Question

Hi

the mean of 12 numbers is 40 if each number is divided by 8 what will be the mean of the new numbers.


Thanks

Answer 1

Hi there!

_______________________

What is Mean?

The average of a given set of numbers is called the Arithmetic mean, or simply the mean, of the given numbers.

Mean = $\frac{Sum \: of \: observations }{Number \: of \: observations }$

​

_______________________

For your solution to the given question refer to the attachment.

Thanks for the question!

☺️☺️☺️

Answer 2

$\underline{\bold{Solution:-}}$


$let \: the \: numbers \: be \: x_{1} \: x_{2} \: x_{3} ..... x_{12}.$

Total number = 12

Mean = 40

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

Each number is divided by 8.

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

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