Class 11

Math

JEE Main Questions

Statistics

The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. One rechecking, it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases. (i) If wrong item is omitted(ii) If it is replaced by 12.

$∑x_{i}=200$

for 19 terms $=200−8=192=∑x_{i}$

$σ=n1 ⋅∑x_{i}−(x)_{2} $

let incorrect sum be $e∑$$2=n1 ⋅e∑x_{i}−100 $

$4=201 e∑x_{i}−100$

$e∑x_{i}=104⋅20=2080$

correct $∑x_{i}$ for 19 terms = $2080−64=2016$

(i)$x=19192 =10.1$

$σ=191 ⋅2016−(10.1)_{2} $

$=106.1−102 =4.1 =2.024$

(ii) n = 20 $∑x_{i}=204$

$∑x_{i}=2016+144=2160$

$x=20204 =10.2$

$σ=201 ⋅2160−(10.2)_{2} $

$=108−104.04 =3.96 =1.98$