Check it out!

1

1.3.1: Differences Between Populations and Samples

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

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

1.3.1: Differences Between Populations and Samples

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.

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

• There are 15 ways Hannah can choose 2 out of the 6 essays.

6

1.3.1: Differences Between Populations and Samples

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

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

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

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

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

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

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

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