Exploring one-variable data practice questions (AP Statistics)

Sample questions

All 4 free AP Statistics questions on this unit, from the free AP Statistics Practice Exam and the free AP Statistics Free-Response Practice Questions (FRQ) with Answers. Each answer is behind its own toggle; the whole paper, its PDF and the full answer key are on the exam page.

1. Question 12 marks · Shape, center & spread
   A distribution of household incomes is strongly skewed to the right. Which of the following is most likely true?
   • A.
     The mean is greater than the median
   • B.
     The mean is less than the median
   • C.
     The mean equals the median
   • D.
     The median is pulled toward the high incomes
   • E.
     The standard deviation is zero
   Show answerFrom the free AP Statistics Practice Exam →
2. Question 22 marks · Resistant statistics
   A data set of 25 house prices has one extreme outlier added to it. Which pair of statistics is MOST resistant to the outlier?
   • A.
     Mean and standard deviation
   • B.
     Mean and range
   • C.
     Median and IQR
   • D.
     Median and standard deviation
   • E.
     Range and IQR
   Show answerFrom the free AP Statistics Practice Exam →
3. Question 32 marks · z-scores
   Scores on a test are approximately normal with mean 70 and standard deviation 10. A student scores 85. The z-score is:
   • A.
     $1.5$, meaning the score is 1.5 standard deviations above the mean
   • B.
     $1.5$, meaning the score is 1.5 points above the mean
   • C.
     $15$, the distance from the mean
   • D.
     $0.85$, the percentile of the score
   • E.
     $-1.5$, since most students scored lower
   Show answerFrom the free AP Statistics Practice Exam →
4. Question 44 marks · Comparing distributions
   Comparing distributions. A consumer magazine tested 40 batteries of Brand A and 40 batteries of Brand B, recording how long each battery ran in a flashlight, in hours. For Brand A the five-number summary was: minimum 19, first quartile 22, median 24, third quartile 28, maximum 41; the mean was 25.3 hours and the standard deviation 4.6 hours. For Brand B the five-number summary was: minimum 14, first quartile 20, median 26, third quartile 31, maximum 36; the mean was 25.5 hours and the standard deviation 5.9 hours.
   (a)

   Compare the distributions of running times for the two brands.

   [2]
   (b)

   Using the 1.5 times IQR rule, determine whether the longest-running Brand A battery is an outlier. Show your work.

   [1]
   (c)

   A camper needs a battery that will run for at least 30 hours on a single trip. Based on the summary statistics, which brand should the camper choose? Justify your answer.

   [1]
   Show answerFrom the free AP Statistics Free-Response Practice Questions (FRQ) with Answers →

Key terms

The definitions and formulas AP Statistics expects for exploring one-variable data, typeset as they appear on the paper.

Shape, center, spread and outliers

The four things to mention when describing or comparing distributions, in context and with comparative language ("the median for A is higher than for B"). Shape: symmetric, skewed left or right, unimodal or bimodal.

Mean and median; resistance

The mean is pulled toward the tail of a skewed distribution and toward outliers; the median is resistant. In a right-skewed distribution the mean exceeds the median.

$$\bar{x} = \frac{\sum x_i}{n}$$

Standard deviation

The typical distance of values from the mean, with $n - 1$ in the denominator for a sample. It is not resistant; use the IQR with the median for skewed data.

$$s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n - 1}}$$

Interquartile range and the 1.5 IQR rule

The IQR is the range of the middle half of the data. A value is an outlier if it lies more than $1.5 \times IQR$ below the first quartile or above the third.

$$IQR = Q_3 - Q_1, \qquad \text{outlier if } x < Q_1 - 1.5\,IQR \text{ or } x > Q_3 + 1.5\,IQR$$

z-score

How many standard deviations a value lies from the mean; negative below, positive above. It lets you compare values from different distributions.

$$z = \frac{x - \mu}{\sigma}$$

Normal distribution and the empirical rule

The symmetric bell curve described by $N(\mu, \sigma)$. About 68 percent of values lie within one standard deviation of the mean, 95 percent within two and 99.7 percent within three.

Percentile

The $p$th percentile is the value below which $p$ percent of the data lie. Read it from a cumulative relative frequency graph or from a Normal table via the z-score.

Frequently asked questions

Other AP Statistics topics

• Exploring two-variable data
• Collecting data
• Probability, random variables and distributions
• Sampling distributions
• Inference for proportions
• Inference for means
• Chi-square tests
• Inference for slopes

All AP Statistics topics · AP Statistics exam guide · All free practice exams