I know we can set the following values to the android:gravity and android:layout_gravity properties:
Their names should help you:
android:gravity sets the gravity of the contents (i.e. its subviews) of the View it's used on. android:layout_gravity sets the gravity of the View or Layout relative to its parent. And an example is here.
Short Answer: use android:gravity or setGravity() to control gravity of all child views of a container; use android:layout_gravity or setLayoutParams() to control gravity of an individual view in a container.
Long story: to control gravity in a linear layout container such as LinearLayout or RadioGroup, there are two approaches:
1) To control the gravity of ALL child views of a LinearLayout container (as you did in your book), use android:gravity (not android:layout_gravity) in layout XML file or setGravity() method in code.
2) To control the gravity of a child view in its container, use android:layout_gravity XML attribute. In code, one needs to get the LinearLayout.LayoutParams of the view and set its gravity. Here is a code example that set a button to bottom in a horizontally oriented container:
import android.widget.LinearLayout.LayoutParams;
import android.view.Gravity;
...
Button button = (Button) findViewById(R.id.MyButtonId);
// need to cast to LinearLayout.LayoutParams to access the gravity field
LayoutParams params = (LayoutParams)button.getLayoutParams();
params.gravity = Gravity.BOTTOM;
button.setLayoutParams(params);
For horizontal LinearLayout container, the horizontal gravity of its child view is left-aligned one after another and cannot be changed. Setting android:layout_gravity to center_horizontal has no effect. The default vertical gravity is center (or center_vertical) and can be changed to top or bottom. Actually the default layout_gravity value is -1 but Android put it center vertically.
To change the horizontal positions of child views in a horizontal linear container, one can use layout_weight, margin and padding of the child view.
Similarly, for vertical View Group container, the vertical gravity of its child view is top-aligned one below another and cannot be changed. The default horizontal gravity is center (or center_horizontal) and can be changed to left or right.
Actually, a child view such as a button also has android:gravity XML attribute and the setGravity() method to control its child views -- the text in it. The Button.setGravity(int) is linked to this developer.android.com entry.

Look at the image to be clear about gravity
If a we want to set the gravity of content inside a view then we will use "android:gravity", and if we want to set the gravity of this view (as a whole) within its parent view then we will use "android:layout_gravity".
The android:gravity sets the gravity (position) of the children whereas the android:layout_gravity sets the position of the view itself. Hope it helps
android:layout_gravity is the Outside gravity of the View. Specifies the direction in which the View should touch its parent's border.
android:gravity is the Inside gravity of that View. Specifies in which direction its contents should align.
Android | CSS
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android:layout_gravity | float
android:gravity | text-align
Take layout-gravity as "Lay-outside-gravity".