Question

For the following particle size distribution data, calculate the arithmetic mean, geometric mean, count median, and diameter of the particle with average surface area. Particle size (diameter) Number

1 3

3 5

5 2

8 1

Answer 1

Arithmetic mean of n numbers = sum of numbers / n

= (13+35+52+81)/4 = 45.25

Geometric mean of n numbers = n root of product of numbers

= (13×35×52×81)^1/4 = 37.2

Median is number in the middle when all numbers are written in ascending order, if n is odd or arithmetic mean of two middle numbers, if n is even.

Here n = 4, Median is mean of two middle numbers , 35 and 52. Hence median = 43.5

Diameter of particle of average surface area is , square root of average of square of diameters, that is

√ ( (13^2 + 35^2 + 52^2 + 81^2) / 4 ) = 51.6