Lesson 26Lesson 26

Making InferencesMaking Inferences

We often need to use existing data to We often need to use existing data to make an educated guess about the future. make an educated guess about the future. You might use your knowledge of how You might use your knowledge of how often a teacher gives a quiz in science to often a teacher gives a quiz in science to infer when the next quiz will be. Or you infer when the next quiz will be. Or you might use your favorite team’s record to might use your favorite team’s record to infer whether the team will win the next infer whether the team will win the next game or the next five games.game or the next five games.

Example 1Example 1

John studied the data in this table which shows the John studied the data in this table which shows the changing population of his hometown. From these changing population of his hometown. From these data, he estimated the population of his hometown data, he estimated the population of his hometown in the year 2010. What is a good estimate of what in the year 2010. What is a good estimate of what the population will be in the year 2010?the population will be in the year 2010?

Strategy: Look for a pattern in the population Strategy: Look for a pattern in the population data.data.

Step 1: Round the population to the nearest 500.Step 1: Round the population to the nearest 500.

Step 2: Find the differences of the population data Step 2: Find the differences of the population data estimates (Step 1) for each 10-year period.estimates (Step 1) for each 10-year period.

Step 3: Look for a pattern. The differences of Step 2 Step 3: Look for a pattern. The differences of Step 2 reveal a pattern.. Three of the five differences are reveal a pattern.. Three of the five differences are 2000. The two exceptions are 500 from 2000. You 2000. The two exceptions are 500 from 2000. You can project based on a difference of 2000.can project based on a difference of 2000.

Step 4:Estimate what the population will be in Step 4:Estimate what the population will be in the year 2010. Using 2000 as an estimate of the year 2010. Using 2000 as an estimate of the differences between the population figures, the differences between the population figures, add 2000 to the estimated population 14,500.add 2000 to the estimated population 14,500.

SolutionSolution

The estimated population of John’s hometown The estimated population of John’s hometown in the year 2010 is 16,500.in the year 2010 is 16,500.

Example 2Example 2 Samantha collected data about the price of a popular Samantha collected data about the price of a popular

chocolate bar at the local candy shop. She drew a chocolate bar at the local candy shop. She drew a graph of the prices in five-year intervals over a 20-graph of the prices in five-year intervals over a 20-year period. If the trend continues, what will be the year period. If the trend continues, what will be the price in 2005?price in 2005?

Strategy: Use a trend Strategy: Use a trend line to predict the future line to predict the future price.price.

Step 1: Draw a line Step 1: Draw a line through he existing through he existing points of the graph. points of the graph. This line is called a This line is called a trend line. It does not trend line. It does not have to pass through all have to pass through all the points since it the points since it approximates the approximates the overall direction of the overall direction of the set of points.set of points.

Step 2: Extend the horizontal axis so that the year Step 2: Extend the horizontal axis so that the year 2005 is represented. Draw the vertical line 2005 is represented. Draw the vertical line representing 2005.representing 2005.

Step 4: Determine the price in the year 2005. The Step 4: Determine the price in the year 2005. The price is the point of intersection of the trend line and price is the point of intersection of the trend line and the vertical line for the year 2005. It is around 73 the vertical line for the year 2005. It is around 73 cents.cents.

SolutionSolution

The price will be approximately 73 cents.The price will be approximately 73 cents.