It is very difficult to calculate density from Young's modulus. Graph on the webpage is covering huge array of Young's modulus for specific density for metals and alloys.
Graph like this are used to show where materials from mechanical properties view are in relation to the density.
You can't - there is no direct connection between density and Young's modulus (note that the Ashby map you have shown has a double-log scale). There is a trend that light-weight materials also have a lower Young's modulus, but this is only a trend.
The most primitive "answer" that came to my mind instantly, is the Rayleigh notion of (squared) speed of sound: c^2 = E \rho, providing E = c^2 \rho. Once you have measured c^2 and \rho, you should be able to calculate E.
Asatur Zh. Khurshudyan Hey, ( im using speed of sound in km/h , density kg/m^3 ).. But im not sure weather its correct.. What would be the ringt path for units convertions (m/h)/(kg/m^3), somehow ending up in paskals?
Asatur Zh. Khurshudyan , but what would be the most common value of c to use, since it differs depending of the temperature of air and even altitute..?
Mohsen Bazargan It's the usual definition of speed of sound in solids. Have a look at the section "Speed of sound in solids" via this link: https://en.wikipedia.org/wiki/Speed_of_sound. You can also find it in practically any textbook of mathematical physics or continuum mechanics.