How to change colour of all elements of a group, at once, in Illustrator

I have a group of objects of the same colour, consisting of compound paths, regular paths and groups of these. How to change the colour of all objects at once? When I tried to use colour picker or change it through color palette the colour remained the same but the graphics was rendered with a very tiny outline of the new colour, which I guess is not printable. Usually I had to change the colour of all objects individually.

Edit:
I’m sorry if I was not too precise. I mean to apply new colour / swatch to all member objects of the group at once, not to change properties of a commonly shared swatch.

Edit 2:
I received very useful answers, however my goal was to pick a colour from another object, serving as a source. When I tried to select all objects, for example with ctrl-a, and then use a eyedropper to pick up a desired colour, it didn’t work for some objects in some groups. Please have a look at my answer where several methods are listed.

Answer

Attribution
Source : Link , Question Author : ellockie , Answer Author : Scott