Exercises: Extracting Information from Data

Define metadata. Give three examples of metadata that might be stored with a photo taken on a smartphone, and explain one way someone could use this metadata.

In the summer, ice cream sales and the number of sunburns both rise. Does this mean that eating ice cream causes sunburns? Explain the difference between correlation and causation, and name a variable that could explain both trends.

A school collected this data:

1. a) How many students ride the bus and have a GPA above 3.0?

1. b) What percent of the bus riders have a GPA above 3.0?

Jayden recorded how many hours he studied and his quiz score for five quizzes:

1. a) Describe the correlation (positive, negative, or none) and how strong it looks.

1. b) Use the pattern to estimate the score for 6 hours of studying. What makes this estimate risky?

1. c) Do these data prove that studying more causes higher scores? Explain.

The student council wants to know whether students like the cafeteria food. It sends an email survey only to students enrolled in AP courses, and 40% of those students reply.

1. a) Identify two sources of bias in this data collection.

1. b) Explain how the conclusions might differ from the opinions of the whole school.

1. c) Suggest one way to collect better data.

A club collected the following sign-up data and wants to count how many different students signed up from Texas.

1. a) Identify at least three problems with the data.

1. b) How would a program that counts rows with State equal to "TX" differ from the correct count? What would you do to clean the data first?

A bike-share company in Denver recorded the number of trips on one Tuesday in October:

1. a) What percent of these trips happened during the commute periods (7-9 AM and 5-7 PM)? Round to the nearest tenth of a percent.

1. b) The city wants to use this dataset to decide where to add more bikes. Describe at least three limitations of the data.

1. c) Describe what additional data you would collect to make a better decision, and explain how it would reduce bias or error.

A company says that students who use its study app more than 5 hours per week have an average GPA of 3.4, while the average GPA of non-users is 2.9. The company surveyed 200 users and 800 non-users.

1. a) The company claims, "Our app raises your GPA." Evaluate this claim. Include at least two possible confounding variables.

1. b) Explain how the way the students were chosen might bias the result.

1. c) Design a better study that could provide stronger evidence about whether the app helps. Say what you would measure and how you would assign students to groups.