check it out! 1 1.3.1: differences between populations and samples
TRANSCRIPT
![Page 2: Check it out! 1 1.3.1: Differences Between Populations and Samples](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649ec65503460f94bd1e3d/html5/thumbnails/2.jpg)
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
![Page 3: Check it out! 1 1.3.1: Differences Between Populations and Samples](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649ec65503460f94bd1e3d/html5/thumbnails/3.jpg)
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
![Page 4: Check it out! 1 1.3.1: Differences Between Populations and Samples](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649ec65503460f94bd1e3d/html5/thumbnails/4.jpg)
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.
![Page 5: Check it out! 1 1.3.1: Differences Between Populations and Samples](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649ec65503460f94bd1e3d/html5/thumbnails/5.jpg)
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
![Page 6: Check it out! 1 1.3.1: Differences Between Populations and Samples](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649ec65503460f94bd1e3d/html5/thumbnails/6.jpg)
• There are 15 ways Hannah can choose 2 out of the 6 essays.
6
1.3.1: Differences Between Populations and Samples
![Page 7: Check it out! 1 1.3.1: Differences Between Populations and Samples](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649ec65503460f94bd1e3d/html5/thumbnails/7.jpg)
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
![Page 8: Check it out! 1 1.3.1: Differences Between Populations and Samples](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649ec65503460f94bd1e3d/html5/thumbnails/8.jpg)
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
![Page 9: Check it out! 1 1.3.1: Differences Between Populations and Samples](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649ec65503460f94bd1e3d/html5/thumbnails/9.jpg)
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
![Page 10: Check it out! 1 1.3.1: Differences Between Populations and Samples](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649ec65503460f94bd1e3d/html5/thumbnails/10.jpg)
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
![Page 11: Check it out! 1 1.3.1: Differences Between Populations and Samples](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649ec65503460f94bd1e3d/html5/thumbnails/11.jpg)
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
![Page 12: Check it out! 1 1.3.1: Differences Between Populations and Samples](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649ec65503460f94bd1e3d/html5/thumbnails/12.jpg)
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
![Page 13: Check it out! 1 1.3.1: Differences Between Populations and Samples](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649ec65503460f94bd1e3d/html5/thumbnails/13.jpg)
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
![Page 14: Check it out! 1 1.3.1: Differences Between Populations and Samples](https://reader035.vdocuments.net/reader035/viewer/2022062308/56649ec65503460f94bd1e3d/html5/thumbnails/14.jpg)
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