NCERT Class XI Mathematics - Statistics - Solutions
© examsnet.com
Question : 30
Total: 34
The mean and standard deviation of six observations are 8 and 4, respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations.
Solution:
Let x 1 , x 2 , x 3 , x 4 , x 5 , x 6
⇒x 1 + x 2 + x 3 + x 4 + x 5 + x 6
Now if each observation is multiplied by 3 then
New mean =
=
Also ,
( x 1 2 + x 2 2 + x 3 2 + x 4 2 + x 5 2 + x 6 2 ) − ( 8 ) 2
⇒x 1 2 + x 2 2 + x 3 2 + x 4 2 + x 5 2 + x 6 2
If each observation is multiplied by 3, then
New variance
=
( 9 x 1 2 + 9 x 2 2 + 9 x 3 2 + 9 x 4 2 + 9 x 5 2 + 9 x 6 2 ) − ( 24 ) 2
=
∴ New S.D. =√ 144
⇒
Now if each observation is multiplied by 3 then
New mean =
=
Also ,
⇒
If each observation is multiplied by 3, then
New variance
=
=
∴ New S.D. =
© examsnet.com
Go to Question: