Change password for Apple ID by clicking on App Store in Mac .
Open app store in Mac , take cursor on top menu bar > store > click on sign in .

Again click on forgot Apple ID or password .

Click on continue .

If you select the box of reset by email and click on continue , a mail will be sent to your rescue mail address , open that rescue web mail account when initially the Apple ID was created , by entering its mail address and password .
Click on the link reset password received , enter the new password and verify it , finally click on reset password .
The Apple ID password is changed .
If you check the box of answer security questions , a pop window appears , click on drop down arrows of day / month / year and fill up the credentials and click on continue .

Fill up the answers in the fields and click on continue .

Enter the new password in the field and verify it and click on continue and click reset password .

Also , the Apple ID password can be changed by taking cursor on top menu bar clicking on itunes > account > sign in . Again click on forgot Apple ID or password , enter you Apple ID and click on continue , the same procedure would be repeated as described above , same way where Apple ID is used in some applications like iTunes , messages , App Store , iBook , open system preferences - game centre .
Now , a new query any one know how to change the Apple ID password from recovery mode , any suggestions still welcome .