Question

Average of 8 numbers is 24. If all the numbers are multiplied by 8 what is the
average of the product of the numbers ?
(a) 8
(b)21
(c) 168
(d) None of these​

Answer 1

Answer:

d)none of these

Step-by-step explanation:

given:(a+b+c+d+e+f+g+h)÷2=24

so if we mulitiply lhs by 8 we have to multiply rhs by 8.

hence, 24×8=192

Answer 2

(d) None of these​

The average of the product of the numbers is 192.

Step-by-step explanation:

Formulas :

Mean= (Sum of observations) ÷ (Number of observations)          (a)

Sum of observations = Mean x  (Number of observations)          (b)

Given : The average of 8 numbers is 24.

By using (b), sum of 8 numbers= 8 x 24= 192

Let the numbers be $x_1,x_2,x_3,x_4 , x_5,x_6, x_7,x_8$.

Such that $x_1+x_2+x_3+x_4 + x_5+x_6+x_7+x_8=192$

If all the numbers are multiplied by 8  , then the sum of 8 numbers would become

$8x_1+8x_2+8x_3+8x_4 + 8x_5+8x_6+8x_7+8x_8\\\\=8(x_1+x_2+x_3+x_4 + x_5+x_6+x_7+x_8)$

$=8(192)=1536$

Using (1) , the  average of the product of the numbers = (1536)÷8 =192

hence, the average of the product of the numbers is 192.

So , the correct answer is "(d) None of these​"

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