Problem 3064. Cycling — Normalized Power

In cycling, a power meter is an indispensable tool to record power output (in Watts) and measure fitness gains and performance metrics. When analyzing the data though, many different workouts can yield approximately the same average power, despite major differences between workouts (e.g., a long steady effort vs. sprints or intervals). Normalized power (NP) is a method to measure the effect of more intense efforts on the overall workout. NP is calculated by the following four steps (from Training and Racing with a Power Meter by Allen and Coggan):

1. Calculate a 30-second rolling average of the power data
2. Raise these values to the fourth power
3. Average the resulting values
4. Take the fourth root of the result

You will be provided with the 30-second rolling average power data set (vector). Write a function to return the average power (using the rolling average data) and the normalized power using steps 2–4 above. Round the values to the nearest integer.