Body temperatures are recorded to one decimal place and grouped as 36.0-36.4, 36.5-36.9, 37.0-37.4, 37.5-37.9. What is the true (continuous) lower boundary of the class 37.0-37.4?

Subtract half the gap between consecutive classes. The gap is $37.0-36.9=0.1$, so the adjustment is $\frac{0.1}{2}=0.05$ and the true lower boundary is $37.0-0.05=36.95$ (the class really runs 36.95-37.45, of width 0.5). 36.9 subtracts the whole gap and lands on the upper LIMIT of the previous class. 37.0 is the stated limit, which is precisely what the correction replaces — using it as l would overstate the median by 0.05. 36.5 is the lower limit of the previous class.