Trees and forests are important to the ecology of any town, city, or state. Urban planners need to know about the different trees present in a city to make sure there is enough green space to promote recreation. Foresters need to know about the types of trees in a forest to combat outbreaks of disease and other pests that harm forests.

In this section, you will use sampling techniques in order to describe a neighborhood forest.

Susana wants to know what types of trees and how many of each type are in her neighborhood. Instead of counting every tree in the neighborhood, Susana randomly selected 25 houses out of the 240 in her neighborhood to survey the types of trees.

Use the interactive below to determine the number of each of the four types of trees that Susana found at the 25 houses. Click on the leaf or tree to see the number of that type of tree that Susana found. Use the information below to complete the table that follows.

Copy and paste the table below into your notes, and use the information in the interactive to complete the table.

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Type of Tree	Number of Trees
White Oak	30
Cedar Elm	24
Loblolly Pine	42
Pecan	20

Now that Susana has completed her survey, she is ready to use it to make predictions about the population of trees in her neighborhood.

Susana can set up and solve a proportion relating the ratio of each type of tree in her sample to the ratio of each type of tree in her neighborhood.

Watch the video below to see how Susana set up and solved a proportion to determine the number of white oak trees in her entire neighborhood.

Use what you have seen so far to answer the following questions.

• Based on the data that Susana collected, how many pecan trees are there in her neighborhood?

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  Need a hint?

  Set up and solve a proportion using two ratios of number of pecan trees : number of houses.
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  Check Your Answer

  
• Based on the data that Susana collected, about how many cedar elm trees are there in her neighborhood?

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  Need a hint?

  Set up and solve a proportion using two ratios of number of cedar elms : number of houses.
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  Check Your Answer

  

Pause and Reflect

When using a sample to make predictions about a population, why is it important to make sure that the sample is representative of the population?

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The predictions are only valid if the characteristics of the sample are very close to the characteristics of the population.

What is one way you can help to make sure your sample is representative of the population?

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Using a random sample, where every member of the population has an equal chance of being selected for the sample, helps make sure the sample is representative of the population.

Practice

Reginald wanted to know which pet was most popular among seventh graders at his school. He randomly surveyed 60 students during seventh grade lunch. The results of his survey are shown in the graph below. Use this graph to answer questions 1 – 3.

1. How many of the students surveyed said that their favorite pet was a cat?

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   30% of the students surveyed, or 30% of 60, said that their favorite pet was a cat. Use this information to determine the number of students that 30% of 60 represents.
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   30% = 0.30
   0.30 × 60 = 18
   
   18 students said that their favorite pet was a cat.
2. If there are 340 seventh grade students in Reginald’s school, how many of them should Reginald expect to say that a dog was their favorite pet?

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   35% of the students surveyed said that a dog was their favorite pet. If the sample is representative of the population, then 35% of the population should say that a dog was their favorite pet.
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   35% = 0.35
   0.35 × 340 = 119
   
   Reginald should expect that 119 students would say that a dog was their favorite pet.
3. Of the 340 seventh grade students, how many more would Reginald expect to favor dogs as pets over cats?

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   Need a hint?

   Use the data to determine how many of the 340 students would favor dogs and how many would favor cats.
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   Check Your Answer

   Dogs:	Cats:
   35% = 0.35	30% = 0.30
   0.35 × 340 = 119	0.30 × 340 = 102
   119 students would favor dogs.	102 students would favor cats.
   119 − 102 = 17
   17 more students would favor dogs than would favor cats.