Data Sharing between Fragments and Activity in Android

Ive asked a similar question before and didn't get an answer and seems many other ppl are searching for an answer. So I am posting this question to hopefully get a clear answer that everyone can benefit from.

I have an activity with 2 fragments in it. I want fragment2 to set a boolean variable in Activity when a checkbox is checked so that fragment1 can know if the checkbox was checked.

This is my Code:

Activity:

public class modestab extends Activity{
    public static Context appContext;

    public boolean lf=false;

    public void onCreate(Bundle savedInstanceState){
        appContext=this;
super.onCreate(savedInstanceState);
ActionBar tabbar= getActionBar();
        tabbar.setNavigationMode(ActionBar.NAVIGATION_MODE_TABS);
        ActionBar.Tab ModesTab =tabbar.newTab().setText("Modes");
        ActionBar.Tab CatTab =tabbar.newTab().setText("Categories");

        Fragment ModesFragment =new modes();
        Fragment CatFragment =new cats();

        ModesTab.setTabListener(new MyTabsListener(ModesFragment));
        CattTab.setTabListener(new MyTabsListener(CatFragment));

        tabbar.addTab(ModesTab);
        tabbar.addTab(CatTab);


    }

Fragment 1:(Where I want to read the boolean lf set in Acitivity above:

@TargetApi(11)
public class tabmodes extends Fragment{
@Override
    public View onCreateView(LayoutInflater inflater, ViewGroup container, Bundle savedInstanceState)
    {
View V=inflater.inflate(R.layout.tab_modes, container, false);
button1.setOnClickListener(new View.OnClickListener() {

            @Override
            public void onClick(View v) {
                // TODO Auto-generated method stub
                if(lf==false) //lf here is the lf in Activity which I want to get

Fragment 2: Where I want to set lf in Activity

.....
lifecheck.setOnCheckedChangeListener(new CompoundButton.OnCheckedChangeListener(){
              @Overri