Numerical Methods

Mean and Standard Deviation

The mean value of $N$ data points is,

$\large \langle x\rangle = \frac{1}{N}\sum\limits_{i=1}^Nx_i$.

The standard deviation $\Delta x$, is the square root of the mean of the squares $\langle x^2\rangle=\frac{1}{N}\sum x_i^2$ minus the square of the mean $\langle x\rangle^2=\left(\frac{1}{N}\sum x_i\right)^2$.

$\Delta x=\sqrt{\langle x^2\rangle -\langle x\rangle^2}$.

The form below will calculate the mean and standard deviation of the column of numbers that are put in the textbox below.

To make the histogram, the interval between $x_{min}$ and $x_{max}$ is divided into 100 bins and each data point is sorted into one of these bins.