Question
Number of Students versus Average Test Grade
The table shows how the number of students and their respective average test scores on an eighth-grade math exam relate to one another.
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 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.
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 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.
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.
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The table shows how the number of students and their respective average test scores on an eighth-grade math exam relate to one another.
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 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.
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 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.
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.
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Answers
GPT-4o mini
To determine which scatterplot correctly represents the given data, let's list the data points based on the table:
| Number of Students | Average Test Grade |
|--------------------|--------------------|
| 24 | 78 |
| 4 | 98 |
| 3 | 50 |
| 7 | 42 |
| 18 | 86 |
| 26 | 92 |
| 14 | 90 |
| 16 | 87 |
| 4 | 61 |
Data points derived from this table are:
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. Two different grades for 4 students which are (4, 98) and (4, 61).
Now let's compare the data points listed above with the described options for the scatterplots:
1. **First option**: This includes the points (3, 50), (4, 61), (4, 98), (7, 42), (14, 90), (16, 87), (18, 86), (24, 78), (26, 92) which matches correctly.
2. **Second option**: This does not match because it swaps x and y.
3. **Third option**: The point (6, 61) is incorrect as the data points only have (4, 61).
4. **Fourth option**: The point (10, 90) is wrong as it does not exist in the data table.
5. **Fifth option**: Similar to before, the point (20, 92) is incorrect.
Based on the analysis, the correct scatterplot is the **first option**, which includes all the relevant data points appropriately.
| Number of Students | Average Test Grade |
|--------------------|--------------------|
| 24 | 78 |
| 4 | 98 |
| 3 | 50 |
| 7 | 42 |
| 18 | 86 |
| 26 | 92 |
| 14 | 90 |
| 16 | 87 |
| 4 | 61 |
Data points derived from this table are:
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. Two different grades for 4 students which are (4, 98) and (4, 61).
Now let's compare the data points listed above with the described options for the scatterplots:
1. **First option**: This includes the points (3, 50), (4, 61), (4, 98), (7, 42), (14, 90), (16, 87), (18, 86), (24, 78), (26, 92) which matches correctly.
2. **Second option**: This does not match because it swaps x and y.
3. **Third option**: The point (6, 61) is incorrect as the data points only have (4, 61).
4. **Fourth option**: The point (10, 90) is wrong as it does not exist in the data table.
5. **Fifth option**: Similar to before, the point (20, 92) is incorrect.
Based on the analysis, the correct scatterplot is the **first option**, which includes all the relevant data points appropriately.