AP STATISTICS UPDATED 3 COMPREHENSIVE
STUDY GUIDE 2026
◉ If a graph is skewed, should we calculate the median or the mean?
Why?
Answer: median; it is resistant to skews and outliers
◉ If a graph is roughly symmetrical, should we calculate the median
or the mean? Why?
Answer: mean; generally is more accurate if the data has no outliers
◉ What is in the five number summary?
Answer: Minimum, Q1, Median, Q3, Maximum
◉ Relationship between variance and standard deviation?
Answer: variance=(standard deviation)^2
◉ variance definition
Answer: the variance is roughly the average of the squared
differences between each observation and the mean
◉ standard deviation
,Answer: the standard deviation is the square root of the variance
◉ What should we use to measure spread if the median was
calculated?
Answer: IQR
◉ What should we use to measure spread if the mean was
calculated?
Answer: standard deviation
◉ What is the IQR? How much of the data does it represent?
Answer: Q3-Q1; 50%
◉ How do you calculate standard deviation?
Answer: 1. Type data into L1
2. Find mean with 1 Variable Stats
3. Turn L2 into (L1-mean)
4. Turn L3 into (L2)^2
5. Go to 2nd STAT over to MATH, select sum(
6. Type in L3
7. multiply it by (1/n-1)
8. Square root it
,◉ What is the formula for standard deviation?
Answer:
◉ Categorical variables vs. Quantitative Variables
Answer: Categorical: individuals can be assigned to one of several
groups or categories
Quantitative: takes numberical values
◉ If a possible outlier is on the fence, is it an outlier?
Answer: No
◉ Things to include when describing a distribution
Answer: Center (Mean or Median), Unusual Gaps or Outliers, Spread
(Standard Deviation or IQR), Shape (Roughly Symmetric,
slightly/heavily skewed left or right, bimodal, range)
◉ Explain how to standardize a variable. What is the purpose of
standardizing a variable?
Answer: Subtract the distribution mean and then divide by standard
deviation. Tells us how many standard deviations from the mean an
observation falls, and in what direction.
, ◉ What effect does standardizing the values have on the
distribution?
Answer: shape would be the same as the original distribution, the
mean would become 0, the standard deviation would become 1
◉ What is a density curve?
Answer: a curve that (a) is on or above the horizontal axis, and (b)
has exactly an area of 1
◉ Inverse Norm
Answer: when you want to find the percentile: invNorm (area, mean,
standard deviation)
◉z
Answer: (x-mean)/standard deviation
◉ pth percentile
Answer: the value with p percent observations less than is
◉ cumulative relative frequency graph
Answer: can be used to describe the position of an individual within
a distribution or to locate a specified percentile of the distribution
STUDY GUIDE 2026
◉ If a graph is skewed, should we calculate the median or the mean?
Why?
Answer: median; it is resistant to skews and outliers
◉ If a graph is roughly symmetrical, should we calculate the median
or the mean? Why?
Answer: mean; generally is more accurate if the data has no outliers
◉ What is in the five number summary?
Answer: Minimum, Q1, Median, Q3, Maximum
◉ Relationship between variance and standard deviation?
Answer: variance=(standard deviation)^2
◉ variance definition
Answer: the variance is roughly the average of the squared
differences between each observation and the mean
◉ standard deviation
,Answer: the standard deviation is the square root of the variance
◉ What should we use to measure spread if the median was
calculated?
Answer: IQR
◉ What should we use to measure spread if the mean was
calculated?
Answer: standard deviation
◉ What is the IQR? How much of the data does it represent?
Answer: Q3-Q1; 50%
◉ How do you calculate standard deviation?
Answer: 1. Type data into L1
2. Find mean with 1 Variable Stats
3. Turn L2 into (L1-mean)
4. Turn L3 into (L2)^2
5. Go to 2nd STAT over to MATH, select sum(
6. Type in L3
7. multiply it by (1/n-1)
8. Square root it
,◉ What is the formula for standard deviation?
Answer:
◉ Categorical variables vs. Quantitative Variables
Answer: Categorical: individuals can be assigned to one of several
groups or categories
Quantitative: takes numberical values
◉ If a possible outlier is on the fence, is it an outlier?
Answer: No
◉ Things to include when describing a distribution
Answer: Center (Mean or Median), Unusual Gaps or Outliers, Spread
(Standard Deviation or IQR), Shape (Roughly Symmetric,
slightly/heavily skewed left or right, bimodal, range)
◉ Explain how to standardize a variable. What is the purpose of
standardizing a variable?
Answer: Subtract the distribution mean and then divide by standard
deviation. Tells us how many standard deviations from the mean an
observation falls, and in what direction.
, ◉ What effect does standardizing the values have on the
distribution?
Answer: shape would be the same as the original distribution, the
mean would become 0, the standard deviation would become 1
◉ What is a density curve?
Answer: a curve that (a) is on or above the horizontal axis, and (b)
has exactly an area of 1
◉ Inverse Norm
Answer: when you want to find the percentile: invNorm (area, mean,
standard deviation)
◉z
Answer: (x-mean)/standard deviation
◉ pth percentile
Answer: the value with p percent observations less than is
◉ cumulative relative frequency graph
Answer: can be used to describe the position of an individual within
a distribution or to locate a specified percentile of the distribution
