1. Check it out! 1 1.3.1: Differences Between Populations and Samples

2. Mrs. Kittle teaches a class in composition and literature. She is conducting a portfolio review with her students, asking them to discuss some of the essays they’ve written over the past semester. Hannah submitted 6 essays this semester, and received the following grades: 100 95 90 85 80 60 Hannah has been asked to select 2 essays to discuss with Mrs. Kittle. Use this information to answer the questions on the following slide. 2 1.3.1: Differences Between Populations and Samples

3. 1.How many possible combinations of 2 essays can be chosen from the 6 that Hannah submitted? 2.What is the lowest possible average grade that Hannah can have in a sample of 2 essays? 3.What is the highest average grade that Hannah can have in a sample of 2 essays? 4.Suppose Hannah was asked to discuss 4 essays instead. What is the lowest possible average grade that Hannah can have in a sample of 4 essays? 5.What is the highest possible average grade that Hannah can have in a sample of 4 essays? 3 1.3.1: Differences Between Populations and Samples

4. 4 1.How many possible combinations of 2 essays can be chosen from the 6 that Hannah submitted? Determining the number of ways to select 2 essays from the total of 6 essays submitted means finding a combination. In combinations, the order in which the items are chosen does not impact the result. The general formula for calculating a combination is, where n is the total number of items from which to choose and r is the number of items actually chosen. Hannah has 6 papers total, so n = 6. She is choosing 2 papers to discuss, so r = 2.

5. Formula for calculating a combination Substitute 6 for n and 2 for r. Simplify. Apply the factorial. Simplify. 5 1.3.1: Differences Between Populations and Samples

6. There are 15 ways Hannah can choose 2 out of the 6 essays. 6 1.3.1: Differences Between Populations and Samples

7. 2.What is the lowest possible average grade that Hannah can have in a sample of 2 essays? To find the lowest possible sample average, select the two essays with the lowest scores and find the average. The two lowest scores are 60 and 80. Recall that an average can be found by adding the values and then dividing the sum by the number of values in the set. 7 1.3.1: Differences Between Populations and Samples

8. Formula for calculating an average Substitute the known values. average = 70Simplify. The lowest possible sample average in a sample of two of Hannah’s essays is 70. 8 1.3.1: Differences Between Populations and Samples

9. 3.What is the highest possible average grade that Hannah can have in a sample of 2 essays? To find the highest possible sample average, select the two essays with the highest scores and find the average. The two highest scores are 100 and 95. 9 1.3.1: Differences Between Populations and Samples

10. Formula for calculating an average Substitute the known values. Simplify. The highest possible sample average in a sample of two of Hannah’s essays is 97.5. 10 1.3.1: Differences Between Populations and Samples

11. 4.Suppose Hannah was asked to discuss 4 essays instead. What is the lowest possible average grade that Hannah can have in a sample of 4 essays? To find the lowest possible sample average, select the four essays with the lowest scores and find the average. The four lowest scores are 60, 80, 85, and 90. 11 1.3.1: Differences Between Populations and Samples

12. Formula for calculating an average Substitute the known values. Simplify. The lowest possible sample average in a sample of four of Hannah’s essays is 78.75. 12 1.3.1: Differences Between Populations and Samples

13. 5.What is the highest possible average grade that Hannah can have in a sample of 4 essays? To find the highest possible sample average, select the four essays with the highest scores and find the average. The four highest scores are 100, 95, 90, and 85. 13 1.3.1: Differences Between Populations and Samples

14. Formula for calculating an average Substitute the known values. Simplify. The highest possible sample average in a sample of four of Hannah’s essays is 92.5. 14 1.3.1: Differences Between Populations and Samples