The following frequency distribution table summarizes the am

The following frequency distribution table summarizes the amount of tar (mg) in non-filtered cigarettes from a simple random sample. Find the mean and the standard deviation of the data. Also compare the computed mean and standard deviation to the actual ones by using the original data in values, which are mean = 21.1 gm and s= 3.2mg

Solution

Getting the midpoints as x values, consider:

Thus,          
          
Mean = Sum(xf) / Sum(f) =    20.94 [ANSWER, MEAN]      

Variance = [Sum(x^2f) - Sum(xf)^2/Sum(f)]/[Sum(f)-1] =    10.50666667      

Standard deviation = sqrt(Variance) =    3.241398875 [ANSWER, STANDARD DEVIATION]

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Comparing these to the ones from the original data, we can say this is quite close.