The mean and the variance of five observations are $4$ and $5.20,$ respectively. If three of the observations are $3, 4$ and $4;$ then the absolute value of the difference of the other two observations, is

  • [JEE MAIN 2019]
  • A

    $7$

  • B

    $5$

  • C

    $1$

  • D

    $3$

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While calculating the mean and variance of 10 readings, a student wrongly used the reading 52 for the correct reading 25. He obtained the mean and variance as 45 and 16 respectively. Find the correct mean and the variance.

 

In a series of $2n$ observation, half of them are equal to $'a'$  and remaining half observations are equal to $' -a'$. If the standard deviation of this observations is $2$ then $\left| a \right|$ equals

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Mean of $5$ observations is $7.$ If four of these observations are $6, 7, 8, 10$ and one is missing then the variance of all the five observations is

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The mean and standard deviation of $40$ observations are $30$ and $5$ respectively. It was noticed that two of these observations $12$ and $10$ were wrongly recorded. If $\sigma$ is the standard deviation of the data after omitting the two wrong observations from the data, then $38 \sigma^{2}$ is equal to$.........$

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Statement $1$ : The variance of first $n$ odd natural numbers is $\frac{{{n^2} - 1}}{3}$
Statement $2$ : The sum of first $n$ odd natural number is $n^2$ and the sum of square of first $n$ odd natural numbers is $\frac{{n\left( {4{n^2} + 1} \right)}}{3}$

  • [AIEEE 2012]