Particle size data for a sample of spherical particles is given as volume percentages recorded in the following size ranges: Volume % Diameter x (um) x ≤ 10 10 < x≤ 20 20 < x≤ 40 40 < x≤ 80 80 < x≤ 160 160 < x≤ 320 320 < x 0 0.01 0.09 0.9 9 90 0 (a) Calculate the volume based cumulative frequency distribution, Qv, and differential frequency distribution, qv, and tabulate values (showing units) at appropriate grid points xi. (b) Calculate number fractions in the given size ranges using grid points as representative sizes for particles in corresponding size bins.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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ISBN:9780079039897
Author:Carter
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Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 4CYU
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Particle size data for a sample of spherical particles is given as volume
percentages recorded in the following size ranges:
Volume %
Diameter x
(um)
x ≤ 10
10 < x≤ 20
20< x≤ 40
40 < x≤ 80
80 < x≤ 160
160 < x≤ 320
320 < x
0
0.01
0.09
0.9
9
90
0
(a) Calculate the volume based cumulative frequency distribution, Qv, and differential
frequency distribution, qv, and tabulate values (showing units) at appropriate grid points x₁.
(b) Calculate number fractions in the given size ranges using grid points as representative
sizes for particles in corresponding size bins.
Transcribed Image Text:Particle size data for a sample of spherical particles is given as volume percentages recorded in the following size ranges: Volume % Diameter x (um) x ≤ 10 10 < x≤ 20 20< x≤ 40 40 < x≤ 80 80 < x≤ 160 160 < x≤ 320 320 < x 0 0.01 0.09 0.9 9 90 0 (a) Calculate the volume based cumulative frequency distribution, Qv, and differential frequency distribution, qv, and tabulate values (showing units) at appropriate grid points x₁. (b) Calculate number fractions in the given size ranges using grid points as representative sizes for particles in corresponding size bins.
(b)
Xi (um)
10
20
40
80
160
320
fi (-)
0
0.134
0.150
0.188
0.235
0.294
Transcribed Image Text:(b) Xi (um) 10 20 40 80 160 320 fi (-) 0 0.134 0.150 0.188 0.235 0.294
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