Mean
Definition
The mean is the average of a set of numbers. It is found by adding up all the values and dividing by the total number of values.
Analogy
Think of the mean as the "middle" value that represents the entire group. Just like how a class representative can give you an idea of what the whole class is like, the mean gives you a sense of what the data set looks like overall.
Related terms
Median: The median is another measure of central tendency. It is the middle value when all values are arranged in order.
Mode: The mode is the value that appears most frequently in a data set.
Outlier: An outlier is a value that significantly differs from other values in a data set and can affect calculations such as the mean.
"Mean" appears in:
Subjects (2)
Study guides (8)
AP Statistics - 1.6 Describing the Distribution of a Quantitative Variable
AP Statistics - 1.7 Summary Statistics for a Quantitative Variable
AP Statistics - 2.5 Correlation
AP Statistics - 4.8 Mean and Standard Deviation of Random Variables
AP Statistics - 4.9 Combining Random Variables
AP Statistics - 4.11 Parameters for a Binomial Distribution
AP Statistics - 5.1 Introducing Statistics: Why Is My Sample Not Like Yours?
AP Statistics - 5.5 Sampling Distributions for Sample Proportions
Additional resources (3)
Practice Questions (20+)
- If the parameter in question is the mean, which type of hypothesis test should be used?
- What is the mean of a binomial random variable representing the number of successes in n independent trials with probability of success p?
- In a statistics class, the scores on a midterm exam are normally distributed with a mean of 75 and a standard deviation of 10. What percentage of students scored below 80 on the exam?
- What does the mean of a random variable represent?
- What does it mean if two random variables have the same mean but different standard deviations?
- How can you find the mean of a linear transformation of a random variable?
- What is the mean of the sum of two independent random variables equal to?
- What is the relationship between the mean and standard deviation of a standard normal distribution?
- A random variable, X, has a mean of 10 and a standard deviation of 2. If you transform X into a new random variable Y by adding a constant of 3 to each value, what is the mean and standard deviation of Y?
- A random variable, X, has a mean of 5 and a standard deviation of 3. If you transform X by multiplying each value by a constant of 6, what is the mean and standard deviation of the transformed variable, Y?
- If X and Y are two independent random variables and Z = X + Y, what is the mean of Z?
- A random variable, X, has a mean of 18. If you transform X by dividing each value by a constant of 2, what is the mean of the transformed variable, Y?
- Two random variables X and Y have means of 25 and 35 and standard deviations of 8 and 12, respectively. If Z = X + 2Y, what is the mean of Z?
- A and B are independent random variables. If A has a mean of 30 and a standard deviation of 12, and Y has a mean of 18 and a standard deviation of 5, what is the standard deviation of X - Y?
- If X has a mean of 20 and a standard deviation of 5, and Y has a mean of 10 and a standard deviation of 3, what is the mean of X + Y?
- X and Y are independent random variables. If X has a mean of 20 and a standard deviation of 4, and Y has a mean of 10 and a standard deviation of 3, what is the standard deviation of X + Y?
- If X has a mean of 15 and a standard deviation of 4, and Y has a mean of 8 and a standard deviation of 2, what is the mean of X - Y?
- If X has a mean of 15 and a variance of 4, and Y has a mean of 8 and a variance of 2, what is the variance of X - Y?
- Which of the following is the correct formula for calculating the mean of a discrete random variable?
- In a standard normal distribution, the mean and standard deviation are:
Resources
© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.