Question

The average of 15 numbers is 18. If each number is multiplied by 9, then the average of the new set of numbers is

Answer 1

Step-by-step explanation:

mean of 15 observations = 18

Sum of 15 observations = 18×15 = 270

If each observation is multiplied by 3

Sum of 15 observations = 18×15×3 = 810

New Mean = 810/15=54

Answer 2

Given:

We have given the average of 15 numbers is 18. And also each number is multiplied by 9.

To Find:

We have to find the average of new set of numbers?

Step-by-step explanation:

• The average of a set of numbers is  defined as the sum of the set of numbers and divide it by total number in the set.
• We should know some properties of the average of number which state that:
• 1) If in a set of numbers the Average of numbers is A and if all the numbers and added by any number n then the average of new numbers will be A+n.

• 2) If in a set of numbers the Average of numbers is A and if all the numbers and Subtracted by any number n then the average of new numbers will be A-n.
• 3) If in a set of numbers the Average of numbers is A and if all the numbers and Multiplied by any number n then the average of new numbers will be nA.
• 4) If in a set of numbers the Average of numbers is A and if all the numbers and Divided by any number n then the avergae of new numbers will be A divides n.
• Now we have given the Average of 15 numbers is 18.
• Each of the number is multiplied by 9, We will use the property 3 written above
• Hence, the average of new set of numbers is $18\times9=162$

Hence, the average of new numbers is 162.