248 M.J. Lewis Fig 9.1.(a)Frequency distribution(F), (b)cumulative distribution(C): see also data in Table 9.5 Table 9. 5. Frequency distribution Size range Mean diameter Number Frequency Cumulative Cumulative (um) in range distributiondistribution volume 0to10 18 1.8 10to20 20to30 129 20.3 2.0 30to4035 18.4 38.7 7.0 40to5045 20.3 0.0 6055 18.5 41.0 640 70to8075 74 96.7 850 80to9085 98.0 90to10095 0.4 100.0 0 mean diameter =45.96 um; d2/ 1=53. 29 um; d3/2=58.86 Am Cumulative volume represents the percentage of the total volume less than the mean diameter of the range Other values which may be calculated from the distribution include the mean diameter nd the median diameter and the standard deviation, which gives an indication of the The simplest is the mean diameter, defined ∑n4/∑248 M. J. Lewis 100 80 60 10 40 20 0 LL *OB 0 0 20 Size 40 (prn) 60 80 100 0 Fig. 9.1. (a) Frequency distribution (F), (b) cumulative distribution (0: see also data in Table 9.5. Table 9.5. Frequency distribution Size range Mean diameter Number Frequency Cumulative Cumulative OLm) of range (pm) in range distribution distribution volume distribution 0 to 10 5 5 1.8 1.8 0 10 to 20 15 15 5.6 7.4 0 20to30 25 35 12.9 20.3 2.0 30to40 35 50 18.4 38.7 7.0 40to50 45 55 20.3 59.0 20.0 50to60 55 50 18.5 77.5 41 .O 60to70 65 32 11.8 89.3 64.0 70to 80 75 20 7.4 96.7 85.0 80to90 85 8 2.9 99.6 98.0 90to 100 95 1 0.4 100.0 100.0 >loo 0 27 1 - mean diameter = 45.96 pm; d2/1 = 53.29 pm; d3/2 = 58.86 pm Cumulative number frequency indicates the percentage of the total number less than the mean diameter of the range. Cumulative volume represents the percentage of the total volume less than the mean diameter of the range. Other values which may be calculated from the distribution include the mean diameter and the median diameter and the standard deviation, which gives an indication of the spread. The simplest is the mean diameter, defined as C nidi /C ni 7