Sometimes a graph is used to make predictions about points that are not indicated on the graph. These predictions are known as interpolationand extrapolation.

Interpolation
predictions about data values between given data

Extrapolation
predictions about data values above or below given data

 

Example 3

Bailey the puppy and Kali the kitten were born at the same time. Their weights were tracked from age 5 weeks to age 45 weeks.


Which animal grew at an overall faster rate? Explain how you can tell.

Bailey grew at an overall faster rate because the blue points on the graph rise more quickly.

Compare the weight gains of Bailey and Kali between 10 and 20 weeks.

Bailey's weight increased from approximately 24 lbs to 40 lbs, which is an increase of 16 lbs. In the same time, Kali's weight increased from approximately 1 lb to 5 lbs, for an increase of approximately 4 lbs.

What happened to the both Bailey's and Kali's weight gain between 20 and 30 weeks?

Both Bailey and Kali gained approximately 5 lbs. Their growth rates were roughly the same between 20 and 30 weeks.

Interpolate Kali's weight at 40 weeks. What information did you use to make this prediction?

Kali was approximately 12 lbs at 40 weeks. This prediction is based on Kali's weight at both 35 and 45 weeks. At 35 weeks, Kali was approximately 12 lbs. At 45 weeks, Kali was still approximately 12 lbs, so it is reasonable that Kali's weight at 40 weeks was also approximately 12 lbs. By 35 weeks, it seems Kali reached full size.

Do you think Bailey was finished growing at 50 weeks? What information did you use in this extrapolation?

There is no evidence in the data provided to suggest that Bailey was finished growing at 50 weeks. Between 40 and 45 weeks, Bailey's weight was still steadily increasing, which suggests it continued to increase into 50 weeks.

Extrapolate Bailey's approximate weight at 55 weeks.

Bailey was likely between 75 to 80 lbs at 55 weeks.