If a score is 130 on a test with a mean of 100 and standard deviation of 15, what does this indicate?

If a score is 130 on a test with a mean of 100 and standard deviation of 15, what does this indicate?

• A. 2 standard deviations above the mean
• B. 1 standard deviation above the mean
• C. 0 standard deviation from the mean
• D. 3 standard deviations above the mean

Answer: (A)

A score can be understood in terms of how far it lies from the mean, measured in units of the standard deviation. To find that distance, subtract the mean from the score and divide by the standard deviation: (130 − 100) ÷ 15 = 2. This shows the score is two standard deviations above the mean. In a roughly normal distribution, a z-score of +2 places you in about the top 2–3% of scores, roughly the 97.5th percentile. It also matches the simple benchmark: two standard deviations above the mean equals 100 + 2×15 = 130.

A score can be understood in terms of how far it lies from the mean, measured in units of the standard deviation. To find that distance, subtract the mean from the score and divide by the standard deviation: (130 − 100) ÷ 15 = 2. This shows the score is two standard deviations above the mean. In a roughly normal distribution, a z-score of +2 places you in about the top 2–3% of scores, roughly the 97.5th percentile. It also matches the simple benchmark: two standard deviations above the mean equals 100 + 2×15 = 130.