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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.
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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?
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1.3.1: Differences Between Populations and Samples
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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1.3.1: Differences Between Populations and Samples