Sampling & Populations

1. Sampling & Populations Predicting the actions of a large group by using a sample.

2. Vocabulary • Sample • Small group • Part of the population being surveyed • Population • Sample representative of a larger group • Entire group being studied

3. Make inferences about a population by analyzing random samples • There is a lake with trout, whitefish and walleye in it. You want to make some inferences about the fish in the pond. • Randomly sample 300 fish • There are 125 trout, 130 whitefish, 45 walleye in the sample. • More trout and whitefish than walleye in the lake. • There are about 1/3 as many walleye as trout or whitefish. • Do not say that whitefish are the most common fish • In our sample this is true, but it’s not significantly bigger. • The sample was random, so having only 5 fish difference will not infer that whitefish is the most common fish.

4. Use sampling to make predictions Example 1: How many texts do middle school students send a day? • What is the population? • All middle school students • What is the sample? • Survey a small group of students so that you can make a generalization about the entire group.

5. Practice Problem • Track migration patterns of a bird species. • What is the population? • An entire bird species • What is the sample? • Tagged birds (specially marked birds to track, use the data on these birds to make a generalization about an entire bird species).

6. Differentiate between biased and unbiased • Not all samples will lead to good predictions about an entire population. • Representative sample • Needed in order to make a valid inference (accurate prediction based on data). • Unbiased • Any member of the population is equally likely to be chose. • Biased • Some members of the population are more likely to be chosen in the sample for one reason or another.

7. Practice Problem • If you were taking a survey of the different colors of leaves in September, which of the following would be an unbiased sample? • 100 fallen leaves collected from the ground • 100 leaves on tree branches • 50 fallen leaves and 50 leaves on branches • 50 fallen oak leaves, 50 oak leaves on branches Biased Biased Unbiased Biased

8. Use sampling to make predictions Three students are running for class president. Jonathan randomly surveyed some of his classmates and recorded the results in the chart. • What percent said they were voting for Della? • If there are 180 students in the class, how many do you think will vote for Della? 7 + 12 + 6 = 25 12 out of 25 voted for Della 12 ÷ 25 = 0.48 The percent of students that said they were voting for Della was 48%. 0.48(100) = 48% Della will have about 86 votes. 12(180) = 25(x) 2160 = 25x 86.4 = x 12 = x 25 180