Question

The mean and standard deviation of a group of 100 observations were found to be 20 and 3 respectively. Later on it was found that three observations were incorrect which were recorded as 21,21 and 18. Find the mean and standard deviation if the incorrect observation are omitted

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Answer 1

Answer:

$Given, number of observation n=100</p><p>Incorrect mean (xˉ)=20</p><p></p><p>We know that</p><p></p><p>xˉ=n∑xi</p><p>⇒20=1001i=1∑100xi</p><p>⇒i=l∑100xi=20×100=2000</p><p></p><p>$

So, the incorrect sum of observations =2000.

So, the incorrect sum of observations =2000.Given incorrect observations are 21,21,18 and these has to be omitted.

So, the incorrect sum of observations =2000.Given incorrect observations are 21,21,18 and these has to be omitted.So, correct sum of observations =2000−21−21−18=2000−60=1940

$Correct mean =100−3Correctsum=971940=20$

$Given, incorrect standard deviation σ=3</strong></p><p></p><p><strong>[tex]Given, incorrect standard deviation σ=3σ=n∑i=1nxi2−(n∑i=1nxi)2</strong></p><p></p><p></p><p><strong>[tex]Given, incorrect standard deviation σ=3σ=n∑i=1nxi2−(n∑i=1nxi)2$

$σ2=n∑i=1nxi2−(xˉ)2</strong></p><p></p><p></p><p><strong>[tex]σ2=n∑i=1nxi2−(xˉ)2 ⇒32=100∑xi2−(20)2</strong></p><p><strong>[tex]σ2=n∑i=1nxi2−(xˉ)2 ⇒32=100∑xi2−(20)2 ⇒Incorrect∑xi2=100(9+400)=40900</strong></p><p></p><p><strong>[tex]σ2=n∑i=1nxi2−(xˉ)2 ⇒32=100∑xi2−(20)2 ⇒Incorrect∑xi2=100(9+400)=40900$

$Correct  i=l∑nxi2=Incorrecti=l∑nxi2−(21)2−(21)2−(18)2</strong></p><p><strong>[tex]Correct  i=l∑nxi2=Incorrecti=l∑nxi2−(21)2−(21)2−(18)2=40900−441−441−324</strong></p><p><strong>[tex]Correct  i=l∑nxi2=Incorrecti=l∑nxi2−(21)2−(21)2−(18)2=40900−441−441−324=39694</strong></p><p></p><p><strong>[tex]Correct  i=l∑nxi2=Incorrecti=l∑nxi2−(21)2−(21)2−(18)2=40900−441−441−324=39694∴ Correct standard deviation = ncorrect∑xi2−(Correctmean)2</strong></p><p><strong>[tex]Correct  i=l∑nxi2=Incorrecti=l∑nxi2−(21)2−(21)2−(18)2=40900−441−441−324=39694∴ Correct standard deviation = ncorrect∑xi2−(Correctmean)2 =9739694−(20)2</strong></p><p><strong>[tex]Correct  i=l∑nxi2=Incorrecti=l∑nxi2−(21)2−(21)2−(18)2=40900−441−441−324=39694∴ Correct standard deviation = ncorrect∑xi2−(Correctmean)2 =9739694−(20)2 =409.216−400</strong></p><p><strong>[tex]Correct  i=l∑nxi2=Incorrecti=l∑nxi2−(21)2−(21)2−(18)2=40900−441−441−324=39694∴ Correct standard deviation = ncorrect∑xi2−(Correctmean)2 =9739694−(20)2 =409.216−400=9.216</strong></p><p><strong>[tex]Correct  i=l∑nxi2=Incorrecti=l∑nxi2−(21)2−(21)2−(18)2=40900−441−441−324=39694∴ Correct standard deviation = ncorrect∑xi2−(Correctmean)2 =9739694−(20)2 =409.216−400=9.216=3.036</strong></p><p></p><p><strong>[tex]Correct  i=l∑nxi2=Incorrecti=l∑nxi2−(21)2−(21)2−(18)2=40900−441−441−324=39694∴ Correct standard deviation = ncorrect∑xi2−(Correctmean)2 =9739694−(20)2 =409.216−400=9.216=3.036$

answer is 3.036

Answer 2

Simple distillation is a method for separating the solvent from a solution. For example, water can be separated from salt solution by simple distillation. This method works because water has a much lower boiling point than salt. When the solution is heated, the water evaporates.

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