In a cumulative frequency graph, the lower quartile is 18 years while the 60th percentile is 48 years. What…

Analyze the question

We need the percentage of the distribution that is either at most 18 years or greater than 48 years.

Concept

• The lower quartile (Q₁) is the 25th percentile, so 25% of the data is at or below 18 years.
• The 60th percentile means 60% of the data is at or below 48 years. So the percentage above 48 years is 100% − 60% = 40%.

Solution

• At most 18 years: 25%
• Greater than 48 years: 100% − 60% = 40%

The two groups do not overlap (18 is less than 48), so we add them:

25% + 40% = 65%

Answer: C (65%)

Tip: Remember these conversions: Q₁ = 25th percentile, Q₂ (median) = 50th percentile, Q₃ = 75th percentile. For "at most a or greater than b" questions, find the part below a and the part above b separately, then add them, provided the ranges don't overlap. Alternatively, find the middle part (between 18 and 48), which is 60% − 25% = 35%, and subtract from 100%: 100% − 35% = 65%. Option B (35%) is the trap, because it is the percentage between 18 and 48 years.