Finding z-scores

Front

What is a z-score?

Back

A z-score indicates how many standard deviations an element is from the mean of a distribution.

Front

How do you calculate a z-score?

Back

Z-score = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

What does a negative z-score indicate?

Back

A negative z-score indicates that the value is below the mean.

Front

What does a positive z-score indicate?

Back

A positive z-score indicates that the value is above the mean.

Front

If the mean weight of wallabies is 9lbs and the standard deviation is 1.5lbs, what weight corresponds to a z-score of -2?

Back

6lbs.

Front

If a student scores 31 on the ACT with a mean of 21 and standard deviation of 5, what is the z-score?

Back

2.00.

Front

What is the z-score for a home priced at $193,000 if the mean is $200,000 and the standard deviation is $10,000?

Back

-0.70.

Front

How do you interpret a z-score of 2.34 in a test score context?

Back

It means the student scored 2.34 standard deviations above the mean.

Front

What is the z-score for a student who scores 28 on the ACT with a mean of 21 and standard deviation of 5?

Back

1.40.

Front

What does it mean if two students have different z-scores but the same raw scores?

Back

It means they performed differently relative to their respective groups.