A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers

Yes

Step-by-step explanation:

Let the numbers be p q r such that p>q>r

So p + q + r = 3q

2q = p+ r

And q< p but q> c,

So by Solving this would give

q= (p+ r)/2

so q is the mean of p & r.

Since the only other number that fits is q,

Then q is the mean of the numbers p,q,r

As so q is also the median of this set

Thus proving that the mean is the same as the median.