Calculation of measurement errors.

Let n is count of measurements then the standard deviation is
\begin{equation}
\sigma = \sqrt{\frac{1}{n(n-1)}\sum\limits_{i=1}^{n}(\Delta x_{i})^2 },
\end{equation}
where \(\Delta x_{i}=x_{i}-\overline{x}\), \(\overline{x}\) is the sample mean. The confidence interval is \(\Delta_{\sigma}x = t_{n,\alpha}\sigma\), where \(t_{n,\alpha}\) is a Student’s t distribution with n − 1 degrees of freedom, \(\alpha=0.95\) (the 95th percentile). We use the function stats.t.ppf((1.0 + 0.95)/2, n-1) from the ‘stats’ package.
Then \(x = \overline{x} \pm \Delta_{s}x\).

In other denotes, the standard deviation is

\(\sigma = \sqrt{\operatorname {Var}(x_{ar}) / (n-1)}\),
where \(\operatorname {Var}(x_{ar})\) is variance and n is count of measurements.
The confidence interval is
\(\Delta_{\sigma}x = \sigma\overline{x}/\sqrt{n}\) (for examle, see wiki

Where X is the sample mean, and S2 is the sample variance. Then has a Student’s t distribution with kn − 1 degrees of freedom Example: alfa = 0.95, from a student t = 3.18 for kn = 4; 0.95 - confidence interval , 60-1 degrees of freedom denoting ppf as the 95th percentile of this distribution We usage function stats.t.ppf((1 + 0.95)/2, kn-1) from scipy package (from scipy import stats)