Question

The mean of 16 numbers is 8. If 2 is added to every number, what will be the new mean?

Answer 1

Answer:

The mean of the new observations = 10

Step-by-step explanation:

Given mean of the 16 numbers  = 8

Here we need to find mean of the 16 numbers when 2 is added to each number

⇒ In a Arithmetic mean if each observation is increased by a value "S" then the mean will also increase by the same value "S"

⇒ In given problem, for the each observation 2 is added therefore the mean will also increase by 2

⇒ the mean = actual mean + 2

                    = 8 + 2 = 10

Answer 2

Answer:

if the number '2' is added to each number , the new mean is: 10

Step-by-step explanation:

given that:

mean of sixteen numbers is 8

we have to find the new mean , if '2' is added to every number.

let the sixteen numbers be   :

x₁ , x₂ , x₃ . . . .    and x₁₆

so the mean 'M' for these 16 observations is

M = (x₁ + x₂ + . . . . + x₁₆)/16

equate mean as '8'

M = 8

8 = (x₁ + x₂ + . . . . + x₁₆)/16

(x₁ + x₂ + . . . . + x₁₆) = (8)(16)

(x₁ + x₂ + . . . . + x₁₆) = 128

if the number '2' is added to each number , the new observations are:

(x₁ + 2) , (x₂ + 2) . . . . .  and (x₁₆ + 2)

so the new mean N is :

[(x₁ + 2) , (x₂ + 2) . . . . .  (x₁₆ + 2)]/16

= [(x₁ +  x₂ +  . . . . .  + x₁₆ ) + (16)(2)]/16

= (x₁ +  x₂ +  . . . . .  + x₁₆ )/16 +  (16)(2)/16

= (x₁ +  x₂ +  . . . . .  + x₁₆ )/16 + 2

from the value (x₁ + x₂ + . . . . + x₁₆) = 128 , substitute in above:

= 128/16 + 2

= 8 + 2

= 10

if the number '2' is added to each number , the new mean is: 10