Question

The mean of 16 number is 8 of 2 is added to every number what will be the new mean

Answer 1

As given mean of 16 no.s is 8 so the addition of the numbers will be 16×8=128.

NOW as per the question 2 is added to each no. so we need to multiply 2×8 which is 16 and add it to 128 that comes to be 144 and then divide it by 16

so the ans comes out to be equal to 9

Answer 2

Answer:

10

Step-by-step explanation:

Given:

• The mean of 16 number is 8.

To Find:

• The mean on addition of '2' to it.

Procedure:

Let's assume

x1, x2 , X3 ,.......,x16 be 16 means , whose mean is 8.

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \ \sf \overline{ \: \: \: X \: \: } = \dfrac{1}{n} { \sum{x1}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \ \sf 8 = \dfrac{x1, x2, x3, .........+x16}{16}$

$\: \: \: \: \: \: \: \: \implies \sf \: x1, x2, x3, .........+x16 = 16 \times 8$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: x1, x2, x3, .........+x16 = 128$

New number are:

(x1 + 2), (x2 + 2),( x3 + 2), .........+(x16 + 2)

$\sf \: \: \: \: \: let \: \: \overline{X} \: be \: the \: mean \: of \: new \: number.$

$\: \: \: \: \: \: \: \: \sf \implies \overline{X'} = \dfrac{(x1 + 2) + (x2 + 2) + .....(x16 + 2)}{16}$

$\: \: \: \: \: \: \: \: \sf \implies \overline{X'} = \dfrac{(x1 + x2 + ..... + x16) + 2 + 16}{16}$

$\: \: \: \: \: \: \: \: \sf \implies \overline{X'} = \dfrac{128 + 32}{16}$

$\: \: \: \: \: \: \: \: \sf \implies \overline{X'} = \dfrac{160}{10}$

$\: \: \: \: \: \: \: \: \sf \implies \overline{X'} = 10$

Points to remember:-

• Finding mean is nothing but finding average

• The concept of Mean , Median and Mode is used all over the world in daily life of a human.

• Mean is the average. This concept is used in research centres to find out number of possibilities of something that could happen. Overall occuring is taken into account and then divided with total number of occuring.