| 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.
Explanation
(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.