Question

a population of particles in a microstructure consists of three different sized spherical particles. The diameters of the particles are: d1= 2, d2= 4, d3= 10 For the particles distributed randomly in the volume in the proportions N1:N2:N3 = 3:6:1 Determine the average particle size, the standard deviation of the particle size, the coefficient of variation, and the mode

Answer 1

From the given data

X	P(X=x)	xP(X=x)	X^2P(X=x)
2	0.3	0.6	1.2
4	0.6	2.4	9.6
10	0.1	1	10
Total:	1	4	20.8

The probabilities are calculated as 3/10 , 6/10. 1/10 i.e. 0.3, 0.6, 0.1 since N = N1 + N2 + N3 = 3+6+1 = 10

Coefficient of Variation CV = SD / Mean *100 = 2.1909 / 4 *100 = 54.7725%

Mode is the value of x which is corresponding to highest probability i.e. highest probability is 0.6, corresponding x is 4

Therefore, Mode = 4