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Math

Algebra

Statistics

If $i=1∑9 (x_{i}−5)=9andi=1∑9 (x_{i}−5)_{2}=45$ then the standard deviation of the 9 items $x_{1},x_{2},…..,x_{9}$ is

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Find the standard deviation for the following data: (i) $x:$ , 3, 8, 13, 18, 23 $f:$ , 7, 10, 15, 10, 6 (ii) $x:$ , 2, 3, 4, 5, 6, 7, 7 $f:$ , 4, 9, 16, 14, 11, 6, 6

Let $x_{1},x_{2},….,x_{n}$ values of variable $X$ and let $_{′}a_{′}$ be non zero real number. Then prove that the variance of the observations $ax_{1},ax_{2},…,ax_{n}$ is $a_{2}$ Var $(X)$ . Also, find their standard deviation.

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The mean and standard deviation of six observation are $8$ and $4$ respectively. If each observation is multiplied by $3$, find the new mean and new standard deviation of the resulting observations.

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