The Mean Of Eight Numbers Is 25. If Five Is Subtracted From Each Numb

1.	The Mean Of Eight Numbers Is 25. If Five Is Subtracted From Each Number, What Will Be The New Mean?
Answer» Let the GIVEN numbers be x1, x2, . . ., x8. Then, the mean of these numbers = (x1 + x2 + ...+ x8)/8. Therefore, (x1 + x2+...+x8)/8 = 25 ⇒ (x1 + x2 + ... + x8) = 200 ……. (A) The NEW numbers are (x1 - 5), (x2 - 5), …… ,(x8 - 5) Mean of the new numbers = {(x1 - 5) + (x1 - 5) + …… + (x8 - 5)}/8 = [(x1 + x2 + ... + x8) - 40]/8 = (200 - 40)/8, [using (A)] = 160/8 = 20 HENCE, the new mean is 20. Let the given numbers be x1, x2, . . ., x8. Then, the mean of these numbers = (x1 + x2 + ...+ x8)/8. Therefore, (x1 + x2+...+x8)/8 = 25 ⇒ (x1 + x2 + ... + x8) = 200 ……. (A) The new numbers are (x1 - 5), (x2 - 5), …… ,(x8 - 5) Mean of the new numbers = {(x1 - 5) + (x1 - 5) + …… + (x8 - 5)}/8 = [(x1 + x2 + ... + x8) - 40]/8 = (200 - 40)/8, [using (A)] = 160/8 = 20 Hence, the new mean is 20.

The Mean Of Eight Numbers Is 25. If Five Is Subtracted From Each Number, What Will Be The New Mean?

Answer»

Let the GIVEN numbers be x1, x2, . . ., x8.

Then, the mean of these numbers = (x1 + x2 + ...+ x8)/8.

Therefore, (x1 + x2+...+x8)/8 = 25

⇒ (x1 + x2 + ... + x8) = 200 ……. (A)

The NEW numbers are (x1 - 5), (x2 - 5), …… ,(x8 - 5)

Mean of the new numbers = {(x1 - 5) + (x1 - 5) + …… + (x8 - 5)}/8

= [(x1 + x2 + ... + x8) - 40]/8

= (200 - 40)/8, [using (A)]

= 160/8

= 20

HENCE, the new mean is 20.

Let the given numbers be x1, x2, . . ., x8.