In: Chemistry
if a chemist observes the density of four different samples of the same metal to be 4.56 g/cm3, 4.50 g/cm3, 4.57 g/cm3 and 4.52 g/cm3, can we say that his work is precise?
what would have to be known to say that his work is accurate?
The accuracy of his work may be determined by calculating :
a) the mean of the following reading
b) calculating standard deviation
So, mean of the density of four different samples of the same metal
= 1/N Σ( x)
x is the density of each sample
N is the number of samples
= mean density
= ( 4.56 + 4.50 + 4.57 + 4.52)/ 4 , g/cm3
= 4.5373 g/cm3
standard deviation, σ = [(Σ((X- )2))/(N)]
= [ {(4.56- 4.5373)2 + (4.50- 4.5373)2 + (4.57- 4.5373)2 + (4.52- 4.5373)2 }/4]
=0.0286
The standard error in the calculation of the density of the metal may be given by
Standard error = σ/N = 0.0143
% Standard error = 0.0143 X 100 = 1.43%
usually an calculation error up 3% is permissible
As the error in only 1.43% the density mesurement is very accurate and multiple repetation are not required.