Answer :
Final answer:
We use z-scores to compare scores from different distributions. The z-score of the ACT is -1.48 and the z-score of the SAT is -1.50. Therefore, a score of 14 on the ACT is relatively better than a score of 1030 on the SAT.
Explanation:
To understand which score is relatively better, we need to translate the scores into z-scores, which are statistical measurements of a score's relationship to the mean in a group of scores. A z-score is a measurement of how many standard deviations a data point is from the mean. The formula for calculating z-score is:
z = (X - μ) / σ
Where: X is the data point, μ is the mean and σ is the standard deviation.
For the SAT score:
z = (1030 - 1518) / 325 = -1.50
For the ACT score:
z = (14.0 - 21.1) / 4.8 = -1.48
Since the ACT z-score (-1.48) is higher than the SAT z-score (-1.50), we conclude that a score of 14 on the ACT is relatively better than a score of 1030 on the SAT, although both scores are below the mean.
Learn more about z-score here:
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