The box-and-whisker plot below represents a data set: $2,4,5,7,8,9,10$. What is the value of the upper quartile ($Q_3$)?

• A. $10$
• B. $9$
• C. $8$
• D. $7$

Answer: (B)

Verified step by step guidance

1. First, arrange the data set in ascending order, which is already given as: 2, 4, 5, 7, 8, 9, 10.
2. Identify the median (Q2) of the data set. Since there are 7 data points, the median is the middle value, which is the 4th number in the ordered list.
3. To find the upper quartile (Q3), focus on the upper half of the data, which consists of the numbers greater than the median. This subset includes the 5th, 6th, and 7th values.
4. Find the median of this upper half subset. The median of these three numbers will be the upper quartile (Q3).
5. Express the calculation of Q3 as the median of the upper half: \(Q3 = \text{median}(8, 9, 10)\).