ACT (Enhanced)MathematicsEasy
A statistician is analyzing a dataset. If the mean of a dataset is 60 and the standard deviation is 8, what is the z-score for a data point with a value of 76?
- A2.0
- B3.0
- C1.5
- D2.5
Show answer & explanationAnswer & explanation
Correct answer: A. 2.0
The z-score formula is z = (x - μ) / σ, where x is the data point, μ is the mean, and σ is the standard deviation. Substituting the given values: z = (76 - 60) / 8 = 16 / 8 = 2.0.
Why the other options are wrong
- B. This would result if the difference was 24 instead of 16.
- C. This would result if the difference was 12 instead of 16.
- D. This would result if the difference was 20 instead of 16.
Z-score (Standard Score)
A z-score measures how many standard deviations a data point is from the mean of a dataset. It standardizes data for comparison.
- Formula: z = (x - μ) / σ.
- Positive z-score means above the mean, negative means below.
- A z-score of 0 means the data point is equal to the mean.
Memory trick: Z-score: X minus Mu, all over Sigma.