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One-variable data: Distributions and measures of center and spread SAT question

Math · Problem-Solving and Data Analysis · Medium · Answer it here, explanation included.

  • For the dot plot titled Class A:
    • The number line ranges from 1 to 7 in increments of 1.
    • The data for the dot plot are as follows:
      • 1: 1 dot
      • 2: 1 dot
      • 3: 3 dots
      • 4: 4 dots
      • 5: 5 dots
      • 6: 6 dots
      • 7: 7 dots
  • For the dot plot titled Class B:
    • The number line ranges from 14 to 20 in increments of 1.
    • The data for the dot plot are as follows:
      • 14: 1 dot
      • 15: 1 dot
      • 16: 3 dots
      • 17: 4 dots
      • 18: 5 dots
      • 19: 6 dots
      • 20: 7 dots

Each of the dot plots shown represents the number of glue sticks brought in by each student for two classes, class A and class B. Which statement best compares the standard deviations of the numbers of glue sticks brought in by each student for these two classes?

ExplanationShow

Choice B is correct. Standard deviation is a measure of the spread of a data set from its mean. The dot plot for class A and the dot plot for class B have the same shape. Thus, the frequency distributions for both class A and class B are the same. Since both class A and class B have the same frequency distribution of glue sticks brought in by each student, it follows that both class A and class B have the same spread of the number of glue sticks brought in by each student from their respective means. Therefore, the standard deviation of the number of glue sticks brought in by each student for class A is equal to the standard deviation of the number of glue sticks brought in by each student for class B.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

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