In the last section, you used color tiles and a random number generator to simulate creating a random sample from a population. In this section, you will compare more than one random sample that is taken from the same population in order to look for patterns.

Revisit the problem from the previous section.

As before, use a random number generator to create a simulation. However, this time, generate three sets of random numbers.

• 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? 3
• 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 sample sets of random numbers.

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

Set 1: 5 blueberries, 6 pears, 5 apples, 4 pineapples
Set 2: 5 blueberries, 6 pears, 6 apples, 3 pineapples
Set 3: 4 blueberries, 8 pears, 4 apples, 4 pineapples

• For your set of random numbers, what percentage of each 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

  Set 1: 25% blueberries, 30% pears, 25% apples, 20% pineapples
  Set 2: 25% blueberries, 30% pears, 30% apples, 15% pineapples
  Set 3: 20% blueberries, 40% pears, 20% apples, 20% pineapples
  These distributions are close to the population, which was 20% blueberries, 40% pears, 25% apples, and 15% pineapples.

  Pause and Reflect

  You generated several random samples of the same size from a population with known characteristics. In general, how does the random sample compare to the population from which it was selected?

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  Check Your Answer

  A random sample is typically representative of the population from which it was selected.

  Practice

  1. A coin collection has 250 coins – 75 pennies, 100 nickels, 25 dimes, and 50 quarters. What would you expect a random sample of 50 coins from this collection to look like?

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     Need a hint?

     A random sample is representative of the population, so it should have a proportional distribution of coins.
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     Check Your Answer

     50 over 250 50 250 = 0.2, so multiply each number of coins by 0.2, which is the scale factor relating the random sample to the population.
     75 × 0.2 = 15 pennies
     100 × 0.2 = 20 nickels
     25 × 0.2 = 5 dimes
     50 × 0.2 = 10 quarters
  2. In a recent election, Candidate A received 110 votes, Candidate B received 70 votes, and Candidate C received 120 votes. A pollster interviewed 50 randomly selected voters as they were leaving the polls. What would you expect the pollster’s results to be?

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     Need a hint?

     A random sample is representative of the population, so it should have a proportional distribution of votes.
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     Check Your Answer

     50 over 300 50 300 = 1 over 6 1 6 , so multiply each number by 1 over 6 1 6 , which is the scale factor relating the random sample to the population. Multiplying 1 over 6 1 6 is the same as dividing by 6.
     110 ÷ 6 ≈ 18 votes for Candidate A
     70 ÷ 6 ≈ 12 votes for Candidate B
     120 ÷ 6 = 20 votes for Candidate C