Virginia SOL Math / Grade 8 / Probability & Statistics

8.PS.3

Scatterplots

What you'll learn

  • Represent bivariate data with a scatterplot
  • Describe the association between two variables
  • Use a line of best fit to make predictions

Words to know

Scatterplot —
a graph of ordered pairs showing two variables
Bivariate data —
data that pairs two variables together
Positive association —
as one variable increases, the other tends to increase
Negative association —
as one variable increases, the other tends to decrease
Line of best fit —
a line that models the trend of the data

Why it matters Scatterplots reveal whether two things are related, such as study time and test scores, and let us make reasonable predictions.

Worked examples

Model ItI do

As hours studied rise, test scores rise. What association is this?

When both variables increase together, the trend goes up from left to right. This is a positive association.

Try It TogetherWe do

A line of best fit is y = 5x + 60. Predict the score for 4 hours of study.

Substitute x = 4: y = 5 times 4 + 60 = 20 + 60 = 80. The predicted score is 80.

Now YouYou do

As outdoor temperature rises, hot-cocoa sales fall. What association is this?

Decide whether the variables move in the same or opposite directions. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.As hours of practice rise, free-throws made rise. What association is this?

  2. 2.Using y = 2x + 4, predict y when x = 3.

  3. 3.Points on a scatterplot show no pattern at all. What association is this?

On Level

The core Quick Check from the book.

  1. 1.As age rises, so does height in children. What association is this?

  2. 2.Using y = 2x + 3, predict y when x = 5.

  3. 3.As price rises, quantity sold falls. What association is this?

  4. 4.A scatterplot shows points scattered with no trend. What association is this?

  5. 5.Using y = -3x + 30, predict y when x = 4.

Challenge

Stretch your thinking.

  1. 1.A line of best fit is y = 4x + 50 relating hours studied (x) to test score (y). Predict the score for 7 hours and interpret the slope.

  2. 2.A scatterplot of outdoor temperature (x) versus hot-soup sales (y) trends downward. Describe the association and what it means.

  3. 3.A line of best fit is y = -2x + 40. Predict y when x = 12, and state whether the association is positive or negative.