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

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.

Answer 2

Answer:

Incorrect mean is 20 . There was 100 observations .

So sum of all observations = 20 × 100 = 2000

$2000 - 21 - 21 - 18 = 1940$

Correct Mean =

$\frac{1940}{100 - 3} = \frac{1940}{97} = 20$

Now , we will find the correct Standard Deviation

We know ,

$σ = \sqrt { \frac{1}{n}Σ(xi) {}^{2} - (x) {}^{2} }$

When incorrect observations were present , the standard deviation was 9

$3 = \sqrt{ \frac{1}{100} Σ(xi) {}^{2} - (20) {}^{2} }$

$9 = \frac{1}{100} Σ(xi) {}^{2} -400$

$40900 = Σ(xi) {}^{2}$

This is the sum when observations were incorrect .

Correct sum when observations are omitted $40900 - 21 {}^{2} - 21 {}^{2} - 18 {}^{2} = 39694$

Correct $Σ(xi) {}^{2} = 39694$

$σ = \sqrt{ \frac{1}{97} (39694) - 400} = \sqrt{409.16 - 400} = \sqrt{9.16} = 3.03$

So , the correct deviation is 3.03 .