What measure describes how many standard deviations a raw score is from the mean?

What measure describes how many standard deviations a raw score is from the mean?

• A. Z scores (Standard scores)
• B. T scores
• C. Percentiles
• D. Confidence intervals

Answer: (A)

Expressing how far a raw score sits from the average in units of standard deviation is captured by a z-score. It is calculated as z = (X − μ) / σ, where X is the observed score, μ is the mean, and σ is the standard deviation. A z-score of 0 means the score is at the mean; positive values indicate above-average performance, negative values below. Because it uses the standard deviation in the denominator, the z-score shows how many standard deviations the score is from the mean, allowing direct comparisons across different tests or distributions. T scores are a scaled version of this idea (mean 50, SD 10), but the direct measure described here is the z-score. Percentiles describe position relative to the distribution, not distance in standard deviation units, and confidence intervals refer to a range for a population parameter rather than a single score’s deviation from the mean.

Expressing how far a raw score sits from the average in units of standard deviation is captured by a z-score. It is calculated as z = (X − μ) / σ, where X is the observed score, μ is the mean, and σ is the standard deviation. A z-score of 0 means the score is at the mean; positive values indicate above-average performance, negative values below. Because it uses the standard deviation in the denominator, the z-score shows how many standard deviations the score is from the mean, allowing direct comparisons across different tests or distributions. T scores are a scaled version of this idea (mean 50, SD 10), but the direct measure described here is the z-score. Percentiles describe position relative to the distribution, not distance in standard deviation units, and confidence intervals refer to a range for a population parameter rather than a single score’s deviation from the mean.