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So I have to find the density and the width for each of the following class. I have the solution but i am confused on something. I am confused on if the answer is correct or incorrect because some sources are saying uppperLimit - lowerLimit = class Width while some are saying it should be lowerLimit2 - lowerLimit1 = Class width. So please have a look at my data and solution and tell me if i am doing it correctly so i can proceed to find the density of it. 

CLASS       FREQUENCY
30.0-32.0   8
32.0-33.0   7
33.0-34.0   10
34.0-34.5   25
34.5-35.0   30
35.0-35.5   40
35.5-36.0   45
36.0-50.0   5

My Solution.

  • We first need to find the class boundaries. In this case, they are 30.0, 32.0, 33.0, 34.0, 34.5, 35.0, 35.5 and 36.0. The class widths are therefore c2 – c1 (i.e., 32.0 – 30.0 = 2.0)
    • So the class width should be --> 2.0, 1.0, 1.0, 0.5, 0.5, 0.5 and 14.0
user372204
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1 Answers1

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Looks to me that you are doing it correctly -- the quantity you want in this case is the width of the bin, which is the distance from the lower bound to the upper bound.

More generally, what you need is the ordinary (Lebesgue) measure of the bin -- your density estimate is essentially comparing the observed mass (i.e. bin count) to the mass of the bin. This generalizes your example to other cases in a natural way. The Lebesgue measure of an interval is just the length of an interval, so that's the right thing whether the intervals touch each other (as in your example) or they don't touch at the endpoints (more generally). Also if you are working in two or more dimensions, the Lebesgue measure of the bin is its area or n-dimensional volume -- therefore in any dimensions, it's easy to know what you need to compute.

Robert Dodier
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