Standard Deviation - Calculating Deviation from Random Number

Question

If I wish to calculate the average deviation from a value in a list, can I use the standard deviation equation using the value in place of the mean?

If so, why? If not, what's a good alternative?

Answer 1

A starting point may be something such as

$$\sqrt{ (100a - 50) ^ 4 } \times 4$$

This formula assumes that $a$ is the ratio of coin flips resulting in heads to total coin flips, or $\frac{h}{T})$. It uses the principle that in perfect conditions the probability of either heads or tails is 50%. And so this measures the absolute deviation from $0.5$.

In the context of randomness I found a score of 9 is an acceptable threshold for detecting anomalies or biases.

There may be more standard or optimal solutions for this however.