HistogramDate: 04/16/2001 at 23:00:13 From: Kelly Subject: Math Problems What is a histogram? Date: 04/17/2001 at 13:27:48 From: Doctor Ian Subject: Re: Math Problems Hi Kelly, To make a histogram, first you count the occurrences of the different kinds of objects that you're keeping track of. For example, you might go around your classroom and write down the grade (A, B, C, D, or F) that everyone got on the latest test: Bill B Betty A Fernando B Karen B Joe F Eliza C Zbignew A Kai B Ellen F Another way to write this information is to organize it by grade, instead of by name: A Betty, Zbignew B Bill, Fernando, Karen, Kai C Eliza D F Joe, Ellen But for the purposes of creating a histogram, you're not interested in individuals, just numbers, so you can replace each list by the number of people it contains: A 2 B 4 C 1 D 0 F 2 The number next to each grade is the 'frequency' with which that grade occurs. That is, the frequency of 'A' grades is 2, the frequency of 'B' grades is 4, and so on. The higher the frequency of a category, the more objects there are in the category. In fact, at this point, you actually _have_ a histogram, but people prefer pictures to numbers, so it's normal to convert each number to a picture, in which the length of a line is proportional to the number it represents. So, for example, a line representing '6' would be twice as long as one representing '3': A ** B **** C * D E ** Note that histograms are only interesting when the categories are defined so that several objects will fall into each one; the following histogram of weights doesn't tell you very much because the categories are too precise: Weight Frequency 100 101 * 102 103 104 * 105 * 106 : 134 135 Categories can also be too broad: Weight Frequency 0- 70 70-140 ************************** 140-210 The hardest thing about making a good histogram is choosing the right categories. I hope this helps. Be sure to write back if you have more questions, about this or anything else. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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