Distribution Compare
About This Worksheet
This worksheet helps twelfth-grade Pre-Calculus students practice comparing probability distributions using expected value and standard deviation. Students work through six pairs of distributions. Each pair already gives the mean and standard deviation, and students decide which distribution has the greater expected value and which has greater variability.
The goal is to help students understand that the mean and standard deviation describe two different features. The mean tells where the distribution is centered, while the standard deviation tells how spread out the outcomes are.
What Students Practice
Students practice comparing means directly to decide which distribution has the greater expected value. They then compare standard deviations to determine which distribution has more variability.
Some pairs have the same mean but different standard deviations. Others have different means and different spreads. This helps students see that the center and spread must be considered separately.
Why This Skill Matters
Two probability distributions can look very different even when they have the same expected value. Standard deviation helps explain that difference by showing how tightly or widely the outcomes are distributed.
This skill is useful when comparing games, risks, investments, or other situations where both the average result and the amount of uncertainty matter.
Common Challenges
Students may assume the distribution with the larger mean also has the larger standard deviation. Remind them that center and spread are separate ideas.
Another common mistake is interpreting a larger standard deviation as “better.” A larger standard deviation simply means more variability. Whether that is desirable depends on the context.
How To Use It
Teachers can use this worksheet after students understand expected value and standard deviation. It works well for independent practice, partner discussion, homework, or a quick comparison activity.
Parents and homeschool teachers can use two simple questions: “Which average is bigger?” and “Which spread number is bigger?” That keeps the two ideas separate.
Grade Alignment
This Grade 12 Pre-Calculus worksheet supports comparison of discrete probability distributions using mean and standard deviation.
Students should already know what expected value and standard deviation represent. After this practice, they can apply those ideas to fair and unfair games.