Question

 If half of the observations in a raw data of 2n values are multiplied by 2 and the other half divided by 2, then *

the mean remains unchanged

the new mean is greater than the original mean

the new mean is less than the original mean

it is not possible to compare the two means because of inadequate data​

Answer 1

Correct option is

B

2

Total number of observations =2n

Half are equal to a and half are equal to −a

Therefore, mean

x

ˉ

=0

Standard deviation:

∑

2n

∣x

i

−

x

ˉ

∣

2

=

2n

2na

2

=a

2

=S.D=2

⇒∣a∣=

2