Question

Q60. The average of a set of "N" numbers comes
down by 2, when the number 80 is replaced
by 66. What is the value of N?
(A) 8
(B) 7
(C) 5
(D) 6

Answer 1

Answer:

(D)6 might be the value of N

Answer 2

Answer:

The value of N is 7.

Step-by-step explanation:

Mean:

• The mean or the average of the data is given by sum of all the elements of the data divided by the number of elements.
• The mean of the data set is

        $\overline{x} =\dfrac{\Sigma N}{N}$

Let the sum of N numbers without 80 be S and the average of them be x.

Then the average can be written as

$x =\dfrac{S+80}{N}$                                  ...(1)

Given the average of a set of N numbers comes down by 2.  

The number 80 is replaced by 66.

Then the new average is given by  

$x-2 =\dfrac{S+66}{N}$

Using the value of x from equation (1)

$\dfrac{S+80}{N}-2 =\dfrac{S+66}{N}$

$\implies \dfrac{S+80-2N}{N} =\dfrac{S+66}{N}$

$\implies S+80-2N =S+66$

$\implies 80-2N =66$

$\implies 2N =80-66=14$

$\implies N =\dfrac{14}{2} =7$

Therefore, the value of N is 7.

 

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