Mini Practice Set Responses ~ Algebra/Data Analysis ~ Item 6


	Item 6 Mini Practice Set Responses

The Knitwear Company wants to know what sock colors teenagers will buy. The company is considering the three options below for collecting data.

Option 1:      Spend five days in the sock department of a randomly selected store and ask every person who enters what color socks they buy.
Option 2:      Spend one day in the sock departments of five randomly selected stores in randomly selected cities and ask every teenager who enters what color socks they buy.
Option 3:      Spend one day in eight randomly selected shopping centers and ask ten randomly selected teenagers at each shopping center what color socks they buy.

Complete the following in the Answer Book:

Which option gives the company the most representative sample of sock colors that teenagers will buy?
Use mathematics to justify why the other two options do not give the company the most representative sample.

Score Level 3 Paper
This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The student correctly chooses Option 2 as the most representative sample of sock colors. The student addresses the concept of variety by stating that Option 2 gives "more options." The justification for Option 1 is clearly presented and indicates that the wrong population is being sampled ("you are asking every person, and you are trying to find what color socks teenagers will buy, not everyone's opinion"). The justification for Option 3 also supports the solution and indicates that the sample size is too small ("you are only asking 10"). Even though Option 3 actually asks 80 teens, the idea that the sample size is too small is the same whether the student says 10 or 80. This response demonstrates a complete understanding and analysis of the problem.
Score Level 1 Paper
This response indicates little attempt to apply a reasonable strategy. The student correctly chooses Option 2 as the most representative sample of sock colors. The justification for Option 1 correctly identifies that the wrong population is sampled. ("Option one is just asking any random person not a teenager but everyone.") However, the justification for Option 3 is unclear. ("Option 3 wont come out as a good percentage because your only getting 80% of teenagers.") Option 3 samples a total of 80 teenagers, not 80% of the teenagers. This response demonstrates a minimal understanding and analysis of the problem. (Compare to this Level 1 anchor paper.)
Score Level 2 Paper
This response indicates an incomplete application of a reasonable strategy. The student correctly chooses Option 2 as the most representative sample of sock colors. The justification for Option 1 correctly observes that the wrong population is sampled ("not everyone may be teenagers"). No justification is required for why Option 2 gives the most representative sample, but the student correctly states "your asking only teenagers." The justification for Option 3 correctly identifies that the sample size is too small ("only asking eighty teenagers not all"). Although the justifications support the solution, there is no indication that "variety" is necessary in a representative sample. This response demonstrates a conceptual understanding and analysis of the problem.

Mini Practice Set Papers ~ Algebra/Data Analysis ~ Item 6

The Knitwear Company wants to know what sock colors teenagers will buy. The company is considering the three options below for collecting data.

Complete the following in the Answer Book:

Which option gives the company the most representative sample of sock colors that teenagers will buy?
Use mathematics to justify why the other two options do not give the company the most representative sample.

Score Level 3 Paper

This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The student correctly chooses Option 2 as the most representative sample of sock colors. The student addresses the concept of variety by stating that Option 2 gives "more options." The justification for Option 1 is clearly presented and indicates that the wrong population is being sampled ("you are asking every person, and you are trying to find what color socks teenagers will buy, not everyone's opinion"). The justification for Option 3 also supports the solution and indicates that the sample size is too small ("you are only asking 10"). Even though Option 3 actually asks 80 teens, the idea that the sample size is too small is the same whether the student says 10 or 80. This response demonstrates a complete understanding and analysis of the problem.

Score Level 1 Paper

This response indicates little attempt to apply a reasonable strategy. The student correctly chooses Option 2 as the most representative sample of sock colors. The justification for Option 1 correctly identifies that the wrong population is sampled. ("Option one is just asking any random person not a teenager but everyone.") However, the justification for Option 3 is unclear. ("Option 3 wont come out as a good percentage because your only getting 80% of teenagers.") Option 3 samples a total of 80 teenagers, not 80% of the teenagers. This response demonstrates a minimal understanding and analysis of the problem. (Compare to this Level 1 anchor paper.)

Score Level 2 Paper

This response indicates an incomplete application of a reasonable strategy. The student correctly chooses Option 2 as the most representative sample of sock colors. The justification for Option 1 correctly observes that the wrong population is sampled ("not everyone may be teenagers"). No justification is required for why Option 2 gives the most representative sample, but the student correctly states "your asking only teenagers." The justification for Option 3 correctly identifies that the sample size is too small ("only asking eighty teenagers not all"). Although the justifications support the solution, there is no indication that "variety" is necessary in a representative sample. This response demonstrates a conceptual understanding and analysis of the problem.