John scores 2.85 where his school mean is 3.0 with deviation 0.7. Ali scores 77 where his school mean is 80 with deviation 10. Who stands better against his school?

1. The two scores are on different scales, so they must be converted to z-scores first. 2. For John the gap is 2.85 minus 3.0, which is minus 0.15, divided by 0.7. 3. That gives a z-score of about minus 0.21 standard deviations. 4. For Ali the gap is 77 minus 80, which is minus 3, divided by 10, giving minus 0.30 standard deviations. 5. Minus 0.21 is higher than minus 0.30, and higher is better for a grade, so John stands better against his school. 6. A z-score of minus 0.43 for John would need a school deviation of about 0.35 rather than 0.7. _Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 2 "Descriptive Statistics", section 2.7 Measures of the Spread of the Data_