Math Problem Statement

The following table gives the average number of hours 7 junior high students were left unsupervised each day and their corresponding overall grade averages.

Hours Unsupervised 0 2.5 3 4 4.5 5 5.5 Overall Grades 100 96 84 80 76 68 64

Draw a scatter plot of the given data.

Solution

To draw the scatter plot of the data provided, we can plot the hours unsupervised on the x-axis and the corresponding overall grades on the y-axis. The points for each pair (Hours Unsupervised, Overall Grades) will represent a coordinate on the plot.

Here is the data:

Hours UnsupervisedOverall Grades
0100
2.596
384
480
4.576
568
5.564

Let me now generate the scatter plot for you. matplotlib.pyplot as plt

Data for the scatter plot

hours_unsupervised = [0, 2.5, 3, 4, 4.5, 5, 5.5] overall_grades = [100, 96, 84, 80, 76, 68, 64]

Create the scatter plot

plt.figure(figsize=(8, 6)) plt.scatter(hours_unsupervised, overall_grades, color='blue', label='Data points')

Adding labels and title

plt.title('Scatter Plot of Hours Unsupervised vs. Overall Grades') plt.xlabel('Hours Unsupervised') plt.ylabel('Overall Grades') plt.grid(True) plt.xticks([0, 1, 2, 3, 4, 5, 5.5], rotation=45) # Adjusting x-ticks for clarity plt.yticks(range(60, 101, 10)) # Adjusting y-ticks for clarity

Show plot

plt.show()Here is the scatter plot showing the relationship between the hours unsupervised and the overall grades. The x-axis represents the number of hours the students were unsupervised, and the y-axis represents their corresponding overall grades.

Would you like to dive deeper into this data, such as analyzing the trend, or would you like further assistance with another concept?

Additional questions:

  1. What is the trend or correlation between the number of hours unsupervised and overall grades?
  2. How can we calculate the line of best fit for this data?
  3. What does the scatter plot suggest about the impact of unsupervised hours on grades?
  4. Can we determine a predictive equation for the overall grades based on unsupervised hours?
  5. What would happen to the grades if the number of unsupervised hours increased even further?

Tip: Scatter plots are a great way to visualize correlations between two variables, but to quantify this relationship, you can use statistical methods like finding the correlation coefficient or fitting a regression model.

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Math Problem Analysis

Mathematical Concepts

Statistics
Data Visualization
Scatter Plots
Correlation

Formulas

Scatter plot visualization
Trend analysis (correlation coefficient)
Line of best fit equation

Theorems

Linear regression
Correlation coefficient interpretation

Suitable Grade Level

Grades 7-9