JEE Main 2016 · Mathematics · Statistics · medium

The mean and standard deviation of 20 observations are 10 and 2 respectively. It is later found that one observation recorded as 8 was actually 12.…

Single correct option

The mean and standard deviation of

20

observations are

10

and

2

respectively. It is later found that one observation recorded as

8

was actually

12

. The correct variance is

Show answer and solution

Answer: (B) $3.96$

Wrong data:

\sum x=20\times10=200

and

\sum x^2=20(\sigma^2+\bar x^2)=20(4+100)=2080

. Correct the data:

\sum x=200-8+12=204

, so the new mean is

10.2

;

\sum x^2=2080-64+144=2160

. Then the variance is

\dfrac{2160}{20}-(10.2)^2=108-104.04=3.96

. Note that the variance changes even though only one value changed, because both the mean and the mean of squares move. Answer:

3.96

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