Average, RMS value, and standard deviation. The average, RMS value, and standard deviation of a vector are related by the formula rms(x)? = avg(x)2 + std(x). (3.5) Average, RMS value, and standard deviation. Use the formula (3.5) to show that for any vector r, the following two inequalities hold: | avg(x)| < rms(r), std(x) < rms(). Is it possible to have equality in these inequalities? If | avg()| = rms(x) is possible, give the conditions on x under which it holds. Repeat for std(x) = rms(x).