Interpreting Data
Interpreting Data
Objectives
Students will explore a variety of data representations in order to:
- understand the concept of correlation.
- represent, analyze, and interpret data.
- draw conclusions and make predictions.
- compare data sets and solve real-world problems.
Essential Questions
How can data be organized and represented to provide insight into the relationship between quantities?
How can probability and data analysis be used to make predictions?
How does the type of data influence the choice of display?
What does it mean to estimate or analyze numerical quantities?
What makes a tool and/or strategy appropriate for a given task?
- What does it mean to estimate or analyze numerical quantities?
- What makes a tool and/or strategy appropriate for a given task?
- How can data be organized and represented to provide insight into the relationship between quantities?
- How does the type of data influence the choice of display?
- How can probability and data analysis be used to make predictions?
Related Unit and Lesson Plans
Related Materials & Resources
The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.
- NCTM’s Line of Best Fit and Positive/Negative Correlation
http://illuminations.nctm.org/ActivityDetail.aspx?ID=146
- Correlation
http://www2.webster.edu/~woolflm/correlation/correlation.html
- An Introduction to Two-Way Tables
http://www.oswego.edu/~srp/stats/2_way_tbl_1.htm
- Two-Way Tables
http://stattrek.com/statistics/two-way-table.aspx
- Line of Best Fit With a Calculator
http://www.regentsprep.org/Regents/math/ALGEBRA/AD4/linefitcalc.htm
Formative Assessment
-
View
Multiple-Choice Items:
Use the table and information below to answer questions 1–3.
Jake surveyed students to find out whether they had gone to the library in the last week and whether they owned a video game system. He used the results from his survey to create the two-way table shown.
Have Been to the Library
Have Not Been to the Library
Own a Video Game System
24
42
Do Not Own a Video Game System
40
14
- How many students did Jake survey?
A
24
B
64
C
66
D
120
- What percentage of students Jake surveyed do not own a video game system?
A
35%
B
45%
C
54%
D
64%
- What is the percentage, rounded to the nearest whole percent, of students who own a video game system and have been to the library in the last week?
A
36%
B
38%
C
57%
D
74%
- Which scatter plot shows neither a positive nor negative correlation?
A
B
C
D
- What is the correlation in the following scatter plot?
A
negative, strong
B
negative, weak
C
positive, strong
D
positive, weak
Use the graph below to answer question 6.
- Claudia examines the correlation between population and housing market prices. What is the general relation between population and housing prices?
A
As the population increases, the prices go down.
B
As the population decreases, the prices go up.
C
As the population increases, the prices go up.
D
No prediction can be made.
- Which scatter plot shows a line of best fit?
A
B
C
D
- Craig plots another set of data about how much someone’s insurance costs per year (in dollars), y, based on the number of years, x, since his/her last accident. He finds the line of best fit has an equation of y = −75x + 900. Based on the line of best fit, how much could people expect their insurance to cost per year if it has been 7 years since their last accident?
A
$375
B
$525
C
$900
D
$1,425
- A scatter plot shows the relationship between the circumference of a tree in inches and the age of the tree in years. In the plot, the age of the tree is on the x-axis and the circumference of the tree is on the y-axis. The slope of the line is 0.45. Which statement describes the meaning of the slope?
A
The circumference of the tree increases by 0.45 inch each year.
B
The circumference of the tree increases by 1 inch every 0.45 year.
C
The circumference of the tree is multiplied by 0.45 each year.
D
The circumference of the tree is multiplied by 1.45 each year.
Multiple-Choice Answer Key:
1. D
2. B
3. A
4. D
5. B
6. C
7. C
8. A
9. A
Short-Answer Items:
- Create a two-way table that could represent the data from the two one-way tables shown.
- Create a scatter plot for the data shown in the table. Describe the correlation. Describe the relationship between the variables.
- Paul creates a scatter plot to show the height of a candle, y, in inches after burning for x hours. He finds that the equation of the line of best fit is y = −0.75x + 6. Determine the value of the slope and y-intercept and explain the meaning of each, using the units described in the problem.
Short-Answer Key and Scoring Rubrics:
- Create a two-way table that could represent the data from the two one-way tables shown.
Answers will vary. A possible two-way table is shown below.
Likes Swimming
Does Not Like Swimming
Likes Football
64
24
Does Not Like Football
8
4
Points
Description
2
The student has the correct totals for both rows and both columns.
1
The student has the correct totals for 2 or 3 of the 4 rows / columns.
0
The student has the correct totals for 0 or 1 of the 4 rows/columns.
11. Create a scatter plot for the data shown in the table. Describe the correlation. Describe the relationship between the variables.
A positive linear correlation exists between the variables. As the height of the basketball player increases, the number of rebounds increases.
Points
Description
2
The scatter plot correctly shows all data points, labels, and titles.
AND
The student correctly identifies that there is a positive linear correlation.
1
The scatter plot correctly shows all data points, labels, and titles.
OR
The student correctly identifies that there is a positive linear correlation.0
Both the scatter plot and correlation description are done incorrectly or are missing.
- Paul creates a scatter plot to show the height of a candle, y, in inches after burning for x hours. He finds that the equation of the line of best fit is y = −0.75x + 6. Determine the value of the slope and y-intercept and explain the meaning of each, using the units described in the problem
The slope is −0.75 and means that the height of the candle is decreasing by 0.75 inch for each hour the candle burns. The y-intercept is 6 which means the candle was 6 inches tall before it started to burn.
Points
Description
2
The student correctly determines the value of both quantities and explains what each means.
1
The student correctly determines the value and meaning of only one quantity.
0
The student does not correctly determine the value of either quantity and does not explain what either quantity means.
Performance Assessment:
Create two related problem scenarios.
- The first problem scenario should be on a topic for which data from a sample of one group can be compared to corresponding data from a sample of another group.
- The second problem scenario should be on two topics for which a single group provides data for both related topics.
With each problem, include appropriate representations, descriptions, interpretations, analyses, conclusions, and predictions. Describe what you want the data to tell about the group you are studying.
Prepare a presentation about your two problems. You must include a visual display for each problem such as a graph, two-way table, or chart that presents your data in an appropriate way, and you must tell why you chose that method to present it. Choose a topic you are interested in. The presentation should be approximately 15 minutes in length.
Performance Assessment Scoring Rubric:Points
Description
4
- The student’s response creates two related problems comparing two samples, with complete descriptions and reasons for choosing the problems and samples.
- The student’s response includes correct and appropriate data representation and sufficient reasons for the choice of representation.
- The student’s response provides complete interpretations and analyses; it describes handling of unforeseen situations, such as outliers.
- The student’s response includes a complete summary set of correct, conclusive statements and predictions, with justification provided, showing complete understanding.
3
- The student’s response creates two related problems comparing two samples, with adequate descriptions and reasons for choosing the problems and samples.
- The student’s response includes correct and appropriate data representation, but reasons for the choice of representation may be lacking.
- The student’s response provides adequate interpretations and analyses; it describes handling of unforeseen situations, such as outliers.
- The student’s response includes an adequate set of correct, conclusive statements and predictions and justifications, with some possible conclusions/predictions missing.
2
- The student’s response creates two related problems comparing two samples, with descriptions and reasons for choosing the problems or samples either lacking or unclear.
- The student’s response includes inappropriate or incorrect data representation and the reason for the choice of representation is lacking.
- The student’s response provides inadequate or incorrect interpretations and analyses or description of the handling of unforeseen situations.
- The student’s response includes inadequate or incorrect conclusive statements and predictions; it provides justification.
1
- The student’s response creates one problem or creates two unrelated problems, with descriptions and reasons for choosing the problems or samples either lacking or unclear.
- The student’s response includes inadequate or incorrect data representation and is missing the reason for the choice of representation.
- The student’s response includes inadequate or incorrect interpretations and analyses and is missing description of the handling of unforeseen situations.
- The student’s response includes inadequate or incorrect conclusive statements and predictions, and it does not provide justification.
0
- The student’s response is missing both problems.
- The student’s response is missing the data representation and the reason.
- The student’s response is missing interpretations/analyses and further descriptions.
- The student’s response is missing conclusive statements, predictions, and justifications.
Final 04/26/13
