Sample Root Mean Square

#654 / Prob & Stats Easy

Calculate the sample root-mean-square for the values: 0, 2, 4, 9, 11

Expand Hint

Logically think through the mathematical operations associated with “root”, “mean”, and “square” and the order they are arranged in.

Hint 2

The sample root-mean-square value:

$$$RMS=\sqrt{\left ( \frac{1}{n} \right )\sum X_{i}^{2}}$$$

where $$n$$ is the number of items or observations and $$X_i$$ is the value of the ith observation.

The sample root-mean-square value:

$$$RMS=\sqrt{\left ( \frac{1}{n} \right )\sum X_{i}^{2}}$$$

where $$n$$ is the number of items or observations and $$X_i$$ is the value of the ith observation.

$$$RMS=\sqrt{\frac{0^2+2^2+4^2+9^2+11^2}{5}}$$$

$$$=\sqrt{\frac{0+4+16+81+121}{5}}=\sqrt{\frac{222}{5}}=\sqrt{44.4}=6.7$$$

6.7

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