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Quizzes > Mathematics > Advanced Math

AP Stats Chapter 2 Practice Problems Quiz: Test Your Data Exploration Skills

Ready to master AP Statistics Unit 2? Try this AP Stats Unit 2 Practice Test!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art collage of charts graphs and data blocks illustrating AP Stats Chapter 2 practice quiz concepts on teal background

This AP Stats Chapter 2 practice quiz helps you build skill in data exploration - graphs, center, spread, and outliers. Use it to spot gaps before the exam and get faster at reading distributions and computing medians, means, IQR, and standard deviation. For a quick warm‑up, take this short stats quiz first.

Which type of plot is most appropriate for displaying the distribution of a single quantitative variable?
Pie chart
Histogram
Line graph
Bar chart
A histogram groups quantitative data into bins and displays the frequency or relative frequency in each bin, effectively showing the shape, center, and spread of the distribution. Bar charts and pie charts are used for categorical data, and line graphs are used for data over time. For more detail on constructing and interpreting histograms, see .
What is the mode of a data set?
The middle value when data are ordered
The value that occurs most frequently
Half the range of the data
The average of all values
The mode is defined as the most frequently occurring value in a data set. Unlike the mean or median, a data set can have more than one mode or no mode at all if no value repeats. For more examples and practice, see .
How do you determine the median for a data set with an even number of observations?
Take the average of the two middle values
Choose the higher of the two middle values
Use the mode of the two middle values
Choose the lower of the two middle values
When there is an even number of observations, the median is calculated by averaging the two middle values in the ordered list. This ensures the median splits the data into two equal halves. See for further explanation.
Which measure of center is most resistant to the effect of outliers?
Mode
Median
Midrange
Mean
The median is not affected by extreme values because it depends only on the middle position of the ordered data. In contrast, the mean is pulled toward outliers, and the midrange (average of min and max) is highly sensitive. For more, see .
What is the interquartile range (IQR) of a distribution?
Half the range of the data
The sum of the first and third quartiles
The difference between the third quartile and the first quartile
The median of the data
The IQR measures the spread of the middle 50% of the data and is calculated as Q3 minus Q1. It is a robust measure of variability because it is not influenced by extreme values. For more details, visit .
If every observation in a data set is increased by 5, what happens to the standard deviation?
It remains the same
It doubles
It decreases by 5
It increases by 5
Adding a constant to every value shifts the entire distribution but does not change the spread. Therefore, the standard deviation remains unchanged. See .
When each value in a data set is multiplied by 3, how does the interquartile range change?
It remains the same
It is multiplied by 9
It is multiplied by 3
It is divided by 3
Multiplying each data value by a constant c multiplies any measure of spread (IQR, standard deviation, range) by that constant. Thus, the IQR is multiplied by 3. For more, see .
Given the data set {3, 7, 8, 9, 10, 12}, what is the five-number summary?
Min=3, Q1=7, Median=8.5, Q3=10, Max=12
Min=3, Q1=8, Median=9, Q3=10, Max=12
Min=3, Q1=7.5, Median=8, Q3=9.5, Max=12
Min=3, Q1=7, Median=9, Q3=10.5, Max=12
With six values, the median is the average of the 3rd and 4th: (8+9)/2=8.5. The lower half {3,7,8} has median Q1=7, and the upper half {9,10,12} has Q3=10. See .
For the data set {5, 7, 8, 9, 12, 14, 22}, which of the following is an outlier according to the 1.5×IQR rule?
5
None of the values are outliers
14
22
Q1=7, Q3=14, IQR=7, so fences are 7 - 1.5×7= - 3.5 and 14+1.5×7=24.5. Every value falls within these limits, so there are no outliers. For more details, see .
If a data set has mean 75 and standard deviation 5, what is the z-score of a value 85?
1.5
- 2.0
2.0
0.8
The z-score is (85 - 75)/5=10/5=2. A z-score indicates how many standard deviations a value is above (positive) or below (negative) the mean. Learn more at .
If a distribution is strongly right-skewed, which relationship between mean and median is most likely?
Mean equals median
Mean is greater than median
No systematic relation
Mean is less than median
In a right-skewed distribution, extreme large values pull the mean to the right, making it larger than the median. The median remains closer to the bulk of the data. See for a visual demonstration.
Calculate the sample standard deviation for the data set {2, 4, 4, 4, 5, 5, 7, 9}.
Approximately 2.50
Approximately 2.14
Approximately 3.00
Approximately 1.75
The mean is 5. Deviations squared sum to 32; dividing by n - 1=7 gives variance ?4.571, and the square root is ?2.14. For step-by-step calculation, see .
In a boxplot, what do the whiskers represent?
The range of the middle 50% of the data
The most extreme data points within 1.5×IQR of the quartiles
The interquartile range
The minimum and maximum data values
The whiskers extend from Q1 down to the lowest data point ? Q1 - 1.5×IQR and from Q3 up to the highest point ? Q3+1.5×IQR. Points beyond those are plotted individually as outliers. For more, see .
According to Chebyshev's theorem, at least what percentage of observations fall within two standard deviations of the mean for any distribution?
75%
99.7%
68%
95%
Chebyshev's theorem states that for any distribution, at least 1 - 1/k² of observations lie within k standard deviations of the mean. For k=2, that is 1 - 1/4=0.75 or 75%. See .
For a roughly bell-shaped distribution, approximately what percentage of data lie within three standard deviations of the mean?
75%
68%
95%
99.7%
The Empirical Rule for normal distributions states that about 68% of data lie within 1 SD, 95% within 2 SD, and 99.7% within 3 SD of the mean. For more, see .
If the mean of a distribution is 50 and the standard deviation is 4, what percentage of data lies between 42 and 58 under the Empirical Rule?
75%
68%
95%
99.7%
42 and 58 are two standard deviations from the mean (50 ± 2×4). Under the Empirical Rule, about 95% of observations lie within two standard deviations. See .
Group A has 30 observations with mean 80, and Group B has 20 observations with mean 70. What is the combined mean of all 50 observations?
74
77
76
75
The weighted mean is (30×80 + 20×70) / 50 = (2400 + 1400)/50 = 3800/50 = 76. For more on weighted averages, see .
If the interquartile range of a data set is 5 and you apply the linear transformation y = 3x - 4 to each observation, what is the IQR of the new data set?
15
11
7
5
A linear transformation y = a?x + b multiplies any measure of spread by |a| and does not change it by b. Here, |3|×5 = 15. For more, see .
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Study Outcomes

  1. Categorize Variables -

    Identify and distinguish between categorical and quantitative data types to choose appropriate analysis methods.

  2. Visualize Distributions -

    Construct and interpret histograms, stemplots, and boxplots to reveal patterns in data exploration.

  3. Compute Measures of Center -

    Calculate mean, median, and mode to summarize the central tendency of a data set effectively.

  4. Assess Variability -

    Determine range, interquartile range, variance, and standard deviation to quantify data spread.

  5. Identify Shape and Outliers -

    Analyze distribution shape and skewness, and detect outliers that may affect interpretation.

  6. Interpret Statistical Summaries -

    Integrate numerical and graphical summaries to draw accurate, context-driven conclusions from data.

Cheat Sheet

  1. Understanding Distribution Shapes -

    Distributions describe how data values are spread; common shapes include symmetric, right-skewed, and left-skewed (UCLA Statistics, 2021). Recognizing the shape helps when tackling ap stats chapter 2 practice problems on frequency tables or histograms. A quick mnemonic: "SRS" for Symmetric, Right, Skewed left or right reminds you of the three key forms.

  2. Mean vs. Median -

    The mean (average) and median (middle value) are measures of center but respond differently to outliers (Khan Academy). In unit 2 ap stats, use the median when data are skewed and the mean when distributions are roughly symmetric. Remember: the median is the "middle kid in line," so extreme values won't pull it off-center.

  3. Standard Deviation & Variance -

    Variance (s²) is the average squared deviation from the mean and standard deviation (s) is its square root: s = √[Σ(x - x̄)²/(n - 1)] (College Board AP Classroom). These metrics quantify typical distance from the mean, essential for ap statistics unit 2 practice tests. Think "V for Variance, S for Spread" to recall their roles.

  4. Interquartile Range (IQR) -

    IQR = Q3 - Q1 measures the middle 50% of data (Penn State Eberly). Use it in ap stats chapter 2 practice problems to assess spread without outlier influence. A handy tip: arrange data, find the 25th (Q1) and 75th (Q3) percentiles, subtract - your IQR gives a robust variability measure.

  5. Identifying Outliers -

    Apply the 1.5×IQR rule: data points < Q1 - 1.5×IQR or > Q3 + 1.5×IQR are considered outliers (Stat Trek). Spotting outliers in your unit 2 ap stats quizzes ensures accurate summaries and graphs. Remember: "1.5×IQR" is your go-to detective tool for unexpected values.

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