Menu Outline Exercise Questions Appendices Lectures Student Projects Books Sections Introduction Atoms Molecules Crystal Structure Crystal Diffraction Crystal Binding Photons Phonons Electrons Band Model Crystal Physics Semiconductors

PHY.K02UF Molecular and Solid State Physics

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.

 $h(x)$ $x$
 48.93604143 48.53157747 43.2703614 41.04113259 41.72530709 34.27043079 40.03291072 42.97470938 32.65101011 39.03965905 37.00798818 37.8660878 42.07839729 56.93465139 37.95862401 39.77710671 41.03986285 30.05015416 49.87822257 37.48547576 44.23982079 32.78949736 44.03677161 38.1934544 35.517587 43.51962823 40.52742231 44.32879479 37.43193236 43.92744429 41.43171689 40.74163966 35.87762997 35.11660922 37.52083001 52.06941564 37.65532732 36.95701979 32.27396041 36.01339484 42.48043803 43.97749761 46.11840513 43.79500387 32.79899397 39.74888419 33.56281564 38.36769353 37.40730183 42.44638057 51.41889956 53.54560098 43.14347192 38.41710071 37.48321308 35.11501967 51.05470159 45.00323271 51.94236895 28.92428926 38.00574095 43.69075213 45.47218716 34.4954267 30.08250867 32.09518039 31.01140193 43.02860258 45.80993405 35.91557593 33.81176334 34.32902902 39.20814289 45.26313474 43.25077008 40.77533028 38.53167631 38.2920963 46.70063445 41.79709824 38.75108865 38.03349918 31.82678014 49.52405687 37.43558925 40.97487349 45.91988162 46.29064411 43.63249776 37.18294573 40.59010026 40.00313424 43.99789748 38.39921861 41.40651006 42.60090969 48.67653765 30.43079337 39.38256313 33.11375694

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