In one group a value of 160.58 has a z-score of -1.5. In a second group a value of 162.85 also has a z-score of -1.5. What does that say?

1. A z-score reports position within a group, measured in that group's own standard deviations. 2. Both values carry a z-score of -1.5. 3. The sign is negative, so both values lie below their own group's mean. 4. The size is 1.5 in each case, so both lie one and a half standard deviations down. 5. So the two values hold matching positions inside two different groups. 6. The raw numbers 160.58 and 162.85 differ, so they are not the same measurement. 7. Matching z-scores do not force the groups to be the same, since each group has its own mean and spread. 8. A negative z-score can never mean the value sits above its average. _Source: OpenStax High School Statistics (CC BY 4.0), section 6.1 The Standard Normal Distribution_