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?
four box plot options are shown, each with a number line from 0 to 32 and different box and whisker configurations. the first box plot has key points 4, 8, 13, 15, 28; the second has 4, 8, 12, 15, 28; the third has 4, 7, 12, 22, 28; the fourth has 4, 7, 11, 15, 28.

Explanation:

Step1: Order the data

First, we order the given data set: \(4, 7, 8, 10, 11, 13, 15, 15, 22, 28\) (wait, wait, original data is 28,13,4,8,15,10,22,7,11,15 – let's re - order correctly: \(4, 7, 8, 10, 11, 13, 15, 15, 22, 28\)? Wait, no, the number of data points: 28,13,4,8,15,10,22,7,11,15 – that's 10 numbers. Let's sort them: \(4, 7, 8, 10, 11, 13, 15, 15, 22, 28\)? Wait, no, 4,7,8,10,11,13,15,15,22,28? Wait, 10 numbers: 4,7,8,10,11,13,15,15,22,28. Wait, no, the original data: 28,13,4,8,15,10,22,7,11,15. Let's list them in order: 4,7,8,10,11,13,15,15,22,28. Wait, no, 10 numbers: positions 1 - 10.

Step2: Find the five - number summary

• Minimum: The smallest number is \(4\).
• Maximum: The largest number is \(28\).
• Median (Q2): Since there are 10 data points (even number), the median is the average of the 5th and 6th values. The 5th value is \(11\), the 6th value is \(13\). So median \(=\frac{11 + 13}{2}=12\)? Wait, no, wait the sorted data: 4,7,8,10,11,13,15,15,22,28. Wait, 5th term: 11, 6th term:13. So median \(=\frac{11 + 13}{2}=12\)? Wait, no, maybe I made a mistake in sorting. Wait original data: 28,13,4,8,15,10,22,7,11,15. Let's sort again: 4,7,8,10,11,13,15,15,22,28. Yes, that's correct. So 5th is 11, 6th is 13. Median is \((11 + 13)/2 = 12\).

• Q1 (First Quartile): The median of the lower half. The lower half is the first 5 numbers: 4,7,8,10,11. The median of these 5 numbers is the 3rd value, which is \(8\).

• Q3 (Third Quartile): The median of the upper half. The upper half is the last 5 numbers:13,15,15,22,28. The median of these 5 numbers is the 3rd value, which is \(15\).

So the five - number summary is: Minimum \(= 4\), Q1 \(= 8\), Median \(= 12\), Q3 \(= 15\), Maximum \(= 28\).

Now let's check the box - plots. The box - plot has the minimum, Q1, median, Q3, maximum marked. Looking at the options, the second box - plot (top right) has minimum 4, Q1 = 8, median = 12, Q3 = 15, maximum = 28.

Answer:

The second box - plot (the one in the top right with 4, 8, 12, 15, 28 marked)