Estimating the standard deviation by simply looking at a histogram I would like to make a quick, rough estimate of what a standard deviation is.
Suppose i have the following histogram

By simply looking at it, I can say that the mean is around 10 or 9.8 (middle value) which, when calculating from my dataset, is actually the 9.98.
I understand that the standard deviation is a measure that is used to quantify the amount of variation or dispersion of a set of data values.
How can I estimate the standard deviation by simply looking at the histogram?

Assume normal distribution where 99.7% (~100%) of values fall within 3 standard deviations from the mean. This implies your $x_{min}$ and $x_{max}$ values define the full span of the domain and are each roughly 3 standard deviations from the mean, leading to:
$$ \sigma = \frac{x_{max} - x_{min}}{6} $$
In above case, $\sigma \approx \frac{20 - (-5)}{6} \approx 4.17$
