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AP Statistics 2.9 A Calculate the Mean and Standard Deviation for a Discrete Random Variable Questions

Practise calculating the expected value, variance, and standard deviation of discrete random variables, including transformed values and sums or differences.

Syllabus
Effective Fall 2026
Course
AP Statistics

Exam points

  • calculate expected value as the probability-weighted sum of every possible discrete outcome
  • calculate variance and standard deviation from deviations about the distribution's expected value
  • use linearity of expectation to find the mean of a transformed, summed, or differenced random variable
  • combine variances for independent random variables and take the square root for the resulting standard deviation

AP Statistics 2.9 A Calculate the Mean and Standard Deviation for a Discrete Random Variable Questions question 1

According to a 2017 national survey in Country B, the mean number of bedrooms in newly built houses was 2.9. Rodney, a researcher, believes the mean number of bedrooms in newly built houses in the country was different in 2024 than it was in 2017. To investigate his belief, he took a large random sample of newly built houses in Country B in 2024 and recorded the number of bedrooms in each house. The distribution of the number of bedrooms for the sampled houses is summarized in the table.

Distribution of the Number of Bedrooms for the Houses Sampled in 2024

Table for Question AP Statistics 2.9 A Calculate the Mean and Standard Deviation for a Discrete Random Variable Questions question 1 — AP Statistics

A.

What is the mean number of bedrooms for the sample of newly built houses in 2024?

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