Use the table to answer the question.

Question

Number of Students versus Average Test Grade

Number of Students 24 4 3 7 18 26 14 16 4
Grade 78 98 50 42 86 92 90 87 61
A math teacher kept track of his students' grades on the last 8th-grade math exam. Which scatterplot represents the data?

(1 point)
Responses

A coordinate graph is titled: Number of Students versus Average Test Grade. It shows number of students on the x-axis from 0 to 26 in increments of 2 and grade on the y-axis from 0 to 100 in increments of 5.
The approximate data points are left parenthesis 3 comma 50 right parenthesis, left parenthesis 4 comma 61 right parenthesis, left parenthesis 4 comma 98 right parenthesis, left parenthesis 7 comma 42 right parenthesis, left parenthesis 14 comma 90 right parenthesis, left parenthesis 16 comma 87 right parenthesis, left parenthesis 18 comma 86 right parenthesis, left parenthesis 24 comma 78 right parenthesis, and left parenthesis 26 comma 92 right parenthesis.
Image with alt text: A coordinate graph is titled: Number of Students versus Average Test Grade. It shows number of students on the x-axis from 0 to 26 in increments of 2 and grade on the y-axis from 0 to 100 in increments of 5. The approximate data points are left parenthesis 3 comma 50 right parenthesis, left parenthesis 4 comma 61 right parenthesis, left parenthesis 4 comma 98 right parenthesis, left parenthesis 7 comma 42 right parenthesis, left parenthesis 14 comma 90 right parenthesis, left parenthesis 16 comma 87 right parenthesis, left parenthesis 18 comma 86 right parenthesis, left parenthesis 24 comma 78 right parenthesis, and left parenthesis 26 comma 92 right parenthesis.

A coordinate graph is titled: Number of Students versus Average Test Grade. It shows grade from 0 to 100 on the x-axis and number of students on the y-axis from 0 to 26.
The approximate data points are left parenthesis 78 comma 24 right parenthesis, left parenthesis 98 comma 4 right parenthesis, left parenthesis 50 comma 3 right parenthesis, left parenthesis 42 comma 7 right parenthesis, left parenthesis 86 comma 18 right parenthesis, left parenthesis 92 comma 26 right parenthesis, left parenthesis 90 comma 14 right parenthesis, left parenthesis 87 comma 10 right parenthesis, and left parenthesis 61 comma 6 right parenthesis.
Image with alt text: A coordinate graph is titled: Number of Students versus Average Test Grade. It shows grade from 0 to 100 on the x-axis and number of students on the y-axis from 0 to 26. The approximate data points are left parenthesis 78 comma 24 right parenthesis, left parenthesis 98 comma 4 right parenthesis, left parenthesis 50 comma 3 right parenthesis, left parenthesis 42 comma 7 right parenthesis, left parenthesis 86 comma 18 right parenthesis, left parenthesis 92 comma 26 right parenthesis, left parenthesis 90 comma 14 right parenthesis, left parenthesis 87 comma 10 right parenthesis, and left parenthesis 61 comma 6 right parenthesis.

A coordinate graph is titled: Number of Students versus Average Test Grade. It shows number of students on the x-axis from 0 to 26 in increments of 2 and grade on the y-axis from 0 to 100 in increments of 5.
The approximate data points are left parenthesis 3 comma 50 right parenthesis, left parenthesis 4 comma 61 right parenthesis, left parenthesis 4 comma 98 right parenthesis, left parenthesis 7 comma 42 right parenthesis, left parenthesis 10 comma 90 right parenthesis, left parenthesis 16 comma 87 right parenthesis, left parenthesis 18 comma 86 right parenthesis, left parenthesis 20 comma 92 right parenthesis, and left parenthesis 24 comma 78 right parenthesis.
Image with alt text: A coordinate graph is titled: Number of Students versus Average Test Grade. It shows number of students on the x-axis from 0 to 26 in increments of 2 and grade on the y-axis from 0 to 100 in increments of 5. The approximate data points are left parenthesis 3 comma 50 right parenthesis, left parenthesis 4 comma 61 right parenthesis, left parenthesis 4 comma 98 right parenthesis, left parenthesis 7 comma 42 right parenthesis, left parenthesis 10 comma 90 right parenthesis, left parenthesis 16 comma 87 right parenthesis, left parenthesis 18 comma 86 right parenthesis, left parenthesis 20 comma 92 right parenthesis, and left parenthesis 24 comma 78 right parenthesis.

A coordinate graph is titled: Number of Students versus Average Test Grade. It shows number of students on the x-axis from 0 to 26 in increments of 2 and grade on the y-axis from 0 to 100 in increments of 5.
The approximate data points are left parenthesis 3 comma 50 right parenthesis, left parenthesis 4 comma 98 right parenthesis, left parenthesis 6 comma 61 right parenthesis, left parenthesis 7 comma 42 right parenthesis, left parenthesis 10 comma 87 right parenthesis, left parenthesis 14 comma 90 right parenthesis, left parenthesis 18 comma 86 right parenthesis, left parenthesis 24 comma 78 right parenthesis, and left parenthesis 26 comma 92 right parenthesis.

Answer 1

To determine which scatterplot corresponds to the data, we need to compare the provided data points against the options. Let's summarize the data points derived from your table:

1. \( (24, 78) \)
2. \( (4, 98) \)
3. \( (3, 50) \)
4. \( (7, 42) \)
5. \( (18, 86) \)
6. \( (26, 92) \)
7. \( (14, 90) \)
8. \( (16, 87) \)
9. \( (4, 61) \)

Now, let's check the options against the valid points from the data:

Valid points based on the provided data:

• \( (3, 50) \)
• \( (4, 61) \)
• \( (4, 98) \)
• \( (7, 42) \)
• \( (14, 90) \)
• \( (16, 87) \)
• \( (18, 86) \)
• \( (24, 78) \)
• \( (26, 92) \)

Analysis of options:

1. First option has:

   • \( (3, 50) \)
   • \( (4, 61) \)
   • \( (4, 98) \)
   • \( (7, 42) \)
   • \( (14, 90) \)
   • \( (16, 87) \)
   • \( (18, 86) \)
   • \( (24, 78) \)
   • \( (26, 92) \) The first option contains all the correct points from the data.

2. Second option has data points that are incorrect. This option swaps the axes, placing grades on the x-axis.

3. Third option has invalid data points, specifically it incorrectly includes \( (10, 90) \) and \( (20, 92) \), which do not exist.

4. Fourth option fails to correctly specify the data; likewise, it includes wrong points.

5. Fifth option is also incorrect, introducing \( (6, 61) \).

With this analysis, the first option is the correct representation of the data.

So the answer is the first scatterplot.