Question

The Lesson Activity will help you meet these educational goals:

Content Knowledge—You will recognize statistical questions and examine the habits of data collected to answer them.
Mathematical Practices—You will construct viable arguments and analyze the reasoning of others.
STEM—You will grow in your understanding of mathematics as a creative human activity.
21st Century Skills—You will use critical-thinking and problem-solving skills and collaborate with others.
Directions
Read the instructions for this self-checked activity. Type in your response to each question, and check your answers. At the end of the activity, write a brief evaluation of your work.

Activity
Part A

For his class survey, Walden chose the question, How many people live in your home, including yourself? He asked his friend Drake to help him with the survey. Walden asked 10 students in his class the question, and Drake posed the same question to 10 more students in their class.

Based on the responses, they wrote these data sets:

Walden’s data set: 2, 2, 2, 3, 3, 3, 3, 4, 4, 4

Drake’s data set: 3, 3, 4, 4, 4, 4, 5, 6, 7, 9

Question 1

Compare the two data sets. Do they have the same center, or is the center of Walden’s data set greater or less than the center of Drake’s data set?


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Question 2
How does the spread of Walden’s data set compare with the spread of Drake’s data set?


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Question 3
Predict the overall shape of the distribution of the two data sets. Will the graphs of the two data sets be skewed to the left, skewed to the right, symmetrical, or uniform?


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Question 4
Are there any outliers in the data sets? If there are outliers, do they lie at the lower end or at the higher end of the data sets?


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Answer 1

Part A) Question 1 The center of Walden’s data, 3, is less than the center of Drake’s data set, 6.

Part A) Question 2 Walden’s data ranges from 2 to 4, and Drake’s data set ranges from 3 to 9. Drake’s data set has a greater spread than Walden’s data set.

Part A) Question 3 The graph of Walden’s data set will be symmetrical about the center, and the graph of Drake’s data set will be skewed to the right.

Part A) Question 4 Walden’s data set doesn’t have any outliers. Drake’s data has an outlier with the value 9, which is at the higher end of the distribution.

Part B) Question 1 The center is 5.

Part B) Question 2 This data set has no spread at all. All the values are the same, so the difference of the highest value and the lowest value in the set is 0.

Part B) Question 3 All the data points would lie at the same point, 5. The graph would be a single bar at the value 5, with no other data points anywhere else.

Part B) Question 4 No. All the observations in the data set are the same, and the only answer to the question is 5. So there is no need to find the center, spread, or shape of the data set.

Part B) Question 5 No, Walden was not asking a statistical question because all the people living in the same house would give him the same answer to his question. So the question did not allow for multiple answers among the population that it was posed to.

Answer 2

The center of Walden’s data, 3, is less than the center of Drake’s data set, 6.

Explanation:

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