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## Homework Statement

I'm having trouble understanding setting up a frequency distribution. I am confident I am doing it right, but the book I'm using differs when calculating width.

The problem gives a bunch of numbers representing the number of counties, divisions, or parishes for each of the 50 states. It then asks to setup a grouped frequency distribution with 6 classes, a histogram, a frequency polygon, and an ogive with the data. The data is as follows:

67 27 15 75 58 64 8 67 159 5

102 44 92 99 105 120 64 16 23 14

83 87 82 114 56 93 16 10 21 33

62 100 53 88 77 36 67 5 46 66

95 254 29 14 95 39 55 72 23 3

## Homework Equations

Width = ceil(Range / number of Classes)

**width can also be rounded up if it's value is a whole number after calculating it. Or one could increase the number of classes by one. This is an important point for me because my book failed to mention it and I was setting it up wrong as a result. Even after correcting though, I wasn't always getting an identical setup.

Range = MaxVal - MinVal

## The Attempt at a Solution

MaxVal = 254

MinVal = 3

Range = 254 - 3 = 251

Width = ceil(251 / 6) ≈ ceil(41.8) = 42

Starting point = MinVal = 3

Class Limits Boundaries Tally Freq

3 - 44 2.5-44.5 didn't even finish these since CL & boundaries

45 - 86 44.5-86.5 were different from book

87 - 128 86.5-128.5

129 - 170 128.5-170.5

171 - 212 170.5-212.5

213 - 254 212.5-254.5

Here's my problem. The book has class limits:

3-45

46-88

89-131

132-174

175-217

218-260

In other words, they've increased the width by rounding up from its original approximate value (41.8) like I did, but then they rounded that up too! From 41.8 → 42 → 43. I was under the impression that you only round up if the width is an approximate value (it has decimal points). The exception, from what I gather, is that one only rounds up from one whole value to the next, is when the width is a whole number after calculating its value. So if I'd calculated W = 252 / 6 = 42, if 252 were the MaxVal. Then, and only then, would I choose to either increase the number of classes from 6 to 7, or increase the width from 42 to 43. But the author of this book seems to want it both ways: round up the value after calculating it and getting an approximate number, then round up again to the next whole number. This is my current plight. Any help is much appreciated.