Question

In: Chemistry

if a chemist observes the density of four different samples of the same metal to be...

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?

Solutions

Expert Solution

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.


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