Question

a chemist attempts to measure the concentration of zinc in drinking water. Per liter of water her measurements are: 3.05 mg, 2.86 mg, 2.94 mg, and 3.08 mg. Calculate the mean value and the standard deviation.

Answer 1

Mean is average of all = ( 3.05+2.86+2.94+3.08) / 4 = 2.9825 mg

Now difference of each is ( 3.05 - 2.9825) = 0.0675

( 2.9825-2.86) = 0.1225 ,    2.9825-2.94 = 0.0425 , 3.08-2.9825 = 0.0975

Now   sum of squares of eahc difference = ( 0.0675^2 + 0.1225^2 + 0.0425^2 + 0.0975^2)

= 0.030875

Variance = sum of squares of differences / total measuremensts = ( 0.030875/4) = 0.00771875

standard deviation = sqrt ( varinace) = sqrt ( 0.00771875) = 0.0878564