CCSS.Math.Content.HSS-MD.A.4
The standard
(+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.
Common Core State Standards for Mathematics
What this standard means
Students need to build a probability distribution from real data, not just from equally likely outcomes. They define the random variable, list possible values, turn frequencies into probabilities, and calculate expected value using a weighted average.
Mastery looks like a clear table with values, probabilities that sum to 1, and a correct expected value in context. Students often confuse expected value with the most common value, forget to divide by the total, or round too early. They also need practice explaining what the expected value means over many trials.
Ways to teach it
- Give groups a class survey on siblings, pets, or streaming services, then have them create a probability table and find the expected value.
- Ask students to write: Why can an expected number be a decimal when the actual outcome must be a whole number?
- Use a four-row frequency table and ask students to find probabilities, check the sum, and calculate expected value in five minutes.
- Have students use recent census or school data to predict totals for a larger group, such as pets in 200 households.
Plan a lesson for CCSS.Math.Content.HSS-MD.A.4
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Related standards
- CCSS.Math.Content.HSS-MD.B.6
(+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
- CCSS.Math.Content.HSS-MD.A.3
(+) Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected ...
- CCSS.Math.Content.HSS-MD.A.1
(+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability dist...
- CCSS.Math.Content.HSS-MD.A.2
(+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.