One student scored 700 on a math test with mean 514 and standard deviation 117. Another scored 30 on a different test with mean 21 and standard deviation 5.3. Who did better against their own test?

1. The two raw scores sit on different scales, so 700 against 30 tells us nothing on its own. 2. Convert each score to a z-score, which counts standard deviations above its own mean. 3. For the first score, 700 minus 514 is 186, and 186 divided by 117 is about 1.59. 4. For the second score, 30 minus 21 is 9, and 9 divided by 5.3 is about 1.70. 5. Both students are above average, since both z-scores are positive. 6. The second student stands about 1.70 standard deviations up against about 1.59 for the first. 7. So the student who scored 30 did better relative to the test they took. 8. Picking the 700 falls for the larger raw number and ignores the two different scales. _Source: OpenStax High School Statistics (CC BY 4.0), section 6.1 The Standard Normal Distribution_