SOLUTION: The average of a set of 6 numbers is 3.5. If the number is 4.2 is added to the set , what is the average of the new set of numbers?

Question 1143708: The average of a set of 6 numbers is 3.5. If the number is 4.2 is added to the set , what is the average of the new set of numbers?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
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Since the average of a set of 6 numbers is 3.5, the sum of these numbers is 6*3.5 = 21. Then the sum of 7 numbers is 21 + 4.2 = 25.2 and the average of 7 numbers is = 3.6. ANSWER

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The solution by tutor @ikleyn shows what is probably the standard way for solving a problem like this.

Here is another method that I often use in problems like this involving averages of numbers that are "close together".

Try it and see if it "works" for you.

(1) The new number is 4.2-3.5 = 0.7 greater than the current average.
(2) To get the new average, that additional 0.7 has to be divided evenly among what is now 7 numbers.
(3) That means the new average is larger by 0.7/7 = 0.1 -- so the new average is 3.5+0.1 = 3.6.
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