Let’s find ways to show patterns in data
Here is a table of data. Each row shows two measurements of a triangle.
| length of short side (cm) | length of perimeter (cm) | |
|---|---|---|
| row 1 | 0.25 | 1 |
| row 2 | 2 | 7.5 |
| row 3 | 6.5 | 22 |
| row 4 | 3 | 9.5 |
| row 5 | 0.5 | 2 |
| row 6 | 1.25 | 3.5 |
| row 7 | 3.5 | 12.5 |
| row 8 | 1.5 | 5 |
| row 9 | 4 | 14 |
| row 10 | 1 | 2.5 |
Here is the table of isosceles right triangle measurements from the warm-up and an empty table.
| length of short sides (cm) | length of perimeter (cm) | |
|---|---|---|
| row 1 | 0.25 | 1 |
| row 2 | 2 | 7.5 |
| row 3 | 6.5 | 22 |
| row 4 | 3 | 9.5 |
| row 5 | 0.5 | 2 |
| row 6 | 1.25 | 3.5 |
| row 7 | 3.5 | 12.5 |
| row 8 | 1.5 | 5 |
| row 9 | 4 | 14 |
| row 10 | 1 | 2.5 |
| length of short sides (cm) | length of perimeter (cm) | |
|---|---|---|
| row 1 | ||
| row 2 | ||
| row 3 | ||
| row 4 | ||
| row 5 | ||
| row 6 | ||
| row 7 | ||
| row 8 | ||
| row 9 | ||
| row 10 |
In addition to the graphic representations of data you have learned, there are others that make sense in other situations. Examine the maps showing the results of the elections for United States president for 2012 and 2016. In red are the states where a majority of electorate votes were cast for the Republican nominee. In blue are the states where a majority of the electorate votes were cast for the Democrat nominee.
Here are four scatter plots. Your teacher will give you four tables of data.
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) | |
|---|---|---|
| row 1 | 6 | 23.57 |
| row 2 | 4 | 18.48 |
| row 3 | 10 | 38.66 |
| row 4 | 8 | 31.12 |
| row 5 | 2 | 13.86 |
| row 6 | 1 | 8.95 |
Organized table
| distance pulled back (in) | distance traveled (in) | |
|---|---|---|
| row 1 | 1 | 8.95 |
| row 2 | 2 | 13.86 |
| row 3 | 4 | 18.48 |
| row 4 | 6 | 23.57 |
| row 5 | 8 | 31.12 |
| row 6 | 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 inches.
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.
A scatter plot shows data points for the relationship between two variables on a pair of coordinate axes, one for each variable.
