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Quizzes > High School Quizzes > Mathematics

AP Stats Chapter 2 Practice Quiz

Boost exam readiness with engaging test reviews

Difficulty: Moderate
Grade: Grade 12
Study OutcomesCheat Sheet
Colorful paper art promoting a trivia quiz on 10th-grade math concepts from chapter five.

What is the mean of the dataset {3, 5, 7}?
3
15
7
5
The mean is calculated by summing all numbers (3 + 5 + 7 = 15) and dividing by the total count (3), which gives 5. This is a fundamental concept in statistics.
In the dataset {1, 2, 2, 3, 4}, what is the mode?
1
3
2
4
The mode is the value that appears most frequently in a dataset. In this case, the number 2 appears twice while the other numbers appear only once.
What is the median of the dataset {3, 1, 4, 2, 5} when arranged in ascending order?
2
3
4
1
After arranging the data in order (1, 2, 3, 4, 5), the middle value is the third number, which is 3. The median splits the dataset into two equal halves.
Which type of graph is most appropriate for displaying the distribution of a continuous dataset?
Pie chart
Histogram
Line plot
Bar graph
Histograms are ideal for continuous data as they illustrate the frequency distribution over intervals. Other graph types like pie charts or bar graphs are less effective in showing the density of continuous data.
What is the range of the dataset {10, 15, 20, 25, 30}?
30
25
15
20
The range is found by subtracting the smallest value from the largest value. Here, 30 minus 10 gives a range of 20.
Which measure of central tendency is most affected by outliers?
Range
Mean
Median
Mode
The mean is sensitive to extreme values because it takes every data point into account. Outliers can significantly alter the mean, while the median and mode remain more robust.
In a symmetric distribution, which of the following statements is true about its measures of central tendency?
Only the mean and mode are equal
The mean, median, and mode are equal
Only the median and mode are equal
Only the mean and median are equal
For a symmetric distribution, the data are balanced around the center. This typically results in the mean, median, and mode being identical.
Which measure is considered the best indicator of variability in a dataset?
Interquartile Range (IQR)
Standard deviation
Range
Variance
Standard deviation is preferred since it provides a measure of spread in the same units as the original data. It accounts for all values in the dataset, unlike the range or IQR.
Which graph is most effective at summarizing the spread and identifying outliers in a dataset?
Stem-and-leaf plot
Histogram
Box plot
Bar graph
Box plots clearly display the median, quartiles, and potential outliers making them very useful for summarizing the spread of data. They offer a visual summary that is easy to interpret.
How is the interquartile range (IQR) of a dataset calculated?
Q3 plus Q1
Q3 minus Q1
Range divided by 2
Median minus Mean
The IQR is determined by subtracting the first quartile (Q1) from the third quartile (Q3). This measure captures the central 50% of the data, avoiding the influence of outliers.
What effect does adding a constant to every data point in a dataset have on its standard deviation?
It increases the standard deviation
It doubles the standard deviation
It leaves the standard deviation unchanged
It decreases the standard deviation
Adding a constant shifts all data points equally, so the overall spread about the mean remains unchanged. This means the standard deviation is not affected by the addition of a constant.
If a dataset has a mean of 50 and a standard deviation of 5, what is the z-score of a value 60?
5
1
2
10
The z-score is calculated by subtracting the mean from the value and then dividing by the standard deviation. For the value 60, (60 - 50) / 5 equals 2.
Approximately what percentage of data in a normal distribution lies within one standard deviation of the mean?
68%
99.7%
34%
95%
In a normal distribution, about 68% of the data falls within one standard deviation of the mean. This is a widely recognized property of the bell curve.
Which of the following is not a measure of spread in a dataset?
Mean
Standard Deviation
Range
Interquartile Range (IQR)
The mean is a measure of central tendency, not of spread. Measures that indicate variability include the range, IQR, and standard deviation.
Why is standard deviation a useful measure for understanding the variability of a dataset?
Because it is not affected by extreme values
Because it minimizes the differences between data points
Because it is expressed in the same units as the data
Because it is always larger than the range
Standard deviation is useful because it represents variability using the same units as the original data, making it easier to interpret. It provides insight into the average deviation of data points from the mean.
If an 11-value dataset has a median of 20 and the six highest values are each increased by 5, what is most likely true about the new median?
It remains the same
It decreases
It increases by 5
It increases by less than 5
In an ordered dataset with an odd number of values, the median is the middle value. Since the six highest values (including the original median) are each increased by 5, the median will also increase by 5.
When a dataset's mean is significantly higher than its median, what can be inferred about its distribution?
The distribution is skewed to the left
There is no outlier effect
The distribution is symmetric
The distribution is skewed to the right
A mean that is much higher than the median typically indicates a right-skewed distribution, where high-value outliers pull the mean upward. This asymmetry is a common indicator of skewness.
If every value in a dataset is multiplied by 3, by what factor do the interquartile range (IQR) and standard deviation change?
IQR is multiplied by 3, but standard deviation is multiplied by 9
Both are multiplied by 3
Both are multiplied by 9
Both remain unchanged
Multiplying every data point by a constant scales all measures of spread by that same constant. Therefore, both the IQR and the standard deviation are multiplied by 3.
For a box plot with Q1 = 15 and Q3 = 30, what is the interval within which data points are not considered outliers according to the 1.5*IQR rule?
[15, 30]
[-7.5, 52.5]
[0, 50]
[10, 40]
Using the 1.5*IQR rule, the lower limit is Q1 - 1.5*(IQR) and the upper limit is Q3 + 1.5*(IQR). Here, IQR = 30 - 15 = 15, so the limits are 15 - 22.5 = -7.5 and 30 + 22.5 = 52.5.
If the mean of a skewed distribution is greater than the median, which characteristic is most likely present?
Bimodality
Left-skewness
Symmetry
Right-skewness
When the mean is greater than the median, it usually indicates that the tail on the right side is longer, meaning the distribution is right-skewed. This occurs because high-value outliers pull the mean upward.
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Study Outcomes

  1. Identify key mathematical concepts presented in chapter five.
  2. Analyze problems using appropriate strategies for solving equations and expressions.
  3. Apply learned concepts to novel problems for practical understanding.
  4. Evaluate personal performance to pinpoint areas needing further review.
  5. Demonstrate increased confidence in tackling test and exam challenges.

AP Stats Chapter Reviews & Practice Tests Cheat Sheet

  1. Properties of the Normal density curve - This bell‑shaped icon always floats above the x‑axis, shelters an area of exactly one underneath, and mirrors itself around its center. The mean and median shake hands right at the peak, making it the superstar of symmetry. Quizlet: Chapter 2 Practice flashcards
  2. Understanding data transformations - Adding a constant shifts all your values up or down without messing with the spread or shape, while multiplying by a constant stretches or squashes both center and spread but leaves that shape intact. It's like moving furniture versus resizing your whole room. Quizlet: AP Stats Formulas Chapter 2
  3. Mastering the 68‑95‑99.7 rule - In a Normal world, about 68% of your data hangs out within one standard deviation of the mean, 95% within two, and a whopping 99.7% within three. This magic guideline helps you eyeball probabilities in a flash. Quizlet: AP Stats Formulas Chapter 2
  4. Calculating z‑scores - A z‑score tells you how many standard deviations an observation sits from the mean, using z = (x − μ)/σ. It's your personal GPS for locating data points on the Normal map. Quizlet: AP Stats Formulas Chapter 2
  5. Interpreting Normal probability plots - Plot your data on a probability plot: if the points cozy up along a straight line, you're in Normal territory; wiggles or curves mean your data might be off the beaten path. It's like a litmus test for Normality. Quizlet: AP Stats Formulas Chapter 2
  6. Effects of linear transformations - Multiply or divide your data by a constant, and you'll see center and spread change in lockstep, but the overall shape never budges. Think of it as resizing an image without changing its proportions. Quizlet: AP Stats Formulas Chapter 2
  7. Using the standard Normal distribution - The standard Normal is just a special case with mean 0 and standard deviation 1, making it the universal translator for different distributions. Whenever you need to compare apples to oranges, convert to z‑scores and you're golden. Quizlet: AP Stats Formulas Chapter 2
  8. Solving Normal distribution problems - Break it down by stating the problem, drawing a sketch, planning with z‑scores, calculating probabilities, and wrapping up in context. A clear strategy keeps errors at bay and confidence sky‑high. Quizlet: AP Stats Formulas Chapter 2
  9. Understanding density curves - Density curves sketch the big picture of your data's pattern, where the area under the curve equals 1 and directly corresponds to proportions. They're like roadmaps for the shape and spread of distributions. Quizlet: AP Stats Formulas Chapter 2
  10. Mean vs. median in skewed curves - On symmetric density curves, mean and median are BFFs at the center; on skewed ones, the mean gets pulled toward the tail while the median stays put. This tug‑of‑war reveals the direction and strength of skew. Quizlet: AP Stats Formulas Chapter 2
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