Task Sets: Understand that statistics can be used to gain information about a population by examining a sample - Common Core Math - Grade 7

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Recall / Warm-Up

A researcher records how every student in a class gets to school -- this entire class is the population she wants to describe: Walk — 8 students, Bus — 12 students, Car — 6 students, Bike — 4 students. How many students make up this population in total?

The population of a class is 30 students. Of that population, 12 students ride the bus to school. What fraction of the population rides the bus?

12/42

2/5

12/18

1/3

A survey asked 20 students what their favorite subject is. The results: Math — 7, Science — 5, English — 4, History — 4. Which statement is supported by the data?

More than half of the students prefer Math.

Math is the most frequently chosen subject in this survey.

Science and English are equally popular across all schools.

History is the least popular subject among all students.

Fluency Practice

To learn the most popular music genre among all 7th graders in a school, a teacher surveys all students in her music class. Is this sample biased or likely representative?

Likely representative — the music class includes students with various preferences.

Biased — only students enrolled in the music class are included, which over-represents students who already like music.

Biased — the sample is too small to be useful.

Likely representative — the teacher has good judgment about which students to include.

A school administrator wants to know students' opinions about the cafeteria menu. She randomly selects 40 student names from the school's complete enrollment list and surveys those students. What type of sampling does this describe?

Voluntary response sampling

Convenience sampling

Random sampling

Stratified sampling

A company posts a survey on its website asking customers to rate its product quality. Customers see the survey and choose whether to respond. Is this sample biased or likely representative of all customers?

Likely representative — the survey is available to any customer who visits the website.

Biased — only customers who visit the website and choose to respond are included, which skews toward those with strong opinions.

Likely representative — a large number of responses will fix any bias.

Biased — the company designed the survey, so the results will favor the company.

A health research team randomly selects $2{,}000$ adults from a national medical registry and finds that those who sleep $7$ – $8$ hours per night have fewer health problems. Which best describes the quality of this study's sample?

Low quality — the sample is too small to tell us anything about all adults.

Low quality — only adults registered in a medical system were eligible, which may miss some groups.

High quality — the sample is large, randomly selected from a broad population, and likely to produce a reliable estimate.

High quality — scientists conducted the study, so it must be reliable.

A student wants to know the favorite color of all 7th graders in her school. She surveys her 5 closest friends and finds that 4 prefer blue. She concludes, 'Blue is the favorite color of 7th graders at our school.' Identify TWO specific problems with her sampling method.

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Understanding Statistics and Sampling

Recall / Warm-Up

Fluency Practice