IanB has identified one problem with the video, but two other things jumped out at me when I watched it.
1. What is the purpose of the "of the same level" at the end of the definition. I simply don't know what this is meant to mean, and it would be better left out.
2. I had trouble with the calculations of the average value of the squared voltage. The first thing I noticed was the division by 7. Why 7? Just because there are 7 points in the calculation doesn't mean that you should divide by it. What you are really trying to do is calculate the area under the curve without using calculus. The example given splits the first quarter of the sine-wave into 6 sections, so the calculation should approximate the area of each of the six sections, add them up and divide by 6! I was very surprised that the answer came out so accurately. According to my calculator, adding the seven squared values does not give an answer of 3.500 (not even close). A better solution would be to calculate the value at 7.5, 22.5..., 82.5 degrees, add them up and divide by six, but a better approximation would be to approximate each section by a trapezium and work with that. (This gives the standard trapezoidal rule for calculating the area under the curve; basically calculate the seven values as in the video, but give a weighting of 2 to all the values except the first and last, and divide by 12.) This gives a very good approximation.
My other comment is that I would have emphasised that what was happening with the calculations on the sine-wave was that we were calculating the instantaneous power, and then averaging that.