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Here is the table of isosceles right triangle measurements from the Warm-up and an empty table.
| length of short sides (in) | length of perimeter (in) |
|---|---|
| 0.25 | 1 |
| 2 | 7.5 |
| 6.5 | 22 |
| 3 | 9.5 |
| 0.5 | 2 |
| 1.25 | 3.5 |
| 3.5 | 12.5 |
| 1.5 | 5 |
| 4 | 14 |
| 1 | 2.5 |
| length of short sides (in) | length of perimeter (in) |
|---|---|
Here are four scatter plots. Your teacher will give you four tables of data.
Scatterplot, x, 0 to 150,000 by 30,000, y, 6,000 to 21,000 by 3,000. Points begin around 2,000 comma 16,000 and trend down and right toward 120,000 comma 7,000.
Scatterplot, x, 72 to 102 by 6, y, 15 to 45 by 5. Points begin around 76 comma 18 and trend up and right toward 100 comma 40.
Scatterplot, x, 10 to 50 by fives, y 10 to 45 by fives. Points begin around 13 comma 12 and trend up and right toward 47 comma 41.
Scatterplot, x, 1,000 to 2,500 by 250, y, 14 to 32 by 2. Points begin around 1,100 comma 29 and trend down and right toward 2,300 comma 16.
Match each table with one of the scatter plots, then write a title and label the axes for each.
Why do you think the values on the grid lines differ by numbers other than 1?
Consider the data collected from pulling back a toy car and then letting it go forward. In the first table, the data may not seem to have an obvious pattern. The second table has the same data and shows that both values are increasing together.
Unorganized table:
| distance pulled back (in) | distance traveled (in) |
|---|---|
| 6 | 23.57 |
| 4 | 18.48 |
| 10 | 38.66 |
| 8 | 31.12 |
| 2 | 13.86 |
| 1 | 8.95 |
Organized table:
| distance pulled back (in) | distance traveled (in) |
|---|---|
| 1 | 8.95 |
| 2 | 13.86 |
| 4 | 18.48 |
| 6 | 23.57 |
| 8 | 31.12 |
| 10 | 38.66 |
A scatter plot of the data makes the pattern clear enough that we can estimate how far the car will travel when it is pulled back 5 in.
Patterns in data can sometimes become more obvious when reorganized in a table or when represented in scatter plots or other diagrams. If a pattern is observed, it can sometimes be used to make predictions. This is a scatter plot for this scenario:
A scatterplot. Horizontal, from 0 to 12, by 2’s, labeled distance pulled back, inches. Vertical, from 0 to 40, by 10’s, labeled distance traveled, inches. 6 data points. Trend linearly upward and right.
A scatter plot is a graph that shows values of 2 variables on a coordinate plane. It can be used to look for relationships between the 2 variables.
Each point on this scatter plot represents the height and weight of 1 dog.