Exploring Correlation Strength and Outliers in Data

A scatterplot shows the relationship between hours studied and test scores for 10 students. If the line of best fit has a positive slope, what does this indicate about the correlation between hours studied and test scores?

• There is a negative correlation between hours studied and test scores.

• There is no correlation between hours studied and test scores.

• There is a positive correlation between hours studied and test scores.

• The correlation is weak between hours studied and test scores.

In a scatterplot of temperature versus ice cream sales, one point shows an unusually high number of sales at a low temperature. How would you describe this point, and what might it indicate about the data?

• An outlier indicating potential external factors affecting sales.

• A trend suggesting higher sales at lower temperatures.

• A data entry error that should be corrected.

• A normal data point indicating typical sales behavior.

A scatterplot displays the number of hours spent on social media versus grades in school. If the correlation coefficient is -0.85, what does this tell you about the relationship between these two variables?

• There is no correlation between hours spent on social media and grades.

• There is a strong positive correlation between hours spent on social media and grades.

• The correlation indicates that more hours on social media lead to higher grades.

• There is a strong negative correlation between hours spent on social media and grades.

You analyze a scatterplot of the number of books read versus reading scores. If one student read 50 books but has a low reading score, how would you classify this data point? What does it suggest about the overall trend?

• The data point indicates that reading more books always leads to higher scores.

• The data point is typical, showing a strong correlation between books read and reading scores.

• The data point is an outlier, suggesting that reading more books does not guarantee higher reading scores.

• The data point suggests that students who read fewer books perform better in reading.

In a scatterplot comparing the amount of rainfall to the number of umbrellas sold, you notice a strong positive correlation. What does this imply about the relationship between these two variables?

• There is no relationship between rainfall and umbrella sales.

• Rainfall decreases the number of umbrellas sold.

• More umbrellas are sold regardless of rainfall.

• There is a direct relationship where increased rainfall leads to more umbrellas sold.

A scatterplot shows the relationship between age and the number of hours spent exercising. If a 70-year-old is an outlier with significantly fewer hours, how might this affect the line of best fit?

• The line of best fit will be pulled upward, indicating a stronger trend.

• The line of best fit will be pulled downward, misrepresenting the trend.

• The line of best fit will become steeper, suggesting increased exercise with age.

• The line of best fit will remain unchanged, accurately reflecting the data.

You create a scatterplot of the distance traveled by cars and their fuel efficiency. If the line of best fit is nearly horizontal, what does this suggest about the correlation between these two variables?

• There is little to no correlation between distance traveled and fuel efficiency.

• There is a strong positive correlation between distance traveled and fuel efficiency.

• Fuel efficiency increases as distance traveled decreases.

• There is a moderate negative correlation between distance traveled and fuel efficiency.

In a scatterplot of students' heights versus their shoe sizes, you find a point where a very short student has an unusually large shoe size. How would you interpret this outlier?

• The outlier indicates a trend where shorter students tend to have larger shoe sizes.

• The outlier is likely a measurement error in the data collection process.

• The outlier represents a student whose shoe size is disproportionately large for their height, indicating a unique case.

• This point suggests that all students with large shoe sizes are short.

A scatterplot shows the relationship between the price of a product and the quantity sold. If the line of best fit slopes downward, what does this indicate about consumer behavior?

• Higher prices lead to increased sales of the product.

• The price has no effect on the quantity sold.

• Consumers buy less of a product when its price decreases.

• Consumers tend to buy more of a product when its price decreases.

You analyze a scatterplot of hours of sleep versus test scores. If the correlation is weak, what does this suggest about the relationship between these two variables?

• There is little to no linear relationship between hours of sleep and test scores.

• There is a strong positive relationship between hours of sleep and test scores.

• More sleep always leads to higher test scores.

• The correlation indicates a perfect linear relationship between the two variables.