Analyzing Scatter Plots and Correlation for Grade 7

A teacher recorded the number of hours students studied and their scores on a test. The data is as follows: (1, 50), (2, 60), (3, 70), (4, 80), (5, 90). Create a scatter plot for this data. What trend do you observe?

• The trend observed is a positive correlation between hours studied and test scores.

• The trend observed is a negative correlation between hours studied and test scores.

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

• The trend observed is a random pattern with no discernible relationship.

Using the data from the previous question, calculate the correlation coefficient. What does this value indicate about the relationship between study hours and test scores?

• 0.85

• 0.20

• 0.50

• 0.75

A store tracks the number of customers and the amount of money spent. The data is: (10, 100), (20, 180), (30, 250), (40, 300). Create a scatter plot for this data. What can you infer from the plot?

• There is no correlation between the number of customers and the amount spent.

• The amount spent decreases as the number of customers increases.

• The spending increases at a constant rate regardless of customer numbers.

• There is a positive correlation between the number of customers and the amount of money spent, but the increase in spending slows down as customer numbers rise.

From the previous question's data, calculate the correlation coefficient. What does this tell you about the relationship between the number of customers and money spent?

• The correlation coefficient indicates the average money spent per customer.

• The correlation coefficient shows the total number of customers.

• The correlation coefficient indicates the strength and direction of the relationship between the number of customers and money spent.

• The correlation coefficient is only relevant for financial data.

A scientist measures the temperature of water and the time it takes to boil. The data is: (10, 5), (20, 4), (30, 3), (40, 2). Create a scatter plot for this data. What pattern do you see?

• There is no correlation between temperature and boiling time; they are independent of each other.

• The pattern observed is a positive correlation; as temperature increases, the time to boil increases.

• The pattern observed is a negative correlation; as temperature increases, the time to boil decreases.

• The pattern observed is a constant relationship; the time to boil remains the same regardless of temperature.

Using the temperature and boiling time data, calculate the correlation coefficient. What does this suggest about the relationship between temperature and boiling time?

• The correlation coefficient suggests a strong direct relationship between temperature and boiling time.

• The correlation coefficient shows a moderate positive relationship between temperature and boiling time.

• The correlation coefficient suggests a strong inverse relationship between temperature and boiling time.

• The correlation coefficient indicates no relationship between temperature and boiling time.

A city measures the number of parks and the average number of visitors per park. The data is: (5, 200), (10, 400), (15, 600), (20, 800). Create a scatter plot for this data. What trend is evident?

• There is no correlation between parks and visitors.

• The trend is a negative linear relationship.

• The trend is a positive linear relationship.

• The trend is a quadratic relationship.

Calculate the correlation coefficient for the parks and visitors data. What does this value indicate about the relationship between the number of parks and visitors?

• 0.50

• 0.20

• -0.10

• 0.85

A farmer records the amount of fertilizer used and the crop yield. The data is: (1, 10), (2, 20), (3, 30), (4, 40). Create a scatter plot for this data. What do you notice about the relationship?

• The relationship is exponential and constant.

• The relationship is quadratic and negative.

• The relationship is random and has no correlation.

• The relationship is linear and positive.

Using the fertilizer and crop yield data, calculate the correlation coefficient. What does this tell you about the effect of fertilizer on crop yield?

• The correlation coefficient shows the exact amount of fertilizer needed for maximum yield.

• A higher correlation coefficient means no relationship between fertilizer and crop yield.

• The correlation coefficient is irrelevant to agricultural practices.

• The correlation coefficient indicates the strength and direction of the relationship between fertilizer and crop yield.