Question

alicia records the total number of points scored in two games by 10 players on her basketball team.
28, 13, 4, 8, 15, 10, 22, 7, 11, 15
which box plot represents the data?

Explanation:

Step1: Order the data

First, we order the data set: \(4, 7, 8, 10, 11, 13, 15, 15, 22, 28\)

Step2: Find the minimum, Q1, median, Q3, maximum

• Minimum: The smallest value is \(4\).
• Q1 (First Quartile): The median of the lower half (\(4, 7, 8, 10, 11\)). The median of this set is \(8\).
• Median (Second Quartile): The middle value of the ordered data. Since there are 10 values, the median is the average of the 5th and 6th values: \(\frac{11 + 13}{2}=12\)
• Q3 (Third Quartile): The median of the upper half (\(13, 15, 15, 22, 28\)). The median of this set is \(15\).
• Maximum: The largest value is \(28\).

So the five - number summary is minimum \( = 4\), Q1 \( = 8\), median \( = 12\), Q3 \( = 15\), maximum \( = 28\). Looking at the box - plots, the first box - plot has minimum \( = 4\), Q1 \( = 8\), median \( = 12\), Q3 \( = 15\), maximum \( = 28\) which matches our calculated five - number summary.

Answer:

The first box - plot (the one with the five - number summary \(4, 8, 12, 15, 28\) and the number line from \(0\) to \(32\) with the box between \(8\) and \(15\) and the median line at \(12\))