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Grade 7 Math · Sampling and Statistical Inference

Grade 7 Sampling and Statistical Inference Practice Test

Build Grade 7 Math skills with five 10-question practice tests on populations, samples, sampling methods, bias, data summaries, variability, and statistical inferences.

Sampling and Statistical Inference Practice Tests

These Grade 7 Math practice tests help students use samples to learn about larger populations. Students identify populations and samples, compare sampling methods, recognize bias, summarize data, and make reasonable inferences.

Skills covered

  • Identifying populations, samples, statistics, and parameters
  • Recognizing simple random, systematic, stratified, and cluster samples
  • Identifying undercoverage, nonresponse, voluntary response, and wording bias
  • Calculating and interpreting mean, median, mode, range, and interquartile range
  • Understanding sampling variability and using sample proportions to estimate populations
  • Making conclusions that are supported by representative samples

How to use these practice tests

A population is the full group a study is about, while a sample is the smaller group from which data are collected. A representative random sample can be used to estimate a population, but sample statistics may vary from one sample to another. Check the sampling method and the data summary before making an inference.

For more Grade 7 Math practice, return to the Grade 7 Math category.

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Grade 7 Sampling and Statistical Inference Practice Tests

A 10-question Grade 7 Math practice test on populations, samples, sampling methods, bias, statistics, variability, and making inferences from data.

Identify the population and sample, recognize bias, calculate or interpret data summaries, and make conclusions supported by representative samples.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

Data set A has values 6,7,8,9,106, 7, 8, 9, 10. What is its range?

Please select an answer first.

Correct answer: A

The correct answer is 44.

  1. Identify the population and sample: Determine who or what the study is about and which observations were actually collected.
  2. Analyze the data: The range is maximum minus minimum: 10−6=410-6=4.
  3. Check the inference: Make sure the conclusion is supported by a representative sample and by the summary being used.

The range is maximum minus minimum: 10−6=410-6=4.

2. QuestionMultiple choice

Two classes have the same mean test score. Class 1 has a smaller range than Class 2. What does this tell you?

Please select an answer first.

Correct answer: B

The correct answer is Class 1 scores are less spread out overall.

  1. Identify the population and sample: Determine who or what the study is about and which observations were actually collected.
  2. Analyze the data: A smaller range indicates less overall distance between the smallest and largest values.
  3. Check the inference: Make sure the conclusion is supported by a representative sample and by the summary being used.

A smaller range indicates less overall distance between the smallest and largest values.

3. QuestionMultiple choice

The median of a sample is 2424 minutes. What is a reasonable interpretation?

Please select an answer first.

Correct answer: C

The correct answer is A typical middle value of the sample is about 24 minutes.

  1. Identify the population and sample: Determine who or what the study is about and which observations were actually collected.
  2. Analyze the data: The median identifies the middle of the ordered sample, so it describes a typical central value.
  3. Check the inference: Make sure the conclusion is supported by a representative sample and by the summary being used.

The median identifies the middle of the ordered sample, so it describes a typical central value.

4. QuestionMultiple choice

A data set has first quartile 1212 and third quartile 2020. What is its IQR?

Please select an answer first.

Correct answer: D

The correct answer is 88.

  1. Identify the population and sample: Determine who or what the study is about and which observations were actually collected.
  2. Analyze the data: The interquartile range is Q3−Q1=20−12=8Q_3-Q_1=20-12=8.
  3. Check the inference: Make sure the conclusion is supported by a representative sample and by the summary being used.

The interquartile range is Q3−Q1=20−12=8Q_3-Q_1=20-12=8.

5. QuestionMultiple choice

A random sample of 100 students finds that 35 walk to school. About how many of 800 students might walk to school?

Please select an answer first.

Correct answer: A

The correct answer is 280280.

  1. Identify the population and sample: Determine who or what the study is about and which observations were actually collected.
  2. Analyze the data: The sample proportion is 35div100=0.3535div100=0.35. Applying it to 800 gives 0.35cdot800=2800.35cdot800=280.
  3. Check the inference: Make sure the conclusion is supported by a representative sample and by the summary being used.

The sample proportion is 35div100=0.3535div100=0.35. Applying it to 800 gives 0.35cdot800=2800.35cdot800=280.

6. QuestionMultiple choice

A random sample of 200 households finds that 60% recycle. What is the best estimate for 1,500 similar households?

Please select an answer first.

Correct answer: B

The correct answer is 900900.

  1. Identify the population and sample: Determine who or what the study is about and which observations were actually collected.
  2. Analyze the data: Use the sample proportion: 0.60cdot1,500=9000.60cdot1{,}500=900 households.
  3. Check the inference: Make sure the conclusion is supported by a representative sample and by the summary being used.

Use the sample proportion: 0.60cdot1,500=9000.60cdot1{,}500=900 households.

7. QuestionMultiple choice

A sample estimate is 48% and a second random sample estimate is 52%. Which conclusion is most reasonable?

Please select an answer first.

Correct answer: C

The correct answer is The two estimates differ because random samples can vary.

  1. Identify the population and sample: Determine who or what the study is about and which observations were actually collected.
  2. Analyze the data: Different random samples can produce different statistics because of sampling variability.
  3. Check the inference: Make sure the conclusion is supported by a representative sample and by the summary being used.

Different random samples can produce different statistics because of sampling variability.

8. QuestionMultiple choice

Why should a sample estimate not usually be reported as an exact fact about the whole population?

Please select an answer first.

Correct answer: D

The correct answer is A sample can differ from the population because of sampling variability.

  1. Identify the population and sample: Determine who or what the study is about and which observations were actually collected.
  2. Analyze the data: Even a good sample gives an estimate, and another random sample could produce a slightly different result.
  3. Check the inference: Make sure the conclusion is supported by a representative sample and by the summary being used.

Even a good sample gives an estimate, and another random sample could produce a slightly different result.

9. QuestionMultiple choice

A random sample of 50 books finds that 18 are fiction. Which is the most appropriate inference?

Please select an answer first.

Correct answer: A

The correct answer is About 36% of the larger group of similar books may be fiction.

  1. Identify the population and sample: Determine who or what the study is about and which observations were actually collected.
  2. Analyze the data: The sample proportion is 18div50=0.3618div50=0.36, which can estimate the proportion in a similar larger population.
  3. Check the inference: Make sure the conclusion is supported by a representative sample and by the summary being used.

The sample proportion is 18div50=0.3618div50=0.36, which can estimate the proportion in a similar larger population.

10. QuestionMultiple choice

Which result gives the strongest basis for generalizing to all seventh graders in a district?

Please select an answer first.

Correct answer: B

The correct answer is A large random sample selected from every school in the district.

  1. Identify the population and sample: Determine who or what the study is about and which observations were actually collected.
  2. Analyze the data: A large random sample covering every school is more likely to represent the district population.
  3. Check the inference: Make sure the conclusion is supported by a representative sample and by the summary being used.

A large random sample covering every school is more likely to represent the district population.

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Frequently asked questions about Grade 7 Sampling and Statistical Inference

What is the difference between a population and a sample?

A population is the complete group being studied. A sample is a smaller group selected from that population to provide data.

Why does a random sample help with inference?

Random selection gives population members a fair chance of being included and makes the sample more likely to represent the population.

How many questions are on this page?

The page includes five mini tests with 10 questions each, for 50 Grade 7 Sampling and Statistical Inference questions in total.