Question

7. The table shows the ages of 20 children in a household. Given that x:y = 1:2, find:
(a) values of x and y;
(b) mean age of the children.

Accepted Answer

Frequencies: Age5:2, Age6:(2x−1), Age7:(y+2), Age8:4, Age9:2, Age10:(y−1). Total=20.
2+(2x−1)+(y+2)+4+2+(y−1)=20
8+2x+2y=20 → 2x+2y=12 → x+y=6.
Given y=2x: x+2x=6 → 3x=6 → x=2, y=4. (Check ratio x:y=2:4=1:2 ✓)

Frequencies become: Age5:2, Age6:2(2)−1=3, Age7:4+2=6, Age8:4, Age9:2, Age10:4−1=3. Sum=2+3+6+4+2+3=20 ✓.

(a) x=2, y=4.
(b) Mean age = Σ(age×freq)/Σfreq = (5×2+6×3+7×6+8×4+9×2+10×3)/20 = (10+18+42+32+18+30)/20 = 150/20 = 7.5 years.

NABTEB Mathematics 2024 Theory — Question 7

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