Question

The average of 8 numbers is 21. if each of the number is multiplied by 8, the average of the new set of numbers is :

Answer 1

Answer:

168

Step-by-step explanation:

$Mean =\frac{\text{Sum of all observations}}{\text{No. of all observations}}$

Let the eight numbers be a,b,c,d,e,f,g,h

Now The average of 8 numbers is 21.

So, $21 =\frac{a+b+c+d+e+f+g+h}{8}$

$21 \times 8 =\frac{a+b+c+d+e+f+g+h}{8}$

$168 =a+b+c+d+e+f+g+h$   ----1

Now each of the number is multiplied by 8

So, Number becomes : 8a,8b,8c,8d,8e,8f,8g,8h

Sum of these numbers = 8a+8b+8c+8d+8e+8f+8g+8h

                                      = 8(a+b+c+d+e+f+g+h)

Using 1

New Sum = 8(a+b+c+d+e+f+g+h) = $8 \times 168=1344$

$\text{New Mean} =\frac{1344}{8}$

$\text{New Mean} =168$

Hence the average of the new set of numbers is 168

Answer 2

Answer:

Average of new set of numbers = 168

Step-by-step explanation:

Average of 8 numbers (x)=21

/* given */

If each of the number is multiplied by 8 , the average of the new set of numbers = 8x

= 8×21

= 168

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