Question

The mean and variance of the marks obtained by the students in a test are 10 and 4 respectively Later, the marks of one of the students is increased from 8 to 12 If the new mean of the marks is $10.2$, then their new variance is equal to :

• A. $3.92$
• B. $3.96$
• C. $4.04$
• D. $4.08$

Answer 1

Answer: (B)

$3.96$

Answer 2

i=1∑n​xi​=10n
i=1∑n​xi​−8+12=(10.2)n
∴n=20
Now 20i=1∑20​xi2​​−(10)2=4⇒i=1∑20​xi2​=2080
20i=1∑20​xi2​−82+122​−(10.2)2
=108−104.04=3.96