A survey records the ages of 300 people only as a grouped frequency table with the classes 0–20, 20–40, 40–60 and 60–80. Which of these can NOT be obtained from that table?

Grouping trades detail for tidiness: once a reading has been dropped into the class 60–80 the table remembers only that it lay between 60 and 80, so the oldest person's exact age is gone for good and the best that can be said is that it lies in the last non-empty class. Everything else listed survives. The median class is found by cumulating the frequencies until half the total is passed, and the class with the greatest frequency — the modal class — can be read straight off. The mean can still be worked out, but only as an ESTIMATE, because the method assumes every reading in a class sits at that class's mark, which is exactly the assumption grouping forces on us. This is the standing trade-off of a grouped table, and it is why the range computed from grouped data is only ever approximate.