Question

The average of a group of 9 numbers is 68. If one of the numbers is replaced by a new number, the average becomes 72.
What is the difference between the new number and the old number?
a. 4
b. 8
c. 16
d. 36

Answer 1

a is the correct answer

Answer 2

Answer: d) 36

Step-by-step explanation:

As we know mean is given by

$\overline{x} = \dfrac{\sum x_i}{n}$

Now as question The average of a group of 9 numbers is 68

$68= \dfrac{\sum x_i}{9} \\\\\Rightarrow \sum x_i= 68\times 9 = 612$

Now

If one of the numbers is replaced by a new number, the average becomes 72.

Therefore

$72= \dfrac{\sum x_i}{9} \\\\\Rightarrow \sum x_i= 72\times 9 = 648$

The difference between the new number and odd number is = 648- 612= 36

Hence , the difference between the two numbers is 36