A club records the number of hours its 80 members exercise per month:
0-15 -> 11, 15-30 -> 19, 30-45 -> 24, 45-60 -> 16, 60-75 -> 10.
A member reports the median as 48.13 hours, having put cf = 11 into the formula. What is the correct median, and what went wrong?

Cumulative frequencies: 11, 30, 54, 70, 80, so $n=80$ and $\frac{n}{2}=40$. The first cf to reach 40 is 54, so the median class is 30-45 with $l=30,f=24,h=15$, and cf must be the cumulative frequency of the row immediately above it, namely 30. Median = $30+\left(\frac{40-30}{24}\right)\times 15=30+6.25=36.25$ hours. Putting cf = 11 uses the cumulative frequency of the FIRST class, two rows too high, which inflates the answer to 48.13. The other options describe two further slips and their results: cf = 19 (the previous class's plain frequency, not its cumulative frequency) gives 43.13, and cf = 54 (the median class's own cumulative frequency) gives 21.25.