The Standard Deviation of a sample of size 10 is 11. If the value of each sampled item is reduced by 2, the new Standard deviation will be

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Solution

The correct option is B 11
Given standard deviation $= 11$
Sample size, $n = 10$
Standard deviation $(S . D) = \sqrt{\frac{\sum (x_{i} - ¯ x)^{2}}{n}} = 11$
Mean $= ¯ x$
New mean $= ¯ x - 2$ (as every item decreases by)
New standard deviation $= \sqrt{\frac{\sum (x_{i} - 2) - (¯ x - 2)^{2}}{n}}$
$= \sqrt{\frac{\sum (x_{i} - 2 - ¯ x + 2)^{2}}{n}}$
$= \sqrt{\frac{\sum (x_{i} - ¯ x)^{2}}{n}}$
$= 11$

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The Standard Deviation of a sample of size 10 is 11. If the value of each sampled item is reduced by 2, the new Standard deviation will be

The correct option is B 11Given standard deviation =11Sample size, n=10Standard deviation (S.D)=√∑(xi−¯x)2n=11Mean =¯xNew mean =¯x−2 (as every item decreases by)New standard deviation =√∑(xi−2)−(¯x−2)2n=√∑(xi−2−¯x+2)2n=√∑(xi−¯x)2n=11