Question

the mean of 20 number is 15 if 2 is added to each number what will be the mean of new set of 20 nhmbers​

Answer 1

Required Answer:-

Whenever a certain number is added/multiplied/subtracted/divided by all the numbers in a given data, the mean will also change accordingly.

Like here:

2 is added to each number in a certain data, then the new mean will be also = previous mean + 2. Hence, The new mean will be

$= 15 + 2$

$= 17$

$\therefore$ The new mean of the data is 17.

Justification:-

Mean is calculated by the sum of all observations by the no. of observations. Then,

Sum of observations at first

$= 15 × 20$

$= 300$

Sum of observations later

$= 300 + (20 × 2)$

$= 340$

Then, new mean

$= 340 / 20$

$= 17$

And this is what we got previously also. Hence, Justified!!

Answer 2

Given:-

$\bigstar$The mean of 20 numbers is 15

To Prove:-

$\bigstar$What will be the mean of new set of 20 numbers?..

Solution:-

$\bigstar$In mathematics, the mean will also increase / reduced by the same quantity, if similar quantity is increased / reduced from each terms.

$\leadsto{ \boxed{ \boxed{ \boxed{ \bold{New \: mean = Earlier \: mean + Increase \: in \: term}}}}}$

$\sf \: \leadsto \: 15 + 2 \\ \\ \sf \: \leadsto \: = 17$

$\bigstar$Hence, the new set of mean will be 17