For a given data set, the mean and median are always nearly equal.?

false. the mean is the sum of all the numbers divided by how many numbers there are. the median is the number that is exactly in the middle when you line all of them up in order.

thus, if you had just a few outliers that were much, much larger or smaller than the rest of the data, this could make the mean very different from the median.

for example, pretend somebody gives you the following set of numbers:

1, 1, 1, 1, 1, 1, 1, 1, 8693

the median of this set is clearly 1, while the mean is 966.7777

Really big difference betwen mean and median in this case! (because 8693) is such an outlier compared to the rest of the data.

No. Mean is the average while the median is in the middle when arranged numerically.

You can have a data set like:

1 1 1 1 1 1 1 1 1 991

The median here is 1, while the mean is 100

This statement would be false, though "nearly equal" is subjective. Let me give you an example where the mean and median would be very different:

1,1,1,1,1,1, 1000, 1000000, 3000000, 10000000

The median of these numbers is 1. The mean is 1,400,000.