If for a distributionΣ$$(x$$−$$5)=3$$,Σ$$(x$$−$$5)2=43$$ and the total number of items is $$18$$, find the mean and standard deviation.

Question

If for a distributionΣ$$(x$$−$$5)=3$$,Σ$$(x$$−$$5)2=43$$ and the total number of items is $$18$$, find the mean and standard deviation.

Infinity Learn · Accepted Answer

Given, Σ(x$$−$$5)=3$$ and Σ$$(x$$−$$5)2=43$$,$$n=18$$∴  Mean $$=5+$$∑$$(x$$−$$5)18=5+318=5+16=316=5.17$$, Now, Σ$$(x$$−$$5)2=43$$⇒Σ$$x2$$−Σ$$10x+$$Σ$$25=43$$⇒Σ$$x2$$−$$10{$$Σ$$(x$$−$$5+5)}+18$$×$$25=43$$⇒Σ$$x2$$−$$10$$Σ$$(x$$−$$5)−$$10$$Σ$$5+450=43$$⇒Σ$$x2$$−$$10(3)$$−$$10$$×$$18$$×$$5+450=43$$⇒Σ$$x2$$−$$30$$−$$900+450=43$$⇒Σ$$x2=523$$ and Σ$$(x$$−$$5)=3$$⇒Σx−$$5$$Σ$$1=3$$⇒Σ$$x=3+5$$×$$18=93$$∵σ$$=$$Σ$$x2n$$−Σ$$xn2=52318$$−$$93182$$ $$=29.06$$−$$(5.17)2$$ $$=29.06$$−$$26.73$$ $$=2.33=1.53$$

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If for a distribution $Σ (x - 5) = 3, Σ (x - 5)^{2} = 43$ and the total number of items is 18, find the mean and standard deviation.

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If for a distributionΣ(x−5)=3,Σ(x−5)2=43 and the total number of items is 18, find the mean and standard deviation.

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Ready to Test Your Skills?

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If for a distribution $Σ (x - 5) = 3, Σ (x - 5)^{2} = 43$ and the total number of items is 18, find the mean and standard deviation.