Distribution Spread Answer Key
About This Worksheet
This worksheet helps twelfth-grade Pre-Calculus students practice finding the mean and standard deviation of a discrete probability distribution. Students work through five distributions and calculate both the center of the distribution and how spread out the values are around that center.
The mean is found using the same expected-value idea from the previous worksheet. The standard deviation then measures how much the possible outcomes typically vary from that mean.
What Students Practice
Students practice finding the mean by multiplying each outcome by its probability and adding those products together. They then use the distribution values, the mean, and the probabilities to calculate the standard deviation.
The worksheet also asks students to describe the center and spread in words. A larger standard deviation means the outcomes are more spread out, while a smaller one means the values stay closer to the mean.
Why This Skill Matters
The mean alone does not tell the whole story of a probability distribution. Two distributions can have the same average but very different amounts of variability. Standard deviation helps describe that difference.
This skill also prepares students for later work with normal distributions, where mean and standard deviation play an especially important role.
Common Challenges
Students may confuse the standard deviation with the mean. Remind them that the mean describes the center, while the standard deviation describes how spread out the values are.
Another common mistake is forgetting that the deviations from the mean must be squared during the standard deviation calculation. This keeps negative and positive deviations from canceling each other out.
How To Use It
Teachers can use this worksheet after students understand expected value. It works well for guided instruction, calculator practice, independent work, or homework.
Parents and homeschool teachers can explain the two ideas simply: “The mean tells us the typical center, and the standard deviation tells us how far the results usually spread away from that center.”
Grade Alignment
This worksheet is intended for Grade 12 Pre-Calculus students studying discrete probability distributions. It reinforces expected value, variability, and statistical interpretation.
Students should already understand expected value. After this practice, they are ready to connect probability tables with histogram shapes and compare distributions.