Question

Question 1 (20 marks) The Fe concentration in a sample was determined 6 trials by a single method as the following (19.4, 19.5, 19.6, 19.8, 20.1 and 20.3 ppm). Calculate mean, standard deviation, variance, spread, relative standard deviation, coefficient of variation, absolute error and relative error for the method, based upon these obtained data (true value is 20.00ppm).

Answer 1

- 19.4+ 19.5+ 19.6+ 19.2 + 20.1 +20.3 ze = o the mean value will be = 118 1/2 ppm = 19.78 ppm The formula of standand deviation ,o=VE (xi-x) N-1 where o=standard deviation population N = the size of the ni = each value of population ł = Mean value gă min) ; - 72 19.4 19.78 0.38 0.1444 19.5 L 19.78 0.28 0.0784 19.6 19.78 0.18 0.0324 19.8 19.78 -0.02 0.0004 20.1 19.78 -0.32 0.1024 20.3 I 19.78 -0.52 0.2704 V 0.1444 +0.0784 +0.0324 +0.0004 + 0.1024 + 0.2704 6-1 - V0.12518 = 0.3545 ② vaniance =0 = (0.3545) : 0.12568

Relative standard deviation/RSD) = I x 100 % ge = 0.3545x100 19.78 = 1.79% co-efficient of variation lev) = - standard deviation mean L. 0.3545 19.72 5 Absolute = 0.0175 errora aprozimate valve. " aphorimate valve- true value = 19.78- 20.00 (where ž= 19.78 = 1-0.221 0.22 ennon li 1 st nt t ean value En ut thue value 2o) (6) Reladive -0.22 , xt = true value - 20.00 a data set are away from Etoio111 -0.011 % The spread in a data set is the measure of how for the numbers in a data set are as the mean or median. The different methods are available for measure of spread: range , intenquantile range and variance Range for this case = 20.3 - 19.4 = 0.9 ( highdest value - lowest valuel variance (0%= 0.12568