A sleep habits and student performance project uses real classroom data to explore whether students who sleep more tend to score higher on quizzes or tests. Students can anonymously survey classmates about average hours of sleep per night and compare those values with a recent score or grade range. The main display is a scatter plot with sleep on the x-axis and score on the y-axis.
This project matters because it connects health, school life, and data analysis in a way students can understand and investigate.
Key Facts
- Independent variable: average hours of sleep per night goes on the x-axis.
- Dependent variable: quiz or test score (%) goes on the y-axis.
- Correlation coefficient r ranges from -1 to 1, where values near 1 show a strong positive linear relationship.
- Line of best fit equation: y = mx + b, where m is the slope and b is the y-intercept.
- Slope formula for two points on a line: m = (y2 - y1) / (x2 - x1).
- Correlation does not prove causation, so sleep data alone cannot prove that more sleep directly caused higher scores.
Vocabulary
- Scatter plot
- A graph that shows paired data values as points on an x-y coordinate plane.
- Correlation
- A measure of how closely two variables are related and how they tend to change together.
- Line of best fit
- A straight line drawn through a scatter plot to model the general trend in the data.
- Outlier
- A data point that is far away from the overall pattern of the rest of the data.
- Anonymity
- A data collection method in which responses are not linked to student names or identities.
Common Mistakes to Avoid
- Putting test score on the x-axis and sleep on the y-axis is wrong because sleep is the explanatory variable being used to compare with performance.
- Claiming that sleep caused the score difference is wrong because a correlation study can show an association but cannot prove cause and effect by itself.
- Collecting names with sleep and grade data is wrong because the project should protect privacy and use anonymous or coded responses.
- Ignoring outliers is wrong because unusual points can strongly affect the line of best fit and should be discussed, even if they are not removed.
Practice Questions
- 1 A line of best fit passes through the points (6, 78) and (8, 88), where x is hours of sleep and y is test score. Find the slope and explain what it means in this project.
- 2 Five students report sleep hours and scores: (5, 70), (6, 76), (7, 82), (8, 88), (9, 91). Estimate whether the relationship is positive, negative, or near zero, and predict the score for 7.5 hours using a reasonable trend.
- 3 A scatter plot shows that students who sleep more often have higher scores, but some students with little sleep still score high. Explain why the project should describe the result as a correlation instead of proof that sleep alone determines performance.