i would say that the harper collins dictionary of mathematics is wrong
i think most would say that a bar chart has a baseline that is not a
quantitative scale ... and, the order in which the bars are listed is
essentially arbitrary
At 11:43 PM 8/12/00 +0000, Alexander Bogomolny wrote:
>The Harper Collins Dictionary of Mathematics gives the following
>definitions:
>
>1. Histogram - a figure that represents a frequency distribution,
>consisting of contiguous rectangles with width proportional to the
>size of the respective class intervals and areas proportional to the
>relative frequencies.
>
>2. Bar chart - a histogram in which all the class intervals are
>of equal width.
>
>Alexander Bogomolny
>http://www.cut-the-knot.com
>
>Sheila King wrote:
>>
>> [cross-posted to sci.stat.edu,sci.stat.math,k12.ed.math]
>>
>> I'm teaching a GE stat course, my first time teaching stat, and am
>> having some points of confusion. Here is one of my questions:
>>
>> Suppose I have a probability distribution as follows:
>>
>> Sample space:
>> 1.5, 2.0, 2.5, 3.5, 4.0, 4.5
>>
>> and each of these outcomes is equally likely. So, if my random variable
>> is x, then
>> P(x=1.5) = 1/6
>> P(x=2) = 1/6
>> and so on...
>>
>> To draw a probability distribution histogram, I wanted to make the bar
>> for each outcome have a height of 1/6, but I became confused over this
>> point:
>> for x=2.0, the bar can only be on half unit wide, because of the
>> neighboring outcomes 1.5 and 2.5
>> (until I had encountered this particular problem, I had always made the
>> bars for each outcome a width of one unit wide, with a height equal to
>> P(x=that outcome) and with the outcome value centered horizontally on
>> the bar).
>> But it seems to me, each of the bars should have an equal width.
>>
>> But if there are six bars (because of six outcomes) and each is only
>> half a unit wide, and 1/6 of a unit tall, then the total area under the
>> distribution is only 1/2 and not 1. This bothered me.
>>
>> But the solution manual shows the probability distribution histograms
>> for this problem exactly as I have described above.
>>
>> Shouldn't the total area under the distribution equal one?
>>
>> Sheila King
>> [EMAIL PROTECTED]
>> http://www.thinkspot.net/sheila/
>> http://www.k12groups.org/
>
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