Question

# This data is from a sample. Calculate the mean, standard deviation, and variance. This data is...

This data is from a sample. Calculate the mean, standard deviation, and variance.

This data is from a sample. Calculate the mean, standard deviation, and variance.

 x 20.5 45.3 10.6 31.8 28.4 30.6 49.8 32.2 27.3

Sample Mean =

Sample Standard Deviation =

Sample Variance =  (Please use the standard deviation above for your calculation.)

Ooops - now you discover that the data was actually from a population! So now you must give the population standard deviation.

Population Standard Deviation =

Solution:

Sample mean = (20.5+45.3+10.6+31.8+28.4+30.6+49.8+32.2+27.3)/9 = 276.5/9 = 30.72

Sample standard deviation = Sqrt(summation(Xi-mean)^2/(n-1)) =Sqrt( (20.5-30.72)^2 +(45.3-30.72)^2+(10.6-30.72)^2+(31.8-30.72)^2+(28.4-30.72)^2+(30.6-30.72)^2+(49.8-30.72)^2+(32.2-30.72)^2+(27.3-30.72)^2)/8) = Sqrt(1106.34/8) = 11.76

Sample variance = (sample standard deviation)^2 = (11.76)^2 = 138.29

Population standard deviation = sqrt(summation(Xi-mean)^2/n) = Sqrt(1106.34/9) = 11.09

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