Percentiles and Z-Scores Quiz

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Questions and Answers

Which percentile lines up with a z-score of -3?

  • 15.87 percentile
  • 0.13 percentile (correct)
  • 50th percentile
  • 2.28 percentile

What is the percentile that corresponds to a z-score of -2?

  • 50th percentile
  • 2.28 percentile (correct)
  • 0.13 percentile
  • 15.87 percentile

What is the percentile that corresponds to a z-score of -1?

  • 15.87 percentile (correct)
  • 0.13 percentile
  • 2.28 percentile
  • 50th percentile

What is the percentile that corresponds to a z-score of 0?

<p>50th percentile (D)</p> Signup and view all the answers

Which of the following statements about z-scores is correct?

<p>A z-score of 0 corresponds to the mean. (B)</p> Signup and view all the answers

What is the z-score for a score that is two standard deviations above the mean?

<p>+1 (C)</p> Signup and view all the answers

What is the z-score for a score that is three standard deviations below the mean?

<p>-3 (A)</p> Signup and view all the answers

If a z-score is 1.5, what can we conclude about the corresponding score?

<p>The score is above the mean. (B)</p> Signup and view all the answers

If a score has a z-score of -0.5, what can we conclude about its position relative to the mean?

<p>The score is below the mean. (C)</p> Signup and view all the answers

Flashcards

What percentile does a z-score of -3 correspond to?

A z-score of -3 is the same as being three standard deviations below the mean, which corresponds to the 0.13th percentile.

What percentile does a z-score of -2 correspond to?

A z-score of -2 is the same as being two standard deviations below the mean, which corresponds to the 2.28th percentile.

What percentile does a z-score of -1 correspond to?

A z-score of -1 represents a value one standard deviation below the mean, which corresponds to the 15.87th percentile.

What percentile does a z-score of 0 correspond to?

A z-score of 0 represents a data point that is exactly at the mean, which is the 50th percentile.

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What does a z-score of +1 represent?

A z-score of +1 indicates a value one standard deviation above the mean.

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What does a z-score of -3 represent?

A z-score of -3 indicates a value three standard deviations below the mean.

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What can we conclude about a score with a z-score of 1.5?

A z-score of 1.5 indicates that the score is 1.5 standard deviations above the mean.

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What can we conclude about a score with a z-score of -0.5?

A z-score of -0.5 indicates that the score is 0.5 standard deviations below the mean.

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What does a z-score tell us?

A z-score measures how many standard deviations a particular value is away from the mean. A positive z-score signifies a value above the mean, while a negative z-score indicates a value below the mean.

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Study Notes

Z-Scores and Percentiles

  • A z-score of -3 corresponds to a percentile of approximately 0.13%.
  • A z-score of -2 corresponds to a percentile of approximately 2.28%.
  • A z-score of -1 corresponds to a percentile of approximately 15.87%.
  • A z-score of 0 corresponds to a percentile of 50% (i.e., the mean).

Properties of Z-Scores

  • A correct statement about z-scores is: z-scores can be positive or negative, depending on whether the score is above or below the mean.
  • A z-score of 2 corresponds to a score that is two standard deviations above the mean.
  • A z-score of -3 corresponds to a score that is three standard deviations below the mean.

Interpreting Z-Scores

  • If a z-score is 1.5, we can conclude that the corresponding score is 1.5 standard deviations above the mean.
  • If a score has a z-score of -0.5, we can conclude that it is 0.5 standard deviations below the mean.

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