Mr. Moore is installing new work benches in the wood shop. He wants the height of the benches to be best for students standing and working on projects. He decides to use the mean height of the students in the school as a guide. The school has 6th, 7th, and 8th grade students. Rather than using the heights of all the students in the school, he decides to take a sample of students.

A: Suppose Mr. Moore decides to use 20 seventh graders as the sample. Is this sample a random sample? Explain your reasoning.

B: Mr. Moore decides to use a random number generator to select 20 students from the school. Suppose that when choosing 20 students using the random generator on the graphing calculator, Mr. Moore’s sample is all eighth graders. Does that mean the sample is not a random sample? Explain your reasoning.

A: Suppose Mr. Moore decides to use 20 seventh graders as the sample. Is this sample a random sample? Explain your reasoning.

Ans: No, because he only chose the seventh graders which is invalid since he wants to have to use the mean height which involves the 6th, 7th and 8th graders.

B: Mr. Moore decides to use a random number generator to select 20 students from the school. Suppose that when choosing 20 students using the random generator on the graphing calculator, Mr. Moore’s sample is all eighth graders. Does that mean the sample is not a random sample? Explain your reasoning.

Ans: No, it is still a random sample. Since he is using a random generator, there is a possibility that the random generator would pick all students from the 8th grade. Unlike the first one, the random generator is not biased towards any grade, it is just a coincidence.

A) That's not a random sample because everyone doesn't have an equal chance of being selected

B) It is a random sample. All from eight grade is just a coincidence (which is very unlikely)

the mean and mad

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