Question

the mean of 12 number is 40. Ifeach number is divided by 8 , what will be the mean of the new number​

Answer 1

Answer :

➡5

Explanation :

$\bold{Let \: the \: numbers \: be \: x_{1} \: , \: x_{2} \: , \: x_{3} \: ,\: ..... \: , \: x_{12}}$

➡Total number = 12

➡Mean = 40

$\to \: \frac{sum \: of \: all \: observation}{total \: number \: of \: observation} = 40 \\ \\ \to \frac{x_{1} + x_{2} + x_{3} + .... + x_{12}}{12} = 40 \\ \\ \to x_{1} + x_{2} + x_{3} + .... + x_{12} = 40 \times 12 \\ \\ \to x_{1} + x_{2} + x_{3} + .... + x_{12} = 480</p><p>$

Each number is divided by 8

$\to new \: mean = \frac{new \: total \: marks}{new \:number \: of \: terms } \\ \\ \to new \: mean = \frac{ \frac{x_{1} + x_{2} + x_{3} + .... + x_{12}}{8} }{12} \\ \\\to new \: mean \: = \frac{x_{1} + x_{2} + x_{3} + .... + x_{12}}{12 \times 8} \\ \\ \to new \: mean = \frac{480}{96} \\ \\ \to new \: mean = 5$

Therefore , the new mean is 5 of the number after dividing them by 8

Answer 2

Step-by-step explanation:

mean of 12 number = 40

Therefore,

Total numbers = 12 x 40 = 480

Dividing by 8

$new \: number \: = \frac{480}{8} = 60 \\ \therefore \: new \: mean = \frac{60}{12} = 5$

Thus, the mean of the new number is 5.