Unit 8, Lesson 13
What Makes a Good Sample?
Grade 7
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100 students in grade 7 are asked how many hours they spend in front of a computer.
If the goal is to have the sample represent the population, which of the samples would work best? Which wouldn't work so well? Explain your reasoning.
An online shopping company tracks how many items they sell in different categories during each month for a year. Three different auditors each take samples from that data. Use the samples to draw dot plots of what the population data might look like for the furniture and electronics categories.
Auditor 1’s sample
A dot plot for “monthly sales of furniture online in hundreds.” The numbers 66 through 74 are indicated. The data titled "Auditor ones sample" are as follows: 67 hundred, 1 dot. 70 hundred, 1 dot. 73 hundred, 1 dot.
Auditor 2’s sample
Auditor 3’s sample
A dot plot for “monthly sales of furniture online in hundreds.” The numbers 66 through 74 are indicated. The data titled "Auditor three's sample" are as follows: 71 hundred, 2 dots. 73 hundred, 1 dot.
Population
Auditor 1’s sample
A dot plot for “monthly sales of electronics online in thousands.” The numbers 38 through 43 are indicated. The data titled "Auditor ones sample" are as follows: 39 thousand, 1 dot. 41 thousand, 1 dot. 43 thousand, 1 dot.
Auditor 2’s sample
A dot plot for “monthly sales of electronics online in thousands.” The numbers 38 through 43 are indicated. The data titled "Auditor two's sample" are as follows: 41 thousand, 1 dot. 43 thousand, 2 dots.
Auditor 3’s sample
A dot plot for “monthly sales of electronics online in thousands.” The numbers 38 through 43 are indicated. The data titled "Auditor three's sample" are as follows: 40 thousand, 1 dot. 41 thousand, 1 dot. 43 thousand, 1 dot.
Population
A sample that is representative of a population has a distribution that closely resembles the distribution of the population in shape, center, and spread.
For example, consider the distribution of plant heights, in cm, for a population of plants shown in this dot plot. The mean for this population is 4.9 cm, and the MAD is 2.6 cm.
A dot plot for “height in centimeters.” The numbers 1 through 11 are indicated. The data are as follows: 1 centimeter, 5 dots; 2 centimeters, 7 dots; 3 centimeters, 8 dots; 4 centimeters, 8 dots; 5 centimeters, 5 dots; 6 centimeters, 3 dots; 7 centimeters, 2 dots; 8 centimeters, 2 dots; 9 centimeters, 1 dot; 10 centimeters, 3 dots; 11 centimeters, 5 dots.
A representative sample of this population should have a larger peak on the left and a smaller one on the right, like this one. The mean for this sample is 4.9 cm, and the MAD is 2.3 cm.
A dot plot for “height in centimeters.” The numbers 1 through 11 are indicated. The data are as follows: 1 centimeter, 1 dot; 2 centimeters, 2 dots; 3 centimeters, 4 dots; 4 centimeters, 4 dots; 5 centimeters, 2 dots; 6 centimeters, 1 dot; 7 centimeters, 1 dot; 10 centimeters, 1 dot; 11 centimeters, 2 dots.
Here is the distribution for another sample from the same population. This sample has a mean of 5.7 cm and a MAD of 1.5 cm. These values are both very different from the population, and the distribution has a very different shape, so it is not a representative sample.
A dot plot for “height in centimeters.” The numbers 1 through 11 are indicated. The data are as follows: 3 centimeters, 1 dot; 4 centimeters, 3 dots; 5 centimeters, 3 dots; 6 centimeters, 2 dots; 7 centimeters, 1 dot; 8 centimeters, 2 dots; 9 centimeters, 1 dot.
A sample is representative of a population if they match closely. They are very alike in shape, center, and spread.
This dot plot shows the distribution for a population.
A dot plot labeled dollars per pound of catfish. The numbers 1.6 through 2.8 in increments of zero point 2 are indicated. The data are as follows: 1 point 6 dollars per pound, 4 dots. 1 point 7 dollars per pound, 20 dots. 1 point 8 dollars per pound, 24 dots. 1 point 9 dollars per pound, 2 dots. 2 dollars per pound, 10 dots. 2 point 1 dollars per pound, 2 dots. 2 point 2 dollars per pound, 6 dots. 2 point 3 dollars per pound, 4 dots. 2 point 4 dollars per pound, 4 dots. 2 point 5 dollars per pound, 6 dots. 2 point 6 dollars per pound, 10 dots. 2 point 7 dollars per pound, 4 dots. 2 point 8 dollars per pound, 4 dots.
This dot plot shows the distribution of a sample that is representative of the population.