if there are ten values each equal to 10 then standard deviation of these values is
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Standard Deviation is the square root of variance.
Variance is expectation of (X-m) square. Where m is mean.
Now, each value is increased by 10. Therefore let's say each x now is x+10. Let's say there are n readings. So the summation now of n readings is (summation x)+10n. And the mean will be m+10. Beacuase mean is total divided by number of readings. So the mean is m+10.
Now if we put these new values (x+10) and (m+10) in the equation, the 10–10 will get cancelled and the variance is same as before. So S.D. is also same.
So standard deviation won't change.
Variance is expectation of (X-m) square. Where m is mean.
Now, each value is increased by 10. Therefore let's say each x now is x+10. Let's say there are n readings. So the summation now of n readings is (summation x)+10n. And the mean will be m+10. Beacuase mean is total divided by number of readings. So the mean is m+10.
Now if we put these new values (x+10) and (m+10) in the equation, the 10–10 will get cancelled and the variance is same as before. So S.D. is also same.
So standard deviation won't change.
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