Which of the following formula is used in calculating standard deviation?

Step 1: The standard deviation for a population of $N$ data points is given by the formula
$\sigma = \sqrt{\dfrac{\sum_{i=1}^{N} (x_i - \bar{x})^2}{N}},$
where $\bar{x}$ is the mean $\bar{x} = \dfrac{\sum x_i}{N}$.

Step 2: Compare with option A: $\sqrt{\dfrac{\bar{x} - x}{\sqrt{N}}}$.
This lacks the sum $\sum$, squared differences $(x_i - \bar{x})^2$, and has incorrect denominator $\sqrt{N}$. Incorrect.

Step 3: Compare with option B: $\sqrt{\dfrac{\sum (x_i - \bar{x})}{N}}$.
This averages the differences $(x_i - \bar{x})$ without squaring them. Incorrect (this resembles mean absolute deviation).

Step 4: Compare with option C: $\sqrt{\dfrac{\sum (x_i - \bar{x})^2}{N}}$.
This matches the standard deviation formula exactly. Correct.

Step 5: Compare with option D: $\sqrt{\dfrac{\sum (x_i - \bar{x})^2}{N}}$ (OCR artifacts like "10 szu" likely irrelevant; appears identical to C, but context suggests possible sample variant—however, standard population uses $N$).
Option C is the clear match.

Step 6: Compare with option E: $\sqrt{\dfrac{(x - \bar{x})^2}{N}}$.
Lacks the sum $\sum$ over all data points. Incorrect.

C