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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The first of the two samples in a group has $100$ items with mean $15$ and standard deviation $3 .$ If the whole group has $250$ items with mean $15.6$ and standard deviation $\sqrt{13.44}$, then the standard deviation of the second sample is:

  • [JEE MAIN 2021]

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The diameters of circles (in mm) drawn in a design are given below:

Diameters $33-36$ $37-40$ $41-44$ $45-48$ $49-52$
No. of circles $15$ $17$ $21$ $22$ $25$

Calculate the standard deviation and mean diameter of the circles.

[ Hint : First make the data continuous by making the classes as $32.5-36.5,36.5-40.5,$ $40.5-44.5,44.5-48.5,48.5-52.5 $ and then proceed.]

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]