Question

The anthmetic mean if 10 numbers is 20. If 5 is subtracted from every number,
what will be the new mean?​

Answer 1

Answer:

The new mean is 15.

Step-by-step explanation:

Gívєn -

Arithmetic mean = 20

Of = 10 number

Tσ fínd -

New mean when 5 is subtracted from each number

Sσlutíσn -

First find the sum of all the Observations

Here ;

• Number of Observations = 10
• Mean = 20
• Sum of Observations = x

★ $\boxed{\sf{Mean = \frac{Sum \: of \: Observations}{No. \: of \: Observations}}}$

$\sf{\implies} \: 20 = \dfrac{x}{10}$

$\sf{\implies} \:x = 10 \times 20$

$\sf{\implies} \:x = 200$

Sum of Observations = 200

$\rule{300}{1.5}$

5 is to be subtracted from each number. Total numbers are 10.

Value to be subtracted =

$\sf{\implies} \:5 \times 10$

$\sf{\implies} \:50$

$\rule{300}{1.5}$

Sum of Observations with value reduced =

$\sf{\implies} \: 200 - 50$

$\sf{\implies} \:150$

$\rule{300}{1.5}$

New mean =

$\sf{\implies} \: \dfrac{150}{10}$

$\sf{\implies} \:15$

$\therefore$ The new mean is 15.