The marks of 49 students give a median class of 40-50, with cumulative frequency 20 before it, f = 16 and h = 10. One more student, who scored 92, is now added to the data. What happens to the median?

The new mark 92 lies well above the median class, so cf (20) and f (16) are untouched; only n changes, from 49 to 50. Before: $40+\left(\frac{24.5-20}{16}\right)\times 10=42.81$. After: $40+\left(\frac{25-20}{16}\right)\times 10=43.13$. The rise is $\frac{0.5}{16}\times 10=0.3125\approx 0.31$ — tiny, which is exactly why the median is called resistant to extreme values, while the mean would jump by roughly $\frac{92-\text{mean}}{50}$. A FALL of about 0.31 is what would happen if the extra mark lay below the median class (cf would become 21); 'unchanged' would need n to stay the same; and 3.1 is ten times too large.