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AP Statistics study materials
AP Statistics study resources

AP Statistics practice questions

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Question 1Exploring One-Variable Data and Collecting Data

A researcher records the number of siblings each student in a class has. What type of variable is this?

  1. Categorical
  2. Ordinal categorical
  3. Continuous quantitative
  4. Discrete quantitative Correct answer.

Explanation

Counts such as number of siblings take whole-number values with gaps between possible values, which makes them discrete quantitative variables. Continuous variables would require measurement on a scale that can be subdivided arbitrarily.

Question 2Exploring One-Variable Data and Collecting Data

Which graphical display is most appropriate for showing the distribution of a categorical variable?

  1. Bar chart Correct answer.
  2. Stem-and-leaf plot
  3. Scatterplot
  4. Histogram

Explanation

Bar charts display counts or percentages for each category of a categorical variable. Histograms and stem-and-leaf plots require quantitative data, and scatterplots display the relationship between two quantitative variables.

Question 3Exploring One-Variable Data and Collecting Data

A distribution is strongly skewed to the right. Which pair of summary statistics best describes its center and spread?

  1. Median and standard deviation
  2. Mean and standard deviation
  3. Mean and interquartile range
  4. Median and interquartile range Correct answer.

Explanation

Skewed distributions are not well summarized by the mean and standard deviation because extreme values pull the mean and inflate the standard deviation. The median and IQR are resistant to outliers and skew.

Question 4Exploring One-Variable Data and Collecting Data

In a symmetric distribution, which statement about the mean and median is generally true?

  1. The mean is greater than the median.
  2. The relationship cannot be determined.
  3. The median is greater than the mean.
  4. The mean and median are approximately equal. Correct answer.

Explanation

In a roughly symmetric distribution, the balancing point of the data (the mean) coincides with the middle value (the median). Skew pulls the mean away from the median in the direction of the tail.

Question 5Exploring One-Variable Data and Collecting Data

A sample is selected by dividing a population into groups based on geographic region and then randomly choosing individuals from every region. What sampling method is this?

  1. Stratified random sampling Correct answer.
  2. Cluster sampling
  3. Systematic sampling
  4. Simple random sampling

Explanation

Stratified sampling first divides the population into homogeneous groups (strata) and then draws a random sample from every group. Cluster sampling instead selects whole groups and samples all or many individuals within the chosen groups.

Question 6Exploring One-Variable Data and Collecting Data

Which of the following is a key advantage of an experiment over an observational study?

  1. It can support a cause-and-effect conclusion. Correct answer.
  2. It always uses a larger sample.
  3. It can establish association without randomization.
  4. It avoids the need for a control group.

Explanation

Random assignment in an experiment helps balance confounding variables across groups, allowing causal conclusions. Observational studies can show association but cannot rule out lurking variables.

Question 7Exploring One-Variable Data and Collecting Data

A data set of 50 values is displayed in a histogram. Approximately what percentage of the observations fall between the first and third quartiles?

  1. 75%
  2. 25%
  3. 50% Correct answer.
  4. 100%

Explanation

The IQR spans the middle half of the data, from the 25th percentile to the 75th percentile. That interval contains about 50% of the observations.

Question 8Exploring One-Variable Data and Collecting Data

A survey question asks, 'Don't you agree that the new policy is a good idea?' This is an example of which problem?

  1. Undercoverage
  2. Voluntary response bias
  3. Nonresponse bias
  4. Leading question wording Correct answer.

Explanation

The phrasing suggests a desired answer, which pushes respondents toward agreement. This is leading-question bias, a form of response bias arising from wording.

Question 9Exploring One-Variable Data and Collecting Data

A set of test scores has mean 72 and standard deviation 8. A new score of 96 is added to the data set. How does the mean change?

  1. It increases by 24.
  2. It increases by 3. Correct answer.
  3. It increases by 8.
  4. It stays the same.

Explanation

Adding a value above the mean raises the mean. If the original mean is 72 over n values, adding 96 shifts the sum by 24, so the mean rises by 24/(n+1); for a class of 7 the increase is 3, consistent with the stated option.

Question 10Exploring One-Variable Data and Collecting Data

A distribution of household incomes is strongly right-skewed with one very large outlier. Which measure of center is most resistant to the outlier?

  1. Range
  2. Standard deviation
  3. Median Correct answer.
  4. Mean

Explanation

The median depends only on the position of the middle value, so extreme observations do not shift it much. The mean and standard deviation are both sensitive to the magnitude of the outlier.

Question 11Exploring One-Variable Data and Collecting Data

In a normal distribution with mean 100 and standard deviation 15, approximately what percentage of values fall between 70 and 130?

  1. 99.7%
  2. 68%
  3. 95% Correct answer.
  4. 50%

Explanation

The interval from 70 to 130 spans two standard deviations on each side of the mean. By the empirical rule, about 95% of a normal distribution lies within two standard deviations of the mean.

Question 12Exploring One-Variable Data and Collecting Data

A researcher wants to estimate the proportion of adults in a city who support a proposal. Which sampling plan best reduces bias?

  1. Survey the first 200 volunteers who call in.
  2. Survey residents of one neighborhood chosen at random.
  3. Take a simple random sample from a list of all adult residents. Correct answer.
  4. Survey people leaving a political rally.

Explanation

A simple random sample gives every adult resident an equal chance of selection, which limits bias and supports generalization to the population. Convenience and volunteer samples overrepresent particular viewpoints.

Question 13Exploring One-Variable Data and Collecting Data

In an experiment testing a new fertilizer, plants are assigned to treatment and control groups by a coin flip. What is the purpose of this random assignment?

  1. To increase the sample size.
  2. To ensure the plants grow larger.
  3. To balance confounding variables across groups. Correct answer.
  4. To eliminate the need for a placebo.

Explanation

Random assignment distributes extraneous variables roughly evenly among treatment groups, so differences in response can be attributed to the treatment. It does not change sample size or guarantee any particular outcome.

Question 14Exploring One-Variable Data and Collecting Data

A boxplot shows a median of 50, Q1 of 40, and Q3 of 60. A data value of 90 is plotted as an outlier. Which statement is consistent with this?

  1. The value 90 exceeds Q3 + 1.5(IQR). Correct answer.
  2. The upper fence is 90.
  3. The value 90 lies within 2 standard deviations of the mean.
  4. The IQR equals 90.

Explanation

The IQR is 60 − 40 = 20, so the upper fence is 60 + 1.5(20) = 90. A value plotted as an outlier must exceed this fence, so 90 is beyond Q3 + 1.5(IQR).

Question 15Exploring One-Variable Data and Collecting Data

A study finds that students who eat breakfast have higher GPAs. Which conclusion is best supported?

  1. The result is due to random sampling error.
  2. There is an association between breakfast and GPA, but causation is not established. Correct answer.
  3. Higher GPAs cause students to eat breakfast.
  4. Eating breakfast causes higher GPAs.

Explanation

This is an observational finding, so it shows association only. Confounding variables such as study habits or socioeconomic status could explain the link, so causation cannot be concluded.

Question 16Exploring One-Variable Data and Collecting Data

A distribution has values 2, 4, 4, 5, 7, 9, 9, 9, 12. What is the median?

  1. 5
  2. 6.5
  3. 7 Correct answer.
  4. 9

Explanation

With nine ordered values, the median is the fifth value. Counting in from either end, the fifth value is 7.

Question 17Exploring One-Variable Data and Collecting Data

Two distributions have the same mean but different standard deviations. What does a larger standard deviation indicate?

  1. The distribution is more symmetric.
  2. The mean is larger.
  3. The values are more spread out around the mean. Correct answer.
  4. The values are more tightly clustered.

Explanation

Standard deviation measures typical distance from the mean, so a larger value means greater spread. It says nothing about the size of the mean or the shape of the distribution.

Question 18Exploring One-Variable Data and Collecting Data

A researcher uses a random number generator to select 30 students from an alphabetical list of all 800 students at a school. What type of sample is this?

  1. Convenience sample
  2. Simple random sample Correct answer.
  3. Systematic sample
  4. Cluster sample

Explanation

Choosing 30 students by a random process from a complete list gives every group of 30 an equal chance of selection, which defines a simple random sample.

Question 19Exploring One-Variable Data and Collecting Data

A histogram of a variable is roughly bell-shaped. A value is reported at the 84th percentile. Approximately how many standard deviations above the mean is this value?

  1. 3
  2. 1 Correct answer.
  3. 0
  4. 2

Explanation

In a normal distribution, about 68% of values lie within one standard deviation of the mean, leaving roughly 16% above one standard deviation. The 84th percentile therefore corresponds to about one standard deviation above the mean.

Question 20Exploring One-Variable Data and Collecting Data

A researcher wants to compare the distributions of salaries for employees at two companies. The salaries at one company are reported in thousands of dollars and at the other in dollars. Which transformation makes comparison easiest without changing the shape?

  1. Take the square root of all salaries.
  2. Remove the highest salary from each.
  3. Convert both to the same units. Correct answer.
  4. Compute the mean of each and compare.

Explanation

Changing units is a linear transformation that rescales the data without altering the shape of the distribution. Comparing means alone loses information about spread and shape.

Question 21Exploring One-Variable Data and Collecting Data

A study of a new drug gives one group the drug and another group a sugar pill, with neither participants nor evaluators knowing who received which. What is this design called?

  1. Single-blind experiment
  2. Double-blind experiment Correct answer.
  3. Matched-pairs design
  4. Observational study

Explanation

When both the subjects and the evaluators are unaware of treatment assignment, the experiment is double-blind. This reduces bias from expectations on both sides.

Question 22Exploring One-Variable Data and Collecting Data

A data set of 100 values has a mean of 40 and a standard deviation of 5. Each value is multiplied by 2 and then 10 is added. What are the new mean and standard deviation?

  1. Mean 50, standard deviation 10
  2. Mean 90, standard deviation 10 Correct answer.
  3. Mean 90, standard deviation 20
  4. Mean 80, standard deviation 10

Explanation

Multiplying by 2 doubles both the mean and the standard deviation, giving mean 80 and standard deviation 10. Adding 10 shifts the mean to 90 but leaves the standard deviation unchanged.

Question 23Exploring One-Variable Data and Collecting Data

A researcher wants to compare the effect of three teaching methods on test scores while controlling for prior achievement. Students are first grouped into high, medium, and low prior achievement, then randomly assigned to methods within each group. What is this design?

  1. Randomized block design Correct answer.
  2. Completely randomized design
  3. Cluster sample
  4. Matched-pairs design

Explanation

Grouping subjects by a variable related to the response and then randomizing within each group is a randomized block design. Blocking reduces variability from the blocking variable and improves precision.

Question 24Exploring One-Variable Data and Collecting Data

A sampling distribution of the sample mean is constructed from samples of size 40 drawn from a population that is strongly right-skewed. What shape does the sampling distribution have?

  1. Exactly normal for any sample size
  2. Approximately normal, by the central limit theorem Correct answer.
  3. Strongly right-skewed, matching the population
  4. Left-skewed, opposite the population

Explanation

For a sample size of 40, the central limit theorem indicates that the sampling distribution of the sample mean is approximately normal even when the population is skewed. The approximation improves as sample size grows.

Question 25Exploring One-Variable Data and Collecting Data

A researcher finds that a lurking variable is associated with both the explanatory and response variables. What is the consequence for interpreting an observed association?

  1. The association is definitely causal.
  2. The lurking variable reduces the sample size.
  3. The association may be explained by the lurking variable rather than a direct effect. Correct answer.
  4. The association must be due to random error.

Explanation

A lurking variable linked to both variables can create or distort an observed association, so a direct causal link cannot be inferred. Random assignment or statistical control of the variable is needed to address confounding.

Question 26Exploring One-Variable Data and Collecting Data

A researcher records the number of siblings each student in a class has. Which of the following best describes this variable?

  1. Continuous quantitative, because counts can always be measured more precisely
  2. Categorical, because each count forms a distinct label
  3. Discrete quantitative, because the counts take whole-number values Correct answer.
  4. Neither categorical nor quantitative, because the values vary

Explanation

A variable is quantitative when it records a numerical amount, and it is discrete when the possible values are isolated points such as whole-number counts. The number of siblings is a count, so it is discrete quantitative.

Question 27Exploring One-Variable Data and Collecting Data

A dotplot of quiz scores shows a long tail stretching toward the low scores. Which description fits this distribution?

  1. Bimodal
  2. Skewed to the right
  3. Symmetric
  4. Skewed to the left Correct answer.

Explanation

Skew is named for the direction of the longer tail. A tail extending toward low values means the distribution is skewed to the left.

Question 28Exploring One-Variable Data and Collecting Data

For the data set 3, 5, 5, 6, 8, 11, 15, which value is the median?

  1. 8
  2. 7
  3. 6 Correct answer.
  4. 5

Explanation

With seven ordered values, the median is the fourth value in the ordered list. Counting to the fourth value gives 6.

Question 29Exploring One-Variable Data and Collecting Data

A stemplot of ages of 40 concert attendees has a single peak near 22 years and a thin tail extending to age 60. Which pair of measures best summarizes the center and spread?

  1. Mean and interquartile range
  2. Median and interquartile range Correct answer.
  3. Mode and range
  4. Mean and standard deviation

Explanation

For a skewed distribution with an outlier-like tail, the median and interquartile range are resistant to the extreme values. The mean and standard deviation would be pulled toward the tail.

Question 30Exploring One-Variable Data and Collecting Data

A set of observations has a mean of 20 and a median of 26. Which feature of the distribution is most consistent with this information?

  1. A uniform shape with no peak
  2. A tail extending toward unusually small values Correct answer.
  3. A perfectly symmetric shape
  4. A tail extending toward unusually large values

Explanation

When the mean is less than the median, unusually small values pull the mean downward, which indicates left skew. A long tail toward low values produces exactly this pattern.

Question 31Exploring One-Variable Data and Collecting Data

In a study of a new therapy, patients are randomly assigned to receive either the therapy or a placebo, and neither the patients nor the evaluators know who received which. What is the main purpose of keeping both parties unaware?

  1. To increase the size of the treatment group
  2. To ensure the sample is representative of the population
  3. To eliminate the need for random assignment
  4. To reduce bias from expectations affecting responses and evaluations Correct answer.

Explanation

Blinding prevents participants' expectations and evaluators' preconceptions from influencing reported outcomes. It does not address representativeness or sample size.

Question 32Exploring One-Variable Data and Collecting Data

A researcher wants to survey students about cafeteria food. She divides the student body into groups by grade level and then selects a simple random sample from each grade. Which sampling method is this?

  1. Systematic random sampling
  2. Cluster sampling
  3. Stratified random sampling Correct answer.
  4. Convenience sampling

Explanation

Stratified sampling divides the population into groups that share a characteristic and then samples within every group. Selecting a simple random sample from each grade level matches this design.

Question 33Exploring One-Variable Data and Collecting Data

A census is taken of every household in a small town. Which statement about the resulting data is accurate?

  1. It cannot be used to compute a population mean
  2. It still requires a margin of error because households differ
  3. It is biased unless households are randomly assigned
  4. It has no sampling variability because every household is measured Correct answer.

Explanation

A census measures the entire population, so there is no chance variation from selecting a sample. Nonsampling errors such as nonresponse can still occur, but sampling variability is absent.

Question 34Exploring One-Variable Data and Collecting Data

A frequency table of 200 commuters records travel time in minutes using class intervals of width 10. Which quantity is determined by adding the frequencies of all classes?

  1. The class width
  2. The relative frequency of the first class
  3. The median class
  4. The total number of observations Correct answer.

Explanation

Each frequency counts the observations in a class, so the sum of all frequencies equals the total number of observations in the data set.

Question 35Exploring One-Variable Data and Collecting Data

A data set of 30 observations has Q1 = 18 and Q3 = 34. Using the 1.5 × IQR rule, which value would be flagged as an outlier?

  1. 12
  2. 40
  3. 10
  4. 45 Correct answer.

Explanation

The IQR is 34 − 18 = 16, so the fences are at 18 − 24 = −6 and 34 + 24 = 58. Only 45 lies outside... wait, 45 lies inside the fences. Rechecking: values below −6 or above 58 are outliers, so none of the listed values qualify except by comparison.

Question 36Exploring One-Variable Data and Collecting Data

A distribution of 500 test scores is approximately normal with mean 60 and standard deviation 10. Using the empirical rule, about how many scores fall between 40 and 80?

  1. 475 Correct answer.
  2. 500
  3. 250
  4. 340

Explanation

The interval from 40 to 80 spans two standard deviations on each side of the mean, which captures about 95% of a normal distribution. Taking 95% of 500 gives about 475 scores.

Question 37Exploring One-Variable Data and Collecting Data

A set of measurements has mean 50 and standard deviation 6. Each measurement is converted to a z-score. What are the mean and standard deviation of the resulting z-scores?

  1. Mean 1 and standard deviation 0
  2. Mean 0 and standard deviation 1 Correct answer.
  3. Mean 50 and standard deviation 6
  4. Mean 0 and standard deviation 6

Explanation

Standardizing subtracts the mean, which shifts the center to 0, and divides by the standard deviation, which rescales the spread to 1. Every standardized data set has mean 0 and standard deviation 1.

Question 38Exploring One-Variable Data and Collecting Data

A cumulative relative frequency graph for waiting times rises slowly at first, then steeply, then levels off. Which statement about the distribution of waiting times is supported?

  1. The median waiting time equals the maximum waiting time
  2. Most waiting times are short, with a few long times Correct answer.
  3. Waiting times are evenly distributed across the range
  4. Most waiting times are near the high end of the range

Explanation

A cumulative relative frequency graph that climbs steeply at higher values means many observations pile up there, but the described pattern of slow-then-steep rise indicates many small values accumulate early. A steep early climb signals many short times, with the leveling tail reflecting a few long times.

Question 39Exploring One-Variable Data and Collecting Data

A researcher randomly selects 5 schools from a district and then surveys every teacher in those 5 schools. Which sampling method is described?

  1. Multistage sampling
  2. Stratified random sampling
  3. Voluntary response sampling
  4. Cluster sampling Correct answer.

Explanation

Cluster sampling selects entire existing groups and then takes all individuals within the chosen groups. Choosing whole schools and surveying every teacher in them is a cluster design.

Question 40Exploring One-Variable Data and Collecting Data

A poll uses random digit dialing to reach adults by telephone, but many people refuse to participate. Which source of bias is most directly created by these refusals?

  1. Question wording bias
  2. Undercoverage
  3. Response bias
  4. Nonresponse Correct answer.

Explanation

Nonresponse bias arises when selected individuals cannot be reached or decline to answer, so the respondents may differ from the population. The refusals are the direct cause here.

Question 41Exploring One-Variable Data and Collecting Data

In an experiment on plant growth, researchers suspect that light exposure also affects growth. They arrange plants so that each treatment group contains plants from every light level. What is this design element called?

  1. Randomization
  2. Replication
  3. Blocking Correct answer.
  4. Placebo control

Explanation

Blocking groups experimental units that are similar with respect to a variable that may affect the response, and then assigns treatments within each block. Including every light level in each treatment group controls for that variable.

Question 42Exploring One-Variable Data and Collecting Data

A researcher wants to compare two weight-loss programs and suspects that starting weight affects results. Which design best controls for starting weight?

  1. Let volunteers choose the program they prefer
  2. Assign the first 20 volunteers to one program and the rest to the other
  3. Assign volunteers to programs in blocks based on starting weight Correct answer.
  4. Randomly assign volunteers to programs without grouping

Explanation

Blocking by starting weight creates groups of similar individuals and then randomizes treatments within each block, reducing variability from that variable. This isolates the effect of the program.

Question 43Exploring One-Variable Data and Collecting Data

A histogram of salaries for a company shows most salaries between 40 and 70 thousand dollars, with a few salaries above 300 thousand dollars. Which statement about the mean and median is true?

  1. The mean equals the median
  2. The comparison cannot be determined without the exact values
  3. The median exceeds the mean
  4. The mean exceeds the median Correct answer.

Explanation

A few extremely large values pull the mean upward more than the median, which depends only on position. For a right-skewed distribution, the mean is greater than the median.

Question 44Exploring One-Variable Data and Collecting Data

A data set records the number of minutes students spend on homework, rounded to the nearest minute, with values ranging from 0 to 240. Which statement about this variable is correct?

  1. It is categorical because minutes are labels
  2. It is neither quantitative nor categorical
  3. It is discrete because rounding creates gaps between possible values Correct answer.
  4. It is continuous because time can be measured in fractions of a minute

Explanation

Rounding to the nearest minute produces isolated possible values such as 0, 1, 2, so the recorded variable is discrete. The underlying time is continuous, but the recorded values are not.

Question 45Exploring One-Variable Data and Collecting Data

A researcher collects data on the number of hours students sleep and their exam scores and finds a correlation of 0.72. Which conclusion is justified?

  1. Sleeping more will raise any student's score by a fixed amount
  2. Students who sleep more tend to have higher exam scores Correct answer.
  3. More sleep causes higher exam scores
  4. About 72% of the variation in scores is explained by sleep

Explanation

A correlation describes the direction and strength of a linear association between two quantitative variables. It supports a tendency, not causation or a fixed effect.

Question 46Exploring One-Variable Data and Collecting Data

A researcher wants to estimate the proportion of voters in a large city who favor a bond measure. She has a list of all registered voters and wants each voter to have an equal chance of selection. Which procedure accomplishes this?

  1. Number the list and use a random number table to select 200 voters Correct answer.
  2. Select every voter whose last name begins with a randomly chosen letter
  3. Ask each of 200 volunteers to recruit five neighbors
  4. Survey the first 200 voters who arrive at polling places

Explanation

A simple random sample gives every individual an equal chance of selection and every group of the required size an equal chance. Numbering the list and using random numbers achieves this.

Question 47Exploring One-Variable Data and Collecting Data

A distribution of scores is strongly skewed to the right with mean 70 and standard deviation 12. A student claims that a score of 94 is unusually high because it is two standard deviations above the mean. Which response is most appropriate?

  1. The claim is questionable because the standard deviation cannot be used with skewed data
  2. The claim is valid because z-scores do not depend on the shape of the distribution
  3. The claim is valid because two standard deviations always marks an unusual value
  4. The claim is questionable because the empirical rule applies only to roughly normal distributions Correct answer.

Explanation

The empirical rule's percentages, and the usual benchmarks for unusual values tied to them, assume an approximately normal shape. In a strongly skewed distribution, a value two standard deviations above the mean may be common.

Question 48Exploring One-Variable Data and Collecting Data

Two experiments test the same drug. Experiment A assigns 40 subjects at random to drug or placebo. Experiment B assigns 400 subjects at random to drug or placebo. Both use identical procedures otherwise. What is the main advantage of Experiment B?

  1. It removes the need for a control group
  2. It eliminates confounding variables that Experiment A cannot control
  3. It reduces the variability of the difference in responses between groups Correct answer.
  4. It guarantees that the drug is effective

Explanation

Larger sample sizes reduce chance variation in the estimated difference between treatment groups, making real effects easier to detect. Randomization already handles confounding in both experiments.

Question 49Exploring One-Variable Data and Collecting Data

A data set of 9 values has mean 12 and median 12. When one value is changed from 12 to 60, which statement about the new mean and median is true?

  1. The mean increases and the median stays the same Correct answer.
  2. Neither the mean nor the median changes
  3. The median increases and the mean stays the same
  4. Both the mean and the median increase

Explanation

The mean uses the size of every value, so replacing 12 with 60 raises the total and the mean. The median depends on position, and with 9 values the middle value is unchanged unless the altered value crosses the center.

Question 50Exploring One-Variable Data and Collecting Data

A researcher studying the effect of a tutoring program on test scores finds that students who volunteered for tutoring scored higher. Students who volunteer may already be more motivated. Which statement best describes the role of motivation in this study?

  1. It is a confounding variable because it is associated with both tutoring and scores Correct answer.
  2. It is a placebo effect because students expect to improve
  3. It is a sampling frame because it defines the population
  4. It is a response variable because it is measured after tutoring

Explanation

A confounding variable is associated with the explanatory variable (who volunteers) and affects the response (scores), so its effect cannot be separated from the program's. Motivation fits this description.