Exploring Scatter Plots for Mathematical Relationships
Scatter plots are a powerful tool for visualizing the relationship between two sets of numerical data. When you want to see if there is a connection or pattern between two variables—such as height and weight, or a number and its square—a scatter plot can help you quickly spot trends, clusters, or outliers. By plotting each pair of values as a point on the graph, you can easily identify whether the variables move together in a predictable way, which is known as correlation.
1234567891011import matplotlib.pyplot as plt # Create two related lists: x values and their squares x = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] y = [i**2 for i in x] plt.scatter(x, y) plt.xlabel("x value") plt.ylabel("x squared") plt.title("Scatter Plot of x vs x squared") plt.show()
When you look at a scatter plot, the arrangement of the points tells you about the mathematical relationship between the two variables. If the points form a straight line, this suggests a linear relationship. If they curve upward or downward, the relationship might be quadratic or another type of function. Randomly scattered points with no pattern indicate little or no correlation. Patterns in scatter plots can help you decide which mathematical model or equation best describes the data.
123456789101112import matplotlib.pyplot as plt # x values and their squares x = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] y = [i**2 for i in x] plt.scatter(x, y, color="green", marker="^", label="x squared") plt.xlabel("x value") plt.ylabel("x squared") plt.title("Customized Scatter Plot of x vs x squared") plt.legend() plt.show()
1. What does each point in a scatter plot represent?
2. How can you add a legend to a matplotlib plot?
3. Fill in the blank: To create a scatter plot, use plt.scatter(x, _ _ _ ).
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Scatter plots are a powerful tool for visualizing the relationship between two sets of numerical data. When you want to see if there is a connection or pattern between two variables—such as height and weight, or a number and its square—a scatter plot can help you quickly spot trends, clusters, or outliers. By plotting each pair of values as a point on the graph, you can easily identify whether the variables move together in a predictable way, which is known as correlation.
1234567891011import matplotlib.pyplot as plt # Create two related lists: x values and their squares x = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] y = [i**2 for i in x] plt.scatter(x, y) plt.xlabel("x value") plt.ylabel("x squared") plt.title("Scatter Plot of x vs x squared") plt.show()
When you look at a scatter plot, the arrangement of the points tells you about the mathematical relationship between the two variables. If the points form a straight line, this suggests a linear relationship. If they curve upward or downward, the relationship might be quadratic or another type of function. Randomly scattered points with no pattern indicate little or no correlation. Patterns in scatter plots can help you decide which mathematical model or equation best describes the data.
123456789101112import matplotlib.pyplot as plt # x values and their squares x = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] y = [i**2 for i in x] plt.scatter(x, y, color="green", marker="^", label="x squared") plt.xlabel("x value") plt.ylabel("x squared") plt.title("Customized Scatter Plot of x vs x squared") plt.legend() plt.show()
1. What does each point in a scatter plot represent?
2. How can you add a legend to a matplotlib plot?
3. Fill in the blank: To create a scatter plot, use plt.scatter(x, _ _ _ ).
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