📚

All Subjects

 > 

📊 

AP Stats

 > 

🎲

Unit 4

4.8 Mean and Standard Deviation of Random Variables

1 min readjune 3, 2020

Kanya Shah


The main takeaway from this section should be knowing how to calculate and interpret the standard deviation and mean. 

Center of a Discrete Random Variable

Mean or Expected value of a discrete variable is its average value over many, many repetitions of the same chance process. To find the mean or expected value of X, multiply each possible value of X by its probability and then add all of the products.
The mean is the balance point of a distribution. Formula: Summation(xi*pi)= mean of X
Critical Tip: DO NOT write the mean of a random variable as a non integer value if it is a decimal because almost all expected values are decimals. 

Variability of a Discrete Random Variable

The standard deviation of a discrete random variable measures how much the values of the variable typically vary from the mean.
The variance of X is SD^2= summation(xi-mean of x)^2 * pi .
The standard deviation of X is the square root of the variance so SD = sqrt(summation(xi-mean of x)^2 * pi)
If you decide to use your calculator, make sure you list how you got to your answer. Use context and don’t just put a number down as the answer. Show work to maximize the amount of points you get.

Resources:

Was this guide helpful?

🔍 Are you ready for college apps?
Take this quiz and find out!
Start Quiz
FREE AP stats Survival Pack + Cram Chart PDF
Sign up now for instant access to 2 amazing downloads to help you get a 5
Browse Study Guides By Unit
📆
Big Reviews: Finals & Exam Prep
✏️
Blogs
✍️
Free Response Questions (FRQs)
👆
Unit 1: Exploring One-Variable Data
✌️
Unit 2: Exploring Two-Variable Data
🔎
Unit 3: Collecting Data
📊
Unit 5: Sampling Distributions
⚖️
Unit 6: Inference for Categorical Data: Proportions
😼
Unit 7: Inference for Qualitative Data: Means
✳️
Unit 8: Inference for Categorical Data: Chi-Square
📈
Unit 9: Inference for Quantitative Data: Slopes
Join us on Discord
Thousands of students are studying with us for the AP Statistics exam.
join now
Play this on HyperTyper
Practice your typing skills while reading Mean and Standard Deviation of Random Variables
Start Game
💪🏽 Are you ready for the Stats exam?
Take this quiz for a progress check on what you’ve learned this year and get a personalized study plan to grab that 5!
START QUIZ
Hours Logo
Studying with Hours = the ultimate focus mode
Start a free study session
📱 Stressed or struggling and need to talk to someone?
Talk to a trained counselor for free. It's 100% anonymous.
Text FIVEABLE to 741741 to get started.
© 2021 Fiveable, Inc.