Is "average speed" equal to $|\text{average velocity}|$?

Question

So, apparently, $\text{instantaneous speed} = |\text{instantaneous velocity}|$.

But what about average speed? Is $\text{average speed} = | \text{average velocity} |$?

I can't find suitable explanations online and I keep finding contradicting explanations as well!

Answer 1

Average speed is given by $$\frac{\displaystyle\int_{t_1}^{t_2}|v(t)|\,dt}{t_2-t_1} $$ where $\int_{t_1}^{t_2}|v(t)|\,dt$ is total distance traveled and $t_2-t_1$ is the change in time.

Answer 2

Average velocity and average speed have one common difference that while average velocity can be zero(that is when you return back to the spot you started from) when average speed is not zero. Also when a man turns back while walking his average velocity not only becomes negative but can also deviate from the absolute value of average speed. Thus there are many cases when $$\text{average speed} = | \text{average velocity} |$$