In previous grades, you used data from a random sample to make inferences and draw conclusions about a population. In this section, you will investigate different simulations that could be used to generate a random sample.

Consider the following problem.

There are 100 pieces of fruit in Sidney’s Fruit Stand. Of those, there are 20 packages of blueberries, 40 pears, 25 apples, and 15 pineapples.

You can use color tiles to represent the fruit at Sidney’s Fruit Stand.

• Use 20 blue tiles to represent the blueberries.
• Use 40 green tiles to represent the pears.
• Use 25 red tiles to represent the apples.
• Use 15 yellow tiles to represent the pineapples.

In the color tile simulation, you can place 100 color tiles in a bag and randomly select 20 of them. Each color tile selected would represent one fruit, and you could record the results.

Another simulation could use a random number generator to select 20 random numbers between one and one hundred.

• Let 1 to 20 (20 total numbers) represent the blueberries.
• Let 21 to 60 (40 total numbers) represent the pears.
• Let 61 to 85 (25 total numbers) represent the apples.
• Let 86 to 100 (15 total numbers) represent the pineapples.

Click the image below to use a random number generator to simulate the random sample. Enter the appropriate numbers in the boxes, then click Randomize Now! to generate the set of 20 random numbers.

• How many sets of numbers do you want to generate? 1
• How many numbers per set? 20
• Number range: From 1 to 100
• Do you wish each number in a set to remain unique? Yes
• Do you wish to sort the numbers that are generated? Yes: Least to Greatest

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View a sample set of random numbers.

• For your set of random numbers, match each number with the fruit that it represents.
  Remember the following:
• Let 1 to 20 (20 total numbers) represent the blueberries.
• Let 21 to 60 (40 total numbers) represent the pears.
• Let 61 to 85 (25 total numbers) represent the apples.
• Let 86 to 100 (15 total numbers) represent the pineapples.

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View Answer from Sample Data

1, 10, 13 = blueberries
21, 36, 39, 40, 41, 51, 54, 59 = pears
65, 69, 73, 75, 76, 81 = apples
86, 90, 93 = pineapples

• For your set of random numbers, how many of each type of fruit are represented?

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View Answer from Sample Data

3 blueberries
8 pears
6 apples
3 pineapples

• For your set of random numbers, what percentage of the sample is each fruit? How does that compare to the known distribution of fruit in the population (the entire fruit stand)?

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View Answer from Sample Data

15% blueberries, 40% pears, 30% apples, 15% pineapples
This distribution is close to the population, which was 20% blueberries, 40% pears, 25% apples, and 15% pineapples.

Pause and Reflect

How do the characteristics of the random sample compare to the characteristics of the population?

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Check Your Answer

The characteristics of the random sample in this case, the distribution of the types of fruit represented in the sample, are close to the characteristics of the population.

If you increased the size of the sample, how do you think that would affect the relationship between the characteristics of the random sample and the characteristics of the population?

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Check Your Answer

As the size of the random sample increases, the characteristics of the sample are closer to the characteristics of the population.

Practice

Describe a simulation that could be used for each of the following situations.

1. A coin collection has 175 coins – 50 pennies, 75 nickels, 20 dimes, and 30 quarters. Create a random sample of 40 coins.

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   Need a hint?

   If you used color tiles or a random number generator, how would you represent each coin in the collection (population)?
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   Check Your Answer

   Place 175 color tiles in a bag: 50 red (pennies), 75 green (nickels), 20 yellow (dimes), and 30 blue (quarters). Randomly select 40 color tiles from the bag.
   
   Use a random number generator. Let 1 to 50 represent pennies, 51 to 125 represent nickels, 126 to 145 represent dimes, and 146 to 175 represent quarters. Generate a list of 40 random numbers, and identify which number represents which coin. Count the distribution of coins simulated by the random number generator.
2. A volleyball league has 90 jerseys. Twenty-five of the jerseys are blue, 15 are purple, 30 are black, and 20 are red. Create a random sample of 25 jerseys.

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   Need a hint?

   If you used color tiles or a random number generator, how would you represent each jersey in the league (population)?
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   Check Your Answer

   Place 90 color tiles in a bag: 25 blue, 15 yellow (to represent purple), 30 green (to represent black), and 20 red. Randomly select 25 color tiles from the bag.
   
   Use a random number generator. Let 1 to 25 represent blue, 26 to 40 represent purple, 41 to 70 represent black, and 71 to 90 represent red. Generate a list of 25 random numbers, and identify which number represents which color. Count the distribution of jerseys simulated by the random number generator.