Q56 / 90 · JEE Main 2022 (26 Jul Shift 2) · Mathematics

The mean and standard deviation of 40 observations are 30 and 5 respectively. It was noticed that two of these observations 12 and 10 were wrongly recorded. If σ is the standard deviation of the data after omitting the two wrong observations from the data, then 38σ2 is equal to _______.

Correct answer: 238

Solution

Given,

Wrong mean =μ1=30

Wrong standard deviation =σ1=5

Now mean ig given by ∑xi40=30

⇒∑xi=1200

Variance is given by σ12=25

⇒∑xi240-302=25

⇒∑xi2=925×40=37000

New sum of mean =∑xi'=1200-10-12=1178

So, new mean =μ1'=117838=31

Now new variance ∑xi2=37000-102-122=36756

So, new S.D. σ1'=3675638-312=σ

36756-312×38=38σ2

⇒38σ2=238

Hence, the correct answer is 238.

Relevant Questions