Superlesson
Project 1-2
Algebra
Chapter 1, Data and Relationships
Some high school seniors must take the SAT test to get into college. What do schools find out about students by looking at their SAT scores? Let's investigate using the Internet and mathematics!
Part A, Working with Pairs of Data
1. Look at the scores on the math and verbal sections of the SAT Web site.
a. Look first at the data from verbal section of the 1997-98 SAT I. Is there a positive association, a negative association, or no association between the score and the percentile?
b. Look at the data from the math section of the 1997-98 SAT I. Is there a positive association, a negative association, or no association between the score and the percentile?
c. The mean score on the verbal section of the SAT I is at about what percentile? How do you know?
d. The mean score on the math section of the SAT I is at about what percentile? How do you know?
2. A scatter graph of the SAT scores will show the relationship of the data.
a. If you were to make a scatter plot with the SAT I verbal scores on the horizontal axis and the percentiles on the vertical axis, what would your graph look like?
b. If you made a scatter plot with the SAT I math scores on the horizontal axis and the percentiles on the vertical axis, what would your graph look like?
Part B, Graphing Data on a Coordinate Plane
3. Plot the data from 2a on coordinate axes. Label each ordered pair.
4. Plot the data from 2b on coordinate axes. Label each ordered pair.
5. Which quadrant(s) do you use to plot the data?
6. What would it mean if you plotted data in Quadrant III?
7. Using your graphs, near what percentile would you expect to find a score of 625 on the SAT I verbal section? How did you find your answer?
8. Using your graphs, near what percentile would you expect to find a score of 710 on the SAT I math section? How did you find your answer?
Part C, Making Connections
9. Ten students took the SAT I test. Their scores are on the following chart.
| Test |
A |
B |
C |
D |
E |
F |
G |
H |
I |
J |
| Verbal |
429 |
312 |
455 |
405 |
795 |
480 |
500 |
750 |
507 |
625 |
| Math |
648 |
482 |
455 |
629 |
410 |
425 |
610 |
762 |
509 |
400 |
a. Make a scatter plot of the scores. Put the verbal score on the horizontal axis and the math score on the vertical axis. Which student would you consider to be the "average" student? Explain your reasoning.
b. Which point represents the student you would consider to be an outlier? Explain your reasoning.
10. Draw a verticle line through the horizontal axis of your scatter plot to represent the mean verbal score and draw a horizontal line through the vertical axis to represent the mean math score. What can you tell about each student now?
11. Find the mean scores of the ten students in the chart above.
a. What are the mean scores of the ten students on both the verbal and the math sections of the SAT I?
b. Did these ten students do better or worse than the national average?