WAEC Mathematics 2015 Paper

Concept:For an even number of ordered data values, the third quartile is the median of the upper half of the data.Explanation:The scores are already arranged in ascending order from $44$ to $75$.There are $n = 20$ scores.First find the median position: $\frac{n}{2} = 10$.The median lies between the 10th and 11th values, so the upper half contains the 11th to 20th scores.The upper half is: $58, 59, 60, 61, 63, 65, 67, 70, 73, 75$.The third quartile $Q_3$ is the median of this upper half.Since there are 10 values in the upper half, take the average of the 5th and 6th values: $63$ and $65$.$Q_3 = \frac{63 + 65}{2} = \frac{128}{2} = 64$.Answer:$Q_3 = 64$, which is option C.