Question

what is the y-coordinate of the center of mass of a plane of the same shape as the histogram of the distribution ?

Answer 1

$C_{y}=\frac{\sum C_{iy}A_i}{\sum A_i}$

where $A_i=df_i$ is area i-th part of histogram,

$C_{iy}=f_i/2$ is y-coordinate of the center of mass of i-th part of histogram,

$f_i$ is frequency,

$d$ is width of interval.

Then:

$C_y=\frac{\sum df_i^2}{2\sum df_i}$