Statistics: Scatter Plots and Correlation Worksheet

Question 1

A scatter plot compares hours studied for a test and test score. The points generally rise from left to right. Describe the direction of the association and explain what it means in context.

Accepted Answer

The association is positive. This means that students who studied more hours generally tended to have higher test scores.

Question 2

A scatter plot compares the age of a used car and its selling price. The points generally fall from left to right and are fairly close to a straight line. Describe the direction and strength of the association.

Accepted Answer

The association is negative and fairly strong. As the age of the car increases, the selling price generally decreases, and the points are close to a linear pattern.

Question 3

A data set has correlation coefficient r = 0.92. Describe the strength and direction of the linear relationship.

Accepted Answer

The data show a strong positive linear relationship because r is close to 1.

Question 4

A data set has correlation coefficient r = -0.18. Describe the strength and direction of the linear relationship.

Accepted Answer

The data show a weak negative linear relationship because r is negative but close to 0.

Question 5

A scatter plot compares shoe size and math test score for students in a class. The points are spread randomly with no clear upward or downward pattern. What type of association is shown?

Accepted Answer

The scatter plot shows little or no association. Shoe size does not appear to be related to math test score in this data set.

Question 6

A line of best fit for predicting a plant's height in centimeters from days after planting is y = 2.4x + 5. What does the slope mean in context?

Accepted Answer

The slope means that the plant's height is predicted to increase by about 2.4 centimeters for each additional day after planting.

Question 7

A line of best fit for predicting monthly electricity cost y from kilowatt-hours used x is y = 0.14x + 18. Predict the cost for a month when 650 kilowatt-hours are used.

Accepted Answer

The predicted cost is y = 0.14(650) + 18 = 91 + 18 = 109. The predicted monthly electricity cost is $109.

Question 8

A line of best fit is y = -3x + 75, where x is the number of hours after noon and y is the temperature in degrees Fahrenheit. Predict the temperature 6 hours after noon.

Accepted Answer

The predicted temperature is y = -3(6) + 75 = -18 + 75 = 57. The predicted temperature is 57 degrees Fahrenheit.

Question 9

A scatter plot of height and arm span for students has one point far away from the rest of the data. What is this point called, and why might it matter?

Accepted Answer

The point is called an outlier. It might matter because it can affect the line of best fit and the correlation coefficient.

Question 10

A scatter plot shows a strong positive association between the number of ice cream cones sold and the number of people wearing sunglasses at a beach. Can you conclude that buying ice cream causes people to wear sunglasses? Explain.

Accepted Answer

No, you cannot conclude causation from correlation alone. A third factor, such as warm sunny weather, may explain why both ice cream sales and sunglasses use increase.

Question 11

A teacher records the following pairs for hours of practice and free throw percentage: (1, 42), (2, 48), (3, 55), (4, 61), (5, 65). Describe the association in the data.

Accepted Answer

The data show a positive association. As the number of practice hours increases, the free throw percentage generally increases.

Question 12

A scatter plot comparing daily screen time and hours of sleep has a negative association. If a student has more daily screen time than another student, what would the trend predict about their hours of sleep?

Accepted Answer

The trend would predict that the student with more daily screen time may have fewer hours of sleep. This is a prediction based on the pattern, not a guarantee for every student.

Statistics: Scatter Plots and Correlation

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