The Mean Of 14 Numbers Is 6. If 3 Is Added To Every Number, What Will

1.	The Mean Of 14 Numbers Is 6. If 3 Is Added To Every Number, What Will Be The New Mean?
Answer» Let the given NUMBERS be X1, X2, x3, ….. x14. Then, the mean of these numbers = x1 + x2 + x3+ ….. x14/14 Therefore, (x1 + x2 + x3 + ….. x14)/14 = 6 ⇒ (x1 + x2 + x3 + ….. x14) = 84 ………………. (A) The new numbers are (x1 + 3), (x2 + 3), (x3 + 3), …. ,(x14 + 3) Mean of the new numbers = (x1 + 3), (x2 + 3), (x3 + 3), …. ,(x14 + 3)/14 = (x1 + x2 + x3 + ….. x14) + 42 = (84 + 42)/14, [Using (A)] = 126/14 = 9 Hence, the new mean is 9. Let the given numbers be x1, x2, x3, ….. x14. Then, the mean of these numbers = x1 + x2 + x3+ ….. x14/14 Therefore, (x1 + x2 + x3 + ….. x14)/14 = 6 ⇒ (x1 + x2 + x3 + ….. x14) = 84 ………………. (A) The new numbers are (x1 + 3), (x2 + 3), (x3 + 3), …. ,(x14 + 3) Mean of the new numbers = (x1 + 3), (x2 + 3), (x3 + 3), …. ,(x14 + 3)/14 = (x1 + x2 + x3 + ….. x14) + 42 = (84 + 42)/14, [Using (A)] = 126/14 = 9 Hence, the new mean is 9.

The Mean Of 14 Numbers Is 6. If 3 Is Added To Every Number, What Will Be The New Mean?

Answer»

Let the given NUMBERS be X1, X2, x3, ….. x14.

Then, the mean of these numbers = x1 + x2 + x3+ ….. x14/14

Therefore, (x1 + x2 + x3 + ….. x14)/14 = 6

⇒ (x1 + x2 + x3 + ….. x14) = 84 ………………. (A)

The new numbers are (x1 + 3), (x2 + 3), (x3 + 3), …. ,(x14 + 3)

Mean of the new numbers

= (x1 + 3), (x2 + 3), (x3 + 3), …. ,(x14 + 3)/14

= (x1 + x2 + x3 + ….. x14) + 42

= (84 + 42)/14, [Using (A)]

= 126/14

= 9

Hence, the new mean is 9.

Let the given numbers be x1, x2, x3, ….. x14.