Exams Joint Entrance Examination Mathematics Statistics Question 118 Question 118 of 208 Medium MCQ
The mean and variance of 20 observations are found to be 10 and 4, respectively. On rechecking, it was found that an observation 9 was incorrect and the correct observation was 11. Then the correct variance is:
Solutions · 1 Post your solution Official solution
Let 20 observation be x1
, x2
,....., x20
Mean =
x1
+ x2
+, .....+ x20
20
= 10
\[ \Rightarrow \] x1
+ x2
+, .....+ x20 = 200
Variance = \[{{\sum\limits_{i = 1}^{i = n} {x_i^2} } \over n} - {\left( {\overline x } \right)^2}\]
\[ \Rightarrow \] 4 = \[{{x_1^2 + x_2^2 + ... + x_{20}^2} \over {20}}\] - 102
\[ \Rightarrow \] x 1 2 + x 2 2 + . . . + x 20 2 {x_1^2 + x_2^2 + ... + x_{20}^2} x 1 2 + x 2 2 + ... + x 20 2 = 2080
Also x1
+ x2
+, .....+ x20 - 9 + 11 = 202
new variance will be
= \[{{x_1^2 + x_2^2 + ... + x_{20}^2 - 81 + 121} \over {20}}\] - \[{\left( {{{202} \over {20}}} \right)^2}\]
= 3.99 Answer the question to unlock