Lesson 1: Organizing Data

Let’s find ways to show patterns in data

1.1: Notice and Wonder: Messy Data

Here is a table of data. Each row shows two measurements of an isosceles right triangle. 

  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
What do you notice? What do you wonder?

1.2: Seeing the Data

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    
  1. How can you organize the measurements from the first table so that any patterns are easier to see? Write the organized measurements in the empty table.
  2. For each of the following lengths, estimate the perimeter of an isosceles right triangle whose short sides have that length. Explain your reasoning for each triangle.
    1. length of short sides is 0.75 cm
    2. length of short sides is 5 cm
    3. length of short sides is 10 cm

1.3: Tables and Their Scatter Plots

Here are four scatter plots. Your teacher will give you four tables of data.

  • Match each table with one of the scatter plots.
  • Use information from the tables to label the axes for each scatter plot.
 

Summary

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.

Practice Problems ▶

Glossary

scatter plot

scatter plot

A scatter plot shows data points for the relationship between two variables on a pair of coordinate axes, one for each variable.