AP Statistics - Chapter 6 Review

Front

What is a random variable?

Back

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).

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What is the mean of a random variable?

Back

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

Front

What is the standard deviation of a random variable?

Back

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

Front

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

Back

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

Front

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

Back

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)).

Front

What is a discrete random variable?

Back

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.

Front

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.

Front

What is the formula for variance?

Back

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

Front

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

Back

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

Front

What is the Central Limit Theorem?

Back

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.