x into eqn -- - - -(i)
x + y = 6 = x + 2x = 6
3x = 6
x = 2
put x = 2 into eqn - - - - - (ii)
y = 2x = 2(2) = 4
(b)
AGE
Frequency
F
Fx
5
2
2
10
6
2(2) - 1 = 3
3
18
7
4 + 2 = 6
6
42
8
4
4
32
9
2
2
18
10
4 - 1 = 3
3
30
\(\sum\) f = 20, \(\sum\)fx = 150
Mean,\(\overline{x}\) = \(\frac{\sum fx}{\sum f}\) = \(\frac{150}{20}\) = 7.5
THEREFORE, mean age = 7.5 years.
Source: Myschool Past Questions Archive (Record #71947)