AP Statistics Flashcards: Introducing Statistics: Are My Results Unexpected?
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.
Why is it important to distinguish between random and non-random variation when analyzing categorical data?
Distinguishing between the two allows us to make inferences about a population and decide if an observed effect is real or just a coincidence of sampling.
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Why is it important to distinguish between random and non-random variation when analyzing categorical data?
Distinguishing between the two allows us to make inferences about a population and decide if an observed effect is real or just a coincidence of sampling.
What does it mean if the variation between observed and expected counts is determined to be 'random'?
It means the difference is likely due to natural sampling variability and is not significant enough to reject the initial assumption or hypothesis.
If a six-sided die is rolled 60 times and the number '4' appears 15 times (observed) instead of the expected 10 times, what statistical question arises?
The question is whether this variation (15 observed vs. 10 expected) is a plausible outcome due to random chance, or if it suggests the die is biased.
What are the two possible explanations for variation between observed and expected counts?
The variation may be attributed to random chance (sampling variability) or it may be the result of a non-random, systematic factor.
A company claims its customers are equally split among four regions. In a sample, the observed counts differ from this expected equal split. What is the first step in the statistical analysis?
The first step is to identify the questions suggested by this variation, primarily whether the difference is due to random sampling or a real preference difference among regions.
Define 'Observed Counts' in the context of categorical data.
Observed counts are the actual frequencies or tallies of outcomes recorded in each category from a sample or experiment.
What is the central question raised by the variation between observed and expected counts in categorical data?
The central question is whether this variation is simply due to random chance or if it indicates a genuine, non-random effect or pattern.
What is meant by 'variation' in the analysis of categorical data counts?
Variation refers to the differences or discrepancies between the data actually collected (observed counts) and the data anticipated under a specific model (expected counts).
What does it imply if the variation between observed and expected counts is determined to be 'not random'?
It implies the difference is statistically significant, suggesting the observed outcome is unlikely to have happened by chance alone and the initial hypothesis may be incorrect.
Define 'Expected Counts' in the context of categorical data.
Expected counts are the theoretical frequencies we would anticipate in each category if a specific assumption or null hypothesis were true.