AP Statistics - Chapter 6 Review

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What is a random variable?

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A random variable is a numerical outcome of a random phenomenon. It can be discrete (taking specific values) or continuous (taking any value within a range).

Tags

CCSS.HSS.MD.A.2

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What is the mean of a random variable?

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The mean (or expected value) of a random variable is the average of all possible values, weighted by their probabilities.

Tags

CCSS.HSS.MD.A.2

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What is the standard deviation of a random variable?

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The standard deviation measures the dispersion or spread of a set of values around the mean. A higher standard deviation indicates more variability.

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How do you calculate the mean of the sum of two independent random variables?

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The mean of the sum of two independent random variables is the sum of their means: E(X + Y) = E(X) + E(Y).

Tags

CCSS.HSS.MD.A.2

Front

How do you calculate the standard deviation of the sum of two independent random variables?

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The standard deviation of the sum of two independent random variables is the square root of the sum of their variances: SD(X + Y) = √(Var(X) + Var(Y)).

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What is a discrete random variable?

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A discrete random variable is one that can take on a countable number of distinct values, such as the number of students in a class.

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What is a continuous random variable?

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A continuous random variable can take on an infinite number of values within a given range, such as the height of students.

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What is the formula for variance?

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Variance is calculated as the average of the squared differences from the mean: Var(X) = E[(X - μ)²].

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What is the relationship between mean and standard deviation in a normal distribution?

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In a normal distribution, the mean indicates the center, while the standard deviation indicates the spread of the data around the mean.

Tags

CCSS.6.SP.A.3

Front

What is the Central Limit Theorem?

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The Central Limit Theorem states that the distribution of the sample means approaches a normal distribution as the sample size increases, regardless of the original distribution.