Midpoints, Limits, Boundaries and Interval Size


New member
May 8, 2017
I got stuck on this problem and want to understand the solution (given by the book) in words that I can actually understand. Basically, how can you use the class midpoint to find class limits, class boundaries, and the class interval? Below is the problem:

"If the class marks (midpoints) in a frequency distribution of the weights of students are 128, 137, 146, 155, 146, 155, 164, 173, and 182 pounds, find a) the class interval size, b) the class boundaries, and c) the class limits, assuming that the weights were measured to the nearest pound."

a) So, part a was easy. Whether you subtract one class midpoint from the next, or subtract the lower limit from the upper limit, the class size should be the same number, right? Given the midpoints, I did 137-128 to get 9. This is the class size... I think. O__O

b) Class boundaries... hm, basically if say there is interval one with limits 110-150, then the boundaries for that interval would be 109.5 and 150.5, right? For this problem, the book explained that a class boundary is between two class midpoints. I didn't understand why, but when I followed the book's solution and wrote everything out arithmetically, it turned out that each boundary was indeed between two class midpoints (inner voice, writhing in the agony of incomprehension: why??). If someone could further clarify this point I would be grateful. So, taking the statement that boundaries are between class midpoints at face value, I added up each of the midpoints and divided by 2:
(128+137)/2 = 132.5; (137+146)/2= 141.5; (146+155)/2= 150.5; (155+164)/2= 159.5; (164+173)/2= 168.5; (182 + 173)/2 = 177.5 . But, two endpoints (according to the book) are still unaccounted for: one on the left extreme and one on the right extreme. For some reason, to find the first class boundary, you have to do 132.5-9 to get 123.5. I get that 9 is the class size, but to get class size don't you usually subtract the lower class limit from the upper class limit? Confusing. :confused: The book triumphantly declares that the class boundaries are 123.5, 132 (not 132.5? inner voice, writhing in the agony of incomprehension: why??), 141.5, 150.5, 159.5, 168.5, 177.5, 186.5.

c) If 123.5 is the first class boundary, the first class limit must be 124. I throw a pleading glance at the book. Yes, it's 124, thank you God! Since the class size is 9, the upper limit of the first class has to be 132. The second class limit will start will 133, accordingly, and end with 141. And so on.

As you can see, I more or less understand the reasoning in the answer to part c). I need help with the concepts and groundwork for parts a) and b). Any part that you are willing to help with will contribute to my psychological fund of emotional peace and stability. (x___x)v Thanks~