True or false the mean is less sensitive to extreme scores than the median and this makes it a better measure than the median for highly skewed distributions

That would be FALSE.

The median is a robust statistic that can only move a little bit even given the largest outlier. A single outlier can affect the mean, the average, arbitrarily much.

When Bill Gates gives a talk at a school of 1000 people, the average wealth of the people in the school goes up by millions, but the median wealth of the people in the school hardly changes at all.