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✍️ Free Response Questions (FRQs)
👆 Unit 1 - Exploring One-Variable Data
✌️ Unit 2 - Exploring Two-Variable Data
🔎 Unit 3 - Collecting Data
🎲 Unit 4 - Probability, Random Variables, and Probability Distributions
📊 Unit 5 - Sampling Distributions
⚖️ Unit 6 - Inference for Categorical Data: Proportions
😼 Unit 7 - Inference for Qualitative Data: Means
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📈 Unit 9 - Inference for Quantitative Data: Slopes
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Best Quizlet Decks for AP Statistics
- Unit 1 Key Terms (15-23%): Exploring One-Variable Data
- Unit 2 Key Terms (5-7%): Exploring Two-Variable Data
- Unit 3 Key Terms (12-15%): Collecting Data
- Unit 4 Key Terms (10-20%): Probability, Random Variables, and Probability Distributions
- Unit 5 Key Terms (7-12%): Sampling Distributions
- Unit 6 Key Terms (12-15%): Inference for Categorical Data: Proportions
- Unit 7 Key Terms (10-18%): Inference for Quantitative Data: Means
- Unit 8 Key Terms (2-5%): Inference for Categorical Data: Chi-Squared
- Unit 9 Key Terms (2-5%): Inference for Quantitative Data: Slopes
- Closing Thoughts
4.8 Mean and Standard Deviation of Random Variables
#anticipatingpatterns
#statisticalinference
⏱️ 1 min read
written by
kanya shah
June 3, 2020
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.
🎥Watch: AP Stats - Probability: Random Variables, Binomial/Geometric Distributions
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