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Calculate mean and standard deviation of a series excluding two variable?

 
 
Reply Wed 14 Dec, 2011 05:05 am
The mean standard deviation and range of distribution of weight of 12 children are 9lbs, 2lbs and 6lbs the median and the mean are same for distribution. find the mean and standard deviation of the distribution, if the lowest and highest children are excluded?
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engineer
 
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Reply Wed 14 Dec, 2011 12:15 pm
@adi bajaj,
Let me assume the the max and min values are evenly distributed around the mean. Since the range is six, the max is 12 and the min is 6.

- Removing these two values will not change the mean, the so new mean is still 9.

- The formula for std deviation is sqrt( sum^2(deviations from the mean) / (n-1) ). So if the std dev = 2 then the std deviation^2 = 4. 4 (n-1) = 44 = sum^2(deviations from the mean).

- The two values you removed each had a deviation of three from the mean. Removing 3^2 from 44 twice leaves you with 26

- Running the formula forward you now have std dev = sqrt ( 26 / 9) = 1.7lbs
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