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
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students turn observed frequency data into probabilities for each possible value of a random variable. They calculate the weighted average and use it to predict totals over many observations.
What Mastery Looks Like
- Students build a complete probability table from frequency data and check that the probabilities sum to 1. They correctly calculate the weighted average and use it to predict a total across many observations.
Common Misconceptions
- Students may divide frequencies by the wrong total or create probabilities that do not sum to 1. They may average outcomes without weighting them, treat the expected value as guaranteed, or forget to scale it for repeated selections.
How to Assess It
- Give this exit ticket: Among 20 households, pet counts were 0:4, 1:8, 2:6, and 3:2. Make the probability distribution, find the expected value, and predict the total pets in 50 households.
Lesson moves
Ways to Teach It
Have pairs draw numbered tiles 40 times with replacement, record frequencies, build a probability distribution, and calculate the expected number.
Ask students to write why an expected value of 1.3 pets does not mean any household has exactly 1.3 pets.
Give teams cards showing frequency tables, distributions, and expected values, then have them match each set and correct any mismatches.
Use a census table of vehicles per household to estimate the average per household and the total for 100 households.
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Printable HSS-MD.A.4 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSS-MD.A.4, with an answer key for the teacher on its own page. No account needed.
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Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSS-MD.A.2
Students must know how to compute and interpret expected value before finding it from an empirically built distribution.
- CCSS.Math.Content.HSS-MD.A.1
Students must define the random variable and organize its probability distribution before using empirical probabilities to compute expected value.
- CCSS.Math.Content.7.SP.C.7b
Empirical probability models from observed frequencies are needed to assign probabilities in a random variable distribution and compute expected value.
Keep exploring
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 ...
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