The number of values of $a \in N$ such that the variance of $3,7,12 a, 43-a$ is a natural number is  (Mean $=13$)

  • [JEE MAIN 2022]
  • A

    $0$

  • B

    $2$

  • C

    $5$

  • D

    infinite

Similar Questions

Let the mean and the variance of $5$ observations $x_{1}, x_{2}, x_{3}, x_{4}, x_{5}$ be $\frac{24}{5}$ and $\frac{194}{25}$ respectively. If the mean and variance of the first $4$ observation are $\frac{7}{2}$ and $a$ respectively, then $\left(4 a+x_{5}\right)$ is equal to

  • [JEE MAIN 2022]

Find the mean, variance and standard deviation using short-cut method

Height in cms $70-75$ $75-80$ $80-85$ $85-90$ $90-95$ $95-100$ $100-105$ $105-110$ $110-115$
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Mean and variance of a set of $6$ terms is $11$ and $24$ respectively and the mean and variance of another set of $3$ terms is $14$ and $36$ respectively. Then variance of all $9$ terms is equal to

The mean and the standard deviation $(s.d.)$  of five observations are $9$ and $0,$ respectively. If one of the observations is changed such that the mean of the new set of five observations becomes $10,$  then their $s.d.$  is?

  • [JEE MAIN 2018]

The mean and standard deviation of the marks of $10$ students were found to be $50$ and $12$ respectively. Later, it was observed that two marks $20$ and $25$ were wrongly read as $45$ and $50$ respectively. Then the correct variance is $............$.

  • [JEE MAIN 2023]