1. Construct and Interpret Scatter Plots
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Look at the ordered pairs for the athletes in the scatter plot.
We are given a scatter plot that shows two races of the same length for 10 athletes.
Here, we will select all statements that are true.
| Athlete 1 | Athlete 2 | Athlete 3 | Athlete 4 | Athlete 5 | Athlete 6 | Athlete 7 | Athlete 8 | Athlete 9 | Athlete 10 | |
|---|---|---|---|---|---|---|---|---|---|---|
| x-coordinate (Time for First Race) | ≈ 15 seconds | 16 seconds | 16 seconds | ≈ 17 seconds | ≈ 17 seconds | ≈ 17 seconds | 18 seconds | 18 seconds | ≈ 19 seconds | ≈ 19 seconds |
| y-coordinate (Time for Second Race) | ≈ 15 seconds | ≈ 15 seconds | 16 seconds | ≈ 15 seconds | 16 seconds | ≈ 19 seconds | 16 seconds | 18 seconds | ≈ 15 seconds | 16 seconds |
After considering the statements separately we will select the correct ones. Let's begin with the first two statements.
We will consider the first two statements.
|
Statement 1 |
|
Nine of the times for the first race were at least 16 seconds. |
|
Statement 2 |
|
Eight of the times for the second race were less than 17 seconds. |
From here we will color the times that are a least 16 seconds for the first race with green. We will also color the times that are less than 17 seconds for the second race with orange.
| Athlete 1 | Athlete 2 | Athlete 3 | Athlete 4 | Athlete 5 | Athlete 6 | Athlete 7 | Athlete 8 | Athlete 9 | Athlete 10 | |
|---|---|---|---|---|---|---|---|---|---|---|
| x-value (Time for First Race) | ≈ 15 seconds | 16 seconds | 16 seconds | ≈ 17 seconds | ≈ 17 seconds | ≈ 17 seconds | 18 seconds | 18 seconds | ≈ 19 seconds | ≈ 19 seconds |
| y-value (Time for Second Race) | ≈ 15 seconds | ≈ 15 seconds | 16 seconds | ≈ 15 seconds | 16 seconds | ≈ 19 seconds | 16 seconds | 18 seconds | ≈ 15 seconds | 16 seconds |
We can see from the table that 9 of the times for the first race were at least 16 seconds, and 8 of the times for the second race were less than 17 seconds. With this information we can conclude that first two statement is correct.
Next we will color the x- and y-values of the points for the athletes who were faster in the second race than the first.
| Athlete 1 | Athlete 2 | Athlete 3 | Athlete 4 | Athlete 5 | Athlete 6 | Athlete 7 | Athlete 8 | Athlete 9 | Athlete 10 | |
|---|---|---|---|---|---|---|---|---|---|---|
| x-value (Time for First Race) | ≈ 15 seconds | 16 seconds | 16 seconds | ≈ 17 seconds | ≈ 17 seconds | ≈ 17 seconds | 18 seconds | 18 seconds | ≈ 19 seconds | ≈ 19 seconds |
| y-value (Time for Second Race) | ≈ 15 seconds | ≈ 15 seconds | 16 seconds | ≈ 15 seconds | 16 seconds | ≈ 19 seconds | 16 seconds | 18 seconds | ≈ 15 seconds | 16 seconds |
There is only one athlete who was faster in the second race, so the statement is false.
We will examine the last two statements.
|
Statement 4 |
|
There were three athletes who had the same time in both races. |
|
Statement 5 |
|
There were three athletes whose times in the two races differed by exactly 1 second. |
To do so we will color the times of the athletes who had the same time in both races with purple. Also, we will color the times of the athletes whose times in the two race different by exactly 1 second with pink.
| Athlete 1 | Athlete 2 | Athlete 3 | Athlete 4 | Athlete 5 | Athlete 6 | Athlete 7 | Athlete 8 | Athlete 9 | Athlete 10 | |
|---|---|---|---|---|---|---|---|---|---|---|
| x-value (Time for First Race) | ≈ 15 seconds | 16 seconds | 16 seconds | ≈ 17 seconds | ≈ 17 seconds | ≈ 17 seconds | 18 seconds | 18 seconds | ≈ 19 seconds | ≈ 19 seconds |
| y-value (Time for Second Race) | ≈ 15 seconds | ≈ 15 seconds | 16 seconds | ≈ 15 seconds | 16 seconds | ≈ 19 seconds | 16 seconds | 18 seconds | ≈ 15 seconds | 16 seconds |
With this information, three athletes had the same time in both races, and two athletes had times that were different by exactly 1 second. Consequently, the forth statement is true and the fifth statement is false. Finally, we will select the correct statements.
