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Quizzes > High School Quizzes > Mathematics

AP Stats Unit 1 Practice Quiz

Master key concepts with focused practice tests

Difficulty: Moderate
Grade: Grade 12
Study OutcomesCheat Sheet
Colorful paper art promoting AP Stats Units Unlocked trivia quiz for high school students.

In a study of the heights of all 12th grade students at a high school, the data collected from a randomly selected group is called a:
Statistic
Parameter
Sample
Population
A sample is a subset of the population that is used to make inferences about the entire group. In this case, only a randomly selected group of students is studied, not the entire population.
Which of the following best describes a variable in statistics?
A summary measure
A characteristic that can take different values
A fixed number that does not change
An unpredictable event
A variable is a characteristic that can vary and take on different values among individuals in a data set. It is not a fixed value or a summary statistic.
What is a parameter in statistics?
A measure summarizing a sample
A variable with unknown values
An estimate from a sample
A numerical summary of a population
A parameter is a numerical value that describes a characteristic of an entire population. It is usually unknown and is estimated through sample statistics.
Which of the following is an example of a quantitative variable?
Favorite color
Birth month
Number of siblings
Type of pet
Number of siblings is a value that is expressed numerically and can be used in mathematical calculations. The other options are categorical or qualitative in nature.
What is the mean of a data set?
The middle value when data is ordered
The most frequently occurring value
The arithmetic average
The difference between the highest and lowest values
The mean is calculated by summing all the values in the data set and then dividing by the number of values. It is the arithmetic average and measures central tendency.
Which of the following measures of central tendency is most affected by outliers?
Mean
Median
Mode
Interquartile range
The mean is sensitive to extreme values because it takes every value into account in its calculation. In contrast, the median and mode are less affected by outliers.
When looking at a histogram, a skew to the right indicates which of the following about the data distribution?
Data are symmetrically distributed
There are no outliers present
The mean is generally less than the median
The median is generally less than the mean
A right-skewed distribution has a long tail on the right side which pulls the mean to a higher value compared to the median. Therefore, the median is typically less than the mean in such distributions.
Which of the following is true about a boxplot?
It displays the mean and standard deviation
It represents only normally distributed data
It shows the median and quartiles
It always displays the mode
A boxplot visually summarizes data using the median, the first and third quartiles, and potential outliers. It does not display the mean, standard deviation, or mode.
How does increasing the sample size primarily affect the standard error of the sample mean?
It makes the standard error equal to the standard deviation
It decreases the standard error
It has no effect on the standard error
It increases the standard error
Increasing the sample size reduces the standard error because the estimate of the mean becomes more precise. The standard error is calculated as the population standard deviation divided by the square root of the sample size.
In an experiment, what is the purpose of random assignment?
To evenly distribute confounding variables among treatment groups
To maximize the sample size
To eliminate the need for a control group
To ensure a representative sample of the population
Random assignment helps to evenly distribute potential confounding variables across the treatment groups. This minimizes biases and ensures that differences in outcomes are more likely due to the treatment.
Which scenario best illustrates Simpson's Paradox?
When a graph's scale is manipulated to exaggerate differences
When outliers distort the mean of a data set
When a small sample leads to a large margin of error
When the aggregated data shows one trend, but partitioned data reveals an opposite trend
Simpson's Paradox occurs when a trend that appears in several different groups of data reverses when the groups are combined. This demonstrates the potential pitfalls of relying solely on aggregated data without considering subgroup trends.
Which of the following is an appropriate conclusion when two variables have a strong correlation?
There is always an outlier in the data
Random sampling was not conducted
One variable causes the other
There is a predictable linear relationship between them
A strong correlation indicates that the two variables tend to change together in a predictable linear pattern. However, correlation does not imply causation, so one variable cannot automatically be assumed to cause the other.
In a scatter plot of two variables, a cluster of points that rises from left to right illustrates which type of correlation?
Positive Correlation
No Correlation
Negative Correlation
Nonlinear Correlation
A rising cluster from left to right indicates that as one variable increases, the other variable also tends to increase, which is characteristic of a positive correlation. This straight-line pattern is a common indicator of a linear relationship.
How can an outlier affect the standard deviation of a data set?
It typically increases the standard deviation
It converts the standard deviation into the interquartile range
It will always decrease the standard deviation
It will have no effect on the standard deviation
Outliers are extreme values that can greatly increase the overall variability of the data. Their presence usually results in a higher standard deviation because they increase the average distance from the mean.
Which of the following must be true for a probability distribution of a discrete random variable?
Each probability must be between 0 and 1, and their sum equals 1
The probabilities can be any real numbers as long as they add up to 0
All probabilities must be negative numbers
The sum of the probabilities of all possible outcomes is less than 1
A valid probability distribution for a discrete random variable requires that each assigned probability is between 0 and 1 and that the total of all probabilities sums exactly to 1. This ensures the outcomes cover all possibilities.
A researcher collects a sample of 50 observations. The population standard deviation is known to be 10. What is the standard error of the mean?
Approximately 7.07
Approximately 10
Approximately 0.71
Approximately 1.41
The standard error of the mean is calculated by dividing the population standard deviation by the square root of the sample size (10/√50). This computation yields roughly 1.41, indicating the variability expected in the sample mean.
In a 95% confidence interval for a population mean, what does the 95% confidence level imply?
The probability that the sample mean equals the population mean is 95%
95% of the sample data lies within the interval
There is a 95% probability that the population mean lies within the interval
If the experiment were repeated many times, approximately 95% of the intervals would contain the population mean
A 95% confidence level means that if the same sampling process were repeated numerous times, about 95% of the confidence intervals calculated from those samples would contain the true population mean. It does not imply a 95% probability for any single interval.
Which of the following statements about the Central Limit Theorem (CLT) is correct?
It allows the use of the normal model for the sampling distribution of the mean for large enough sample sizes
It only applies to populations that are normally distributed
It states that the distribution of sample means will always be skewed
It guarantees that a sample will perfectly represent the population
The Central Limit Theorem tells us that regardless of the shape of the underlying population distribution, the distribution of the sample means will approximate a normal distribution as the sample size increases. This justifies the use of normal probability models in many situations.
A quality control inspector finds that 2% of items produced in a factory are defective. If 200 items are randomly inspected, which of the following approximations is best for estimating the probability of finding exactly 5 defective items?
Use the normal distribution with mean 4 and standard deviation 1.98
Use the Poisson distribution with λ = 2
Use the binomial distribution B(200, 0.02) and calculate exactly for 5
Assume the probability is 5%
Since the problem involves a fixed number of independent trials with a constant probability of defect, the binomial distribution is the appropriate model to use. While other approximations exist, calculating directly with the binomial distribution yields the most accurate result in this case.
When conducting a hypothesis test, which error is made if the null hypothesis is rejected when it is actually true?
Measurement error
Type I error
Type II error
Sampling error
Rejecting a true null hypothesis is known as a Type I error. This error represents a false positive, where the test incorrectly indicates a significant effect when none exists.
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Study Outcomes

  1. Understand basic concepts of data collection and sampling methods.
  2. Analyze graphical representations of data to identify trends and patterns.
  3. Apply probability models to interpret experimental outcomes.
  4. Interpret statistical evidence and assess the reliability of conclusions.
  5. Evaluate and critique statistical studies for potential bias.

AP Stats Unit 1 Test & Practice Cheat Sheet

  1. Categorical vs Quantitative Variables - Categorical variables sort items into groups (think sorting M&Ms by color), while quantitative variables measure values (like weighing your snack!). Spotting the difference helps you pick the right stats tools and avoid embarrassing mix‑ups in your analysis. Study the guide
  2. Measures of Central Tendency - The mean is the "math average," the median is the middle score, and the mode is the most popular pick. In skewed data, the median often saves the day by resisting crazy outliers - so know when to crown each champion! See examples
  3. Measures of Spread - Range is the gap between highest and lowest, IQR zooms in on the middle 50%, variance tells you average squared distance, and standard deviation speaks your data's language in original units. These stats reveal if your data's chill or full‑on roller coaster. Crunch the numbers
  4. Graphical Displays - Histograms show bars of frequency, boxplots highlight the five-number summary and outliers, and stem‑and‑leaf plots give a quick numeric snapshot. These visuals transform raw numbers into eye‑catching stories! Visualize data
  5. Outlier Detection - Outliers are the quirky data points that stick out. Use the IQR rule (below Q1 - 1.5×IQR or above Q3 + 1.5×IQR) to flag these rebels so you can decide if they're genuine insights or just typos. Spot those outliers
  6. Normal Distribution & Empirical Rule - The classic bell curve means ~68% of data lies within ±1 SD, ~95% within ±2 SD, and ~99.7% within ±3 SD of the mean. It's your go‑to model for assessing probabilities and telling data stories. Meet the bell curve
  7. Z‑Scores - A z‑score shows how many standard deviations a value is from the mean: z = (x - μ) / σ. It's like converting currencies - now you can compare apples to oranges across different distributions! Standardize with z‑scores
  8. Data Transformations - Adding or subtracting a constant shifts your center without changing spread, while multiplying or dividing rescales both center and spread. This magic is key when switching units or normalizing data. Transform your data
  9. Five‑Number Summary - Minimum, Q1, median, Q3, and maximum give you a lightning-fast snapshot of your data's distribution. It's the secret sauce behind every boxplot and a great way to size up a dataset in seconds. Five‑number secrets
  10. Comparing Distributions - To compare datasets, check shape (symmetry vs skew), center (mean/median), spread (range/IQR/SD), and outliers. This detective‑style approach turns raw numbers into clear insights and cool discoveries! Compare like a pro
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