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: \(4, 7, 8, 10, 11, 13, 15, 15, 22, 28\) (wait, original data is \(28, 13, 4, 8, 15, 10, 22, 7, 11, 15\), so ordering gives \(4, 7, 8, 10, 11, 13, 15, 15, 22, 28\))

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

• Minimum (\( \text{min} \)): \(4\)
• To find the median (middle value for even number of data points, average of 5th and 6th terms):
• 5th term: \(11\), 6th term: \(13\), so median \(= \frac{11 + 13}{2} = 12\)
• Q1 (median of lower half: \(4, 7, 8, 10, 11\)): middle term is \(8\)
• Q3 (median of upper half: \(13, 15, 15, 22, 28\)): middle term is \(15\)
• Maximum (\( \text{max} \)): \(28\)

Now, let's analyze the box - plots:

• The box plot should have: minimum \( = 4\), Q1 \( = 8\), median \( = 12\), Q3 \( = 15\), maximum \( = 28\)

Looking at the first box - plot:

• The whiskers start at \(4\) (min), the box starts at \(8\) (Q1), the line inside the box is at \(12\) (median), the box ends at \(15\) (Q3), and the whisker ends at \(28\) (max). This matches our calculated values.

Answer:

The first box - plot (the one with minimum at 4, Q1 at 8, median at 12, Q3 at 15, and maximum at 28) represents the data.