The mean and standard deviation of $20$ observations are found to be $10$ and $2$, respectively. On respectively, it was found that an observation by mistake was taken $8$ instead of $12$ . The correct standard deviation is

  • [JEE MAIN 2024]
  • A

    $\sqrt{3.86}$

  • B

    $ 1.8$

  • C

    $\sqrt{3.96}$

  • D

    $1.94$

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If the standard deviation of the numbers $ 2,3,a $ and $11$ is $3.5$  then which of the following is true ?

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Consider the statistics of two sets of observations as follows :

  Size Mean Variance
Observation $I$ $10$ $2$ $2$
Observation $II$ $n$ $3$ $1$

If the variance of the combined set of these two observations is $\frac{17}{9},$ then the value of $n$ is equal to ..... .

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The mean and variance of $10$ observations were calculated as $15$ and $15$ respectively by a student who took by mistake $25$ instead of $15$ for one observation. Then, the correct standard deviation is$.....$

  • [JEE MAIN 2022]