The number of boys and girls in different grades of a school are shown in the table below. Pick the appropriate scatter plot for the data.
| Grades | Boys | Girls |
|---|---|---|
| 8th | 20 | 25 |
| 9th | 30 | 28 |
| 10th | 40 | 35 |
| 11th | 60 | 45 |
| 12th | 80 | 65 |
Answer (2)
The problem involves analyzing data from a table to determine the relationship between the number of boys and girls in different grades.
The data points are (20, 25), (30, 28), (40, 35), (60, 45), and (80, 65).
The scatter plot should show a positive correlation, indicating that as the number of boys increases, the number of girls also increases.
The points should roughly follow a linear pattern, suggesting a linear relationship between the two variables. The appropriate scatter plot will show this positive, roughly linear relationship.
Explanation
Understanding the Data We are given a table showing the number of boys and girls in different grades of a school. Our goal is to pick the appropriate scatter plot for the data. The data points are (20, 25), (30, 28), (40, 35), (60, 45), and (80, 65). We need to plot these points on a scatter plot and observe the relationship between the number of boys and girls.
Analyzing the Relationship Let's analyze the data points. As the number of boys increases, the number of girls also tends to increase. This suggests a positive correlation between the number of boys and the number of girls. The points seem to follow a roughly linear pattern.
Visualizing the Scatter Plot To visualize this, we can imagine a scatter plot with the number of boys on the x-axis and the number of girls on the y-axis. The points would be plotted as follows:
(20, 25)
(30, 28)
(40, 35)
(60, 45)
(80, 65)
These points would form a scatter plot that shows a positive, roughly linear relationship.
Conclusion Based on the data, the scatter plot should show a positive correlation between the number of boys and girls. As the number of boys increases, the number of girls also increases. The points should roughly follow a straight line.
Examples
Scatter plots are useful for visualizing relationships between two variables. For example, you could use a scatter plot to see if there's a relationship between the number of hours you study and your exam scores. If you plot the data and see a positive trend, it suggests that studying more hours tends to lead to higher scores. This can help you make informed decisions about how to allocate your study time.
The scatter plot will show a positive correlation between the number of boys and girls in different grades. As the number of boys increases, the number of girls also tends to increase, reflecting a roughly linear relationship. The data points can be plotted with boys on the x-axis and girls on the y-axis, demonstrating this relationship visually.
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