Mean is the arithmatic average of a given data set. So,

There are seven data in the data set.
According to the given problem,

Combine the like terms of the numerator.
Multiplying 7 to each sides of equation.
53 + p + q + r = 77
53 + p + q + r - 53 = 77 - 53 Subtract 53 from each sides.
p + q + r = 24
Next step is to divide each sides by 3 so that we can write this in form of mean of p, q and r. Therefore,

So, mean of p, q and r = 8.
I hope this helps you!.