AP Statistics Flashcards: Summary Statistics for a Quantitative Variable
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 29 cards to help you master important concepts.
What is the relationship between standard deviation and variance?
The variance is the square of the standard deviation.
Card 1 of 29
All Flashcards (29)
What is the relationship between standard deviation and variance?
The variance is the square of the standard deviation.
What is the Pth percentile?
The Pth percentile is the value in a data set where p% of the data is less than or equal to that value.
If a data set has a minimum of 15 and a maximum of 85, what is its range?
The range is the difference between the maximum and minimum, which is 85 - 15 = 70.
Describe the 1.5 x IQR rule for identifying outliers.
Outliers can be identified as values that fall more than 1.5 times the IQR below the first quartile (Q1) or above the third quartile (Q3).
What are three common measures of variability for quantitative data?
Three common measures of variability are the range, interquartile range (IQR), and standard deviation.
Why is it important to be able to explain the selection of a particular measure of center or variability?
The choice of measure affects the description of the data, and selecting a resistant or nonresistant measure depends on the presence of outliers and skewness.
What are the two main types of numerical summaries calculated for quantitative data?
The two main types are measures of center and position, and measures of variability.
A data set has Q1=50 and Q3=90. Using the 1.5xIQR rule, would a value of 155 be considered an outlier?
Yes, because the upper boundary is Q3 + 1.5(IQR) = 90 + 1.5(40) = 150, and 155 is greater than 150.
Define the median of a data set.
The median is the middle value of a data set that has been ordered from least to greatest.
What is the primary purpose of calculating measures of center and position?
These measures are calculated to describe the typical value and relative standing within a set of quantitative data.
Describe the standard deviation rule for identifying outliers.
Outliers can be identified as values that are 2 or more standard deviations away from the mean.
What is the first step required before you can find the median of a data set?
To find the median, the data set must first be ordered, typically from least to greatest.
What does the standard deviation measure?
Standard deviation is a statistic that measures the variability or spread of data values in a set.
A distribution has a mean of 100 and a standard deviation of 12. Is a value of 75 considered an outlier by the standard deviation rule?
Yes, because 75 is more than 2 standard deviations from the mean (100 - 2*12 = 76).
When is it more appropriate to use the median and IQR to describe a data set instead of the mean and standard deviation?
The median and IQR should be selected when the data set contains outliers or is strongly skewed, as they are resistant to these extreme values.
What are the first quartile (Q1) and third quartile (Q3)?
Q1 is the median of the lower half of the data, and Q3 is the median of the upper half of the data.
A data set has Q1=50 and Q3=90. Using the 1.5xIQR rule, would a value of -15 be considered an outlier?
Yes, because the lower boundary is Q1 - 1.5(IQR) = 50 - 1.5(40) = -10, and -15 is less than -10.
What is the primary purpose of calculating measures of variability?
These measures are calculated to describe the spread or dispersion of values in a set of quantitative data.
What is the interquartile range (IQR)?
The interquartile range (IQR) is a measure of variability calculated as the difference between the third quartile (Q3) and the first quartile (Q1).
An analyst is choosing between the range and the IQR to describe the spread of CEO salaries. Which is likely the better choice and why?
The IQR is the better choice because it is resistant to outliers, and CEO salary data is likely to have some extremely high values that would distort the range.
What does it mean for a statistic to be 'resistant'?
A resistant statistic is one that is not significantly affected by outliers or extreme values in the data set.
For a strongly skewed distribution of house prices, which measure of center would provide a more typical value: the mean or the median?
The median would be a better choice because it is resistant to the influence of a few very high-priced or low-priced homes (outliers).
How does changing the units of measurement of a data set affect its summary statistics?
Changing the units of measurement, such as converting feet to inches, affects all calculated statistics like mean, median, and standard deviation.
Which common measures of center and variability are resistant to outliers?
The median and the interquartile range (IQR) are resistant to outliers.
If a data set has Q1 = 30 and Q3 = 70, what is its interquartile range (IQR)?
The IQR is the difference between Q3 and Q1, which is 70 - 30 = 40.
Which common measures of center and variability are nonresistant to outliers?
The mean, standard deviation, and range are nonresistant to outliers.
Define the mean of a data set.
The mean is the sum of all data values divided by the total number of values.
What is the range of a data set?
The range is a measure of variability calculated as the difference between the maximum and minimum values in a data set.
What is a statistic?
A statistic is a numerical summary of sample data.