AP Statistics Flashcards: Introducing Statistics: Why Be Normal?
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 10 cards to help you master important concepts.
In the context of sampling, what is 'random variation'?
Random variation refers to the expected, chance-based differences in statistics and distribution shapes that occur when multiple samples are drawn from the same population.
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In the context of sampling, what is 'random variation'?
Random variation refers to the expected, chance-based differences in statistics and distribution shapes that occur when multiple samples are drawn from the same population.
If two small, random samples of students' heights from the same large school show slightly different distribution shapes, what is the most likely explanation?
The variation in the shapes of the data distributions is most likely random, resulting from the chance inherent in which students were selected for each sample.
Why must we identify questions suggested by variation in sample shapes?
We must do this to decide if a sample's characteristics are just a random occurrence or if they reflect a meaningful property of the population we wish to understand.
A pollster takes a sample of voter preferences in April and another in October from the same population, and the distribution shapes are very different. What might this suggest?
This significant variation suggests the difference may not be random and could be caused by a non-random event, such as a major political event or campaign influencing voter opinion over time.
What are the two primary explanations for why the shapes of data distributions might vary?
The variation in the shapes of data distributions may be attributed to random chance or to non-random factors that indicate a systematic difference.
What is the primary goal of inferential statistics when dealing with variation between sample distributions?
Inferential statistics helps determine if the observed variation is small enough to be explained by random chance or large enough to conclude a real, non-random difference exists.
What fundamental question arises when observing variation in the shapes of distributions from different samples?
The key question is whether the observed variation is due to random chance (sampling variability) or if it suggests a meaningful, non-random difference between the samples.
A biologist observes that the distribution of wing lengths for a bird species is symmetric in one habitat but skewed in another. What statistical question does this variation suggest?
This suggests the question of whether the difference in distribution shape is due to random sampling variation or a non-random, systematic factor like environmental or genetic differences between the habitats.
What is meant by 'variation in the shapes of distributions of samples'?
This refers to the natural differences in shape, center, and spread that occur when different random samples are taken from the same population.
What does it mean if variation in sample distributions is determined to be 'not random'?
This means the difference in shape is too significant to be attributed to chance alone, suggesting a systematic cause or that the samples originate from different populations.