1. Populations & Samples Florida Math Standard MAFS.7.SP.1.2

2. Activate Prior Knowledge What is a ratio? How would you set up equivalent ratios? What is this called?  1 to 4, 1:4, ¼  3 = 6 4 8  Proportion

3. How would you solve for a missing value in that proportion? 3 = 6 4 x 3 ∙ x = 4 ∙ 6 3x = 24 3 3 x = 8 Cross Products Property states that the products of the diagonals of equivalent fractions are equal. Activate Prior Knowledge

4.  There is a pre-numbered list on the board.  Know which number you represent and when the teacher calls you, come to the board to write down the answer to the following question by your number.  When finished, cover your number with a sticky note so that the data is only revealed when needed. How many different organized sports teams do you play for in one year? Let’s Get Started

5. Simple Random Sample: Each individual is chosen entirely by chance and each member of the population has an equal chance of being included in the sample. Are you the chosen one??? Random Sample # 1

6. Stratified Sampling: When you divide the population into subpopulations, or subgroups, and random samples are taken from each subgroup. Random Sample # 2 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 All the #4 positions in each subgroup would make up the sample.

7. Cluster Sample-When the entire population is divided into clusters, or subgroups, and a random sample is taken from these clusters. All observations from the selected cluster(s) is included in the sample. Random Sample #3 1 2 3 1 2 3

8. 1.Did all the samples yield the same results? Why or why not? 2.From this data, what would you predict to be the mean of the population? 3.What could you do to make a better prediction of the population? 4.Which random sample do you think would be best to make the most accurate predictions about the population? Why? Let’s Compare

9. Making Predictions Using Cross Products Property with your random sample, you can draw inferences about the population. Example: In Ms. Albert’s 6th grade class, 9 out of 14 girls have brown hair. About how many of all 142 6 th grade girls would you expect to have brown hair? Random Sample: 9 out of 14 girls have brown hair Total Population: 142 girls By using Cross Products Property, you could predict that about 91 girls in 6 th grade will have brown hair. Girls with brown hair 9 Total 14142 SamplePopulation

10. Practice While cleaning out her room, Angela found a collection of hair ties under her bed. Out of the 12 she found, 9 of them were brown. About how many total brown hair ties would you expect Angela to have if her collection has a total of 98 hair ties?  Set up a proportion chart  Use Cross Products Property to solve for the missing value 9 ∙ 98 = 12 ∙ x 882 = 12x 12 12 73.5 = x brown hair ties 9x total 1298 samplepopulation

11.  How can you create a random sample that adequately and accurately represent the whole population?  How can you generate multiple samples of the same size?  How would you draw inferences about populations when given characteristics of a random sample of the population? In Conclusion