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AP Statistics Practice Quiz: Introducing Statistics: Why Is My Sample Not Like Yours?

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 7 questions to check your progress.

Question 1 of 7

A researcher takes two different random samples from the same large population of high school students and calculates the mean GPA for each sample. Which of the following statements best explains why the two sample means are likely to be different?

All Questions (7)

A researcher takes two different random samples from the same large population of high school students and calculates the mean GPA for each sample. Which of the following statements best explains why the two sample means are likely to be different?

A) The samples were not large enough to be accurate.

B) One of the sampling methods must have been biased.

C) Variation is a natural and expected occurrence when taking different samples from the same population.

D) One of the researchers must have made a calculation error.

Correct Answer: C

The core concept is that statistics calculated from different samples drawn from the same population will naturally vary. This is known as sampling variability and is an expected part of the statistical process, not necessarily an indication of error or bias.

Two pollsters survey random samples of voters from the same city to estimate the proportion who support a new policy. Pollster A finds 52% support, while Pollster B finds 56% support. The variation between these two statistics primarily raises which of the following statistical questions?

A) Which pollster used a more accurate measurement tool?

B) Is the difference between the proportions likely due to random sampling variation, or does it suggest a non-random factor?

C) How can the population proportion be calculated exactly from these two samples?

D) Why did the sample sizes differ between the two polls?

Correct Answer: B

The existence of variation between sample statistics from the same population forces us to ask whether that variation is simply due to chance (random) or if it points to a systematic, non-random cause (like different polling methodologies or changes over time).

A quality control inspector at a factory randomly selects 50 light bulbs from a large production batch and finds the average lifespan is 980 hours. A colleague, drawing a different random sample of 50 bulbs from the same batch, finds an average lifespan of 1010 hours. Assuming both followed the same correct procedure, this difference is most likely an example of what?

A) Non-random variation suggesting a flaw in the process.

B) Measurement bias from faulty equipment.

C) Random variation due to sampling.

D) A significant change in the manufacturing process between samples.

Correct Answer: C

Since both inspectors took random samples from the same population (production batch) and used the same procedure, the difference in their sample statistics is best explained by the natural, random variation that occurs between any two samples.

A teacher calculates the mean score of a random sample of her students on a test and gets 85. She then gives a new tutoring program to a different random sample of students from the same class, and their mean score on the same test is 92. If this variation is determined to be non-random, what could it suggest?

A) The two samples were simply different due to chance.

B) The tutoring program may have had a systematic effect on student scores.

C) The teacher made a mistake in calculating one of the means.

D) The population mean score is exactly halfway between 85 and 92.

Correct Answer: B

The content states that variation can be random or not. If the variation is determined to be non-random, it suggests a systematic reason for the difference. In this context, the systematic difference between the two groups is the introduction of the tutoring program.

When comparing statistics calculated from different samples drawn from the same population, the observed variation between the statistics can be broadly categorized into which two types?

A) Positive and negative

B) Expected and unexpected

C) Large and small

D) Random and non-random

Correct Answer: D

The provided content explicitly states that 'Variation in statistics for samples from the same population may be random or not.' This is the fundamental distinction used to interpret differences between sample statistics.

A biologist measures the average weight of a random sample of 30 fish from a large lake. One year later, she returns and measures the average weight of a new random sample of 30 fish from the same lake and finds the average weight has decreased. The observation of this variation between the two sample statistics should prompt the biologist to investigate which primary question?

A) Was the sample size of 30 large enough to represent the entire lake?

B) Did the scale used for measurement change between the two years?

C) Is the decrease in average weight a result of random sampling variability, or does it reflect a genuine change in the fish population?

D) What is the exact average weight of all fish in the lake?

Correct Answer: C

The key statistical question raised by the variation in sample statistics is whether the observed difference is simply due to chance (random variation) or if it represents a true, systematic change in the underlying population (non-random variation).

The fundamental principle that statistics from different random samples of the same population will naturally vary leads to which important conclusion about a single sample statistic?

A) A single sample statistic is a precise and exact measure of the population parameter.

B) A single sample statistic is likely biased unless the sample size is extremely large.

C) A single sample statistic is an estimate of the population parameter and contains some uncertainty due to random variation.

D) A single sample statistic is only useful if it is identical to a statistic from another sample.

Correct Answer: C

Because we know that any sample we take is just one of many possible samples, each with a potentially different statistic, we must conclude that our single sample statistic is not the 'true' population value. It is an estimate, and the expected variation tells us there is inherent uncertainty in that estimate.