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Quizzes > High School Quizzes > Mathematics

AP Stats Unit 1 Practice Quiz

Test AP Stats with diverse probability and unit MCQs

Difficulty: Moderate
Grade: Grade 12
Study OutcomesCheat Sheet
Colorful paper art promoting AP Stats MCQ Mania, a trivia challenge for high school students.

This AP Stats MCQ quiz helps you practice Units 1 - 4 and probability with 20 quick questions. Use it to spot weak spots before the exam and build speed. Items cover one‑variable and two‑variable data, sampling and experiments, and basic probability, so you know what to review next.

What is a sample in statistics?
A subset of a population
The entire collection of individuals
A parameter that summarizes a dataset
A method of data collection
A sample is a subset of a population used to make inferences about the larger group. It is not the entire population and does not represent a complete census of all individuals.
Which measure of center is most resistant to outliers?
Range
Mean
Mode
Median
The median is less affected by extreme values since it only depends on the middle value of a sorted list. Outliers can pull the mean significantly, making the median a more robust measure of center.
Which graph is best for displaying the distribution of a continuous variable?
Pie chart
Histogram
Line graph
Bar graph
Histograms are ideal for displaying the distribution of continuous data because they show the frequency of data points within specified intervals (bins). This visual representation makes it easier to identify the shape and spread of the data.
What does the standard deviation measure in a data set?
Variability or spread
Central tendency
Correlation strength
Skewness
Standard deviation quantifies the amount of variation or dispersion of data values around the mean. A larger standard deviation indicates that the data points are spread out over a wider range of values.
Which type of variable typically represents counts and takes on discrete numeric values?
Quantitative discrete variable
Continuous variable
Ordinal variable
Categorical variable
Quantitative discrete variables consist of countable numbers and typically represent counts. They have distinct, separate values unlike continuous variables, which can take on any value within a range.
A data set has a mean of 50 and a standard deviation of 5. What is the z-score for a data value of 60?
2.0
-2.0
1.0
5.0
The z-score is calculated by subtracting the mean from the data value and then dividing by the standard deviation. Here, (60 - 50) / 5 equals 2.
In a box plot, what does the length of the box represent?
The range of the data
The interquartile range (IQR)
The standard deviation
The mean difference
The box in a box plot shows the interquartile range (IQR), which is the difference between the 75th and 25th percentiles. This illustrates the spread of the middle 50% of the data.
Which of the following is not a characteristic of a normal distribution?
Mean equals median equals mode
Bell-shaped curve
Symmetry
High variability
Normal distributions are symmetric, bell-shaped, and have the mean, median, and mode all equal. High variability is not a defining feature of normality; rather, it pertains to the spread and scale of the data.
If the correlation coefficient between two variables is nearly 0, what does this imply?
The variables are completely independent in all forms
A strong linear relationship exists
A weak or no linear relationship exists
A strong curvilinear relationship exists by default
A correlation coefficient near 0 suggests that there is little to no linear relationship between the variables. It does not, however, rule out the possibility of a non-linear association.
A study comparing test scores between two teaching methods uses random assignment of students. What type of study is this?
Observational study
Case-control study
Survey study
Experimental study
Random assignment of participants to different groups is a hallmark of experimental studies. This design helps control for confounding variables and supports causal inference.
Which measure of spread is most influenced by extreme values?
Range
Mode
Median
Interquartile Range (IQR)
The range is calculated as the difference between the maximum and minimum values, making it very sensitive to extreme data points (outliers). Other measures like the IQR are more robust in the presence of outliers.
What is a parameter in the context of statistics?
A measurable characteristic of a sample
A variable that introduces bias into the study
A measurable characteristic of a population
A statistic used to infer the sample distribution
A parameter is a numerical summary that describes a characteristic of the entire population. Unlike a statistic, which describes a sample, a parameter pertains to the full population.
Which graph is used to illustrate the relationship between two quantitative variables?
Scatterplot
Bar graph
Box plot
Histogram
Scatterplots are ideal for displaying the relationship between two quantitative variables. They help reveal patterns, trends, and potential correlations in the data.
What does the p-value in hypothesis testing indicate?
The probability of making a Type II error
The confidence level of the test
The probability that the null hypothesis is true
The chance of obtaining a result as extreme or more extreme than the observed result, assuming the null hypothesis is true
The p-value represents the probability of obtaining the observed data, or something more extreme, when the null hypothesis is true. It is a measure used to determine the strength of evidence against the null hypothesis.
How does increasing the sample size affect a confidence interval for the mean?
It has no effect on the confidence interval
It narrows the interval due to a reduced standard error
It makes the interval wider due to increased variability
It shifts the interval without affecting its width
Increasing the sample size reduces the standard error, which in turn narrows the confidence interval. A narrower interval indicates a more precise estimate of the population mean.
In a right-skewed distribution, which measure of center is most appropriate?
Mean
Median
Mode
Midrange
In a right-skewed distribution, extreme high values pull the mean upward, making it less representative of the data's center. The median, being less influenced by outliers, is a more appropriate measure.
A sample correlation coefficient of 0.85 is found between two variables. Which of the following is a common misinterpretation of this result?
One variable causes changes in the other
The association is statistically significant
There is a strong linear relationship between the variables
The data are free from any measurement error
A high correlation coefficient indicates a strong linear association but does not imply causation. Concluding that one variable causes changes in the other is a common misinterpretation of correlation.
Which statistical test is most appropriate for comparing the means of two independent groups?
Two-sample t-test
Linear regression analysis
Paired t-test
Chi-square test
When comparing the means of two independent groups, the two-sample t-test is the appropriate statistical method. It assesses whether the difference in sample means is statistically significant.
If a sample is taken from a normally distributed population, what is the distribution of the sample mean?
Skewed unless the sample size is very large
Approximately normal only for large samples
Uniformly distributed
Normally distributed regardless of sample size
When sampling from a normally distributed population, the sampling distribution of the mean is also normally distributed regardless of the sample size. This is a key property used in inferential statistics.
To estimate the proportion of students favoring a new teaching method, which sampling method is most likely to produce a representative sample?
Snowball sampling
Convenience sampling
Simple random sampling
Voluntary response sampling
Simple random sampling gives every individual in the population an equal chance of being selected, which minimizes selection bias. This method is most effective in producing a representative sample for estimating proportions.
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Study Outcomes

  1. Analyze core statistical concepts to understand data distributions.
  2. Apply probability rules and sampling methods in various scenarios.
  3. Interpret statistical outputs to draw meaningful inferences.
  4. Evaluate assumptions underlying statistical tests for data validity.
  5. Compare different statistical strategies for effective problem-solving.
  6. Develop targeted study techniques for improved exam performance.

AP Stats MCQ Quiz: Units 1-4 & Probability Cheat Sheet

  1. Categorical vs. Quantitative Variables - Variables come in two flavors: categorical ones sort data into groups (like your favorite ice cream flavor), while quantitative ones are all about numbers you can count or measure. Discrete quantitative data is countable (number of pets), and continuous data can take on any value in a range (your height!).
  2. Frequency & Relative Frequency Tables - These tables are your data's best friends, showing you raw counts or percentages for each category so you can spot patterns in a snap. Use relative frequencies to compare groups of different sizes without breaking a sweat.
  3. Graphical Data Displays - Bar graphs, pie charts, histograms, dot plots, and stem-and-leaf plots each have their superpower for visualizing data. Pick the right graph to highlight trends, clusters, or sneaky outliers hiding in your dataset.
  4. Measures of Center: Mean & Median - The mean is the math whiz's choice, averaging all values but sensitive to extreme scores, while the median sits coolly in the middle, ignoring outliers' drama. Use both to get the full story on your data's "middle ground."
  5. Measures of Spread: Range, IQR & Standard Deviation - Spread tells you how wild your data really is: range gives the simplest gap, IQR focuses on the cozy middle 50%, and standard deviation reveals how far values typically stray from the mean. Together they paint a full picture of data variability.
  6. Identifying Outliers with the 1.5×IQR Rule - Outliers are the rebels of your dataset, and the 1.5×IQR rule is your detective tool to spot them. Flag data points that lie way beyond the middle 50% to see if they're errors, special cases, or your next big insight.
  7. Percentiles & Quartiles - Percentiles rank your data, showing the percentage of observations below a given value, while quartiles slice your data into four equal parts. Together they help you understand where any particular score stands in the grand scheme of your distribution.
  8. Effects of Transformations - Adding or subtracting a constant shifts your data up or down but leaves its spread untouched; multiplying or dividing scales both center and spread. Use transformations to simplify, compare, or visualize data on your own terms.
  9. Normal Distribution & Empirical Rule - The classic bell curve shows how data clusters around the mean: about 68% lies within one standard deviation, 95% within two, and 99.7% within three. Knowing this rule lets you make quick, powerful predictions.
  10. Z‑Scores - A z‑score tells you exactly how many standard deviations a point sits from the mean, letting you compare scores from different distributions as if they were apples to apples. It's your go-to tool for standardizing and spotting extreme values.
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