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Histograms

Discussion in 'Mathematics' started by weebecka, Jan 18, 2011.

  1. A histogram.
    You are talking about a normalised histogram, sometimes also known as a relative frequency histogram.
    A bar chart becomes a histogram when you've got a scale on the x-axis and the data in each bar has x-values between the lower and upper boundaries of the bar. You can still have frequency on the y-axis.
     


  2. A Histogram is a graphical display of data using bars of different heights.
    <table align="center"><tr><td>[​IMG]</td><td align="center">It is similar to a Bar Chart, but a histogram groups data into ranges
    And you decide what ranges to use!
    </td></tr></table>
     
  3. Well I think it's still a histogram because you have grouped data - I'd just call it a rubbish histogram, or a misleading one, or a wrong one, or something like that.
    On a related note, you don't always have to have height = freq/width with unequal classes, as for the (non-rubbish) histograms the area is proportional to the freq, not necessarily equal to it. To show whether or not that it's equal you sometimes get units - so grouping cats by their weight may give you the frequency density units "cats per gram".

     
  4.  
  5. [​IMG]
    or get the students to name it.....
     
  6. Many thanks for the replies, greatly appreciated. I think I'll go with 'misleading histogram'!
     
  7. How is a histogram with equal bar widths misleading?
    The taller the bar, the greater the frequency. Also, the bigger the area the greater the frequency.
    I would call it a 'simple' histogram. It's very easy to interpret, I don't understand why it's misleading.
    Plotting and interpreting histograms with unequal class intervals is more complex and this is where the area of the bar is essential, in determining the frequency,
    The only situation in which I can envisage a histogram with equal bar widths being misleading, is when the vertical scale does not start at zero, but then this is also true for histograms of unequal class width.

     
  8. Sara isn't talking about a histogram with equal bar widths salsamaths. She's talking about one with unequal bar widths and frequencies.
     
  9. Please can you give me an example?
     
  10. I'm not sure how to post pictures, so I will do my best to give an example.


    Time people spent watching tv (in minutes) 0 to 5, 5 to 10, 10 to 20, with frequencies of 10, 20 and 30 respectively. A normal histogram would have frequency densities of 2, 4 and 3 respectively. So, the histogram effectively levels out the fact that the intervals are uneven.


    A frequency chart in this instance with bars drawn to 10, 20 and 30 respectively would, in my opinion, look misleading since the 10 to 20 minute group is given undue prominence in terms of area.


    My question was, does the latter type of chart have a name and an earlier poster suggested 'misleading histogram', a view with which I'm in agreement.


    Many thanks again to all the people who have responded.
     
  11. Time people spent watching tv (in minutes) 0 to 5, 5 to 10, 10 to 20, with frequencies of 10, 20 and 30 respectively. A normal histogram would have frequency densities of 2, 4 and 3 respectively. So, the histogram effectively levels out the fact that the intervals are uneven.

    Since it is a histogram about televisions perhaps it should be a telegram!
    I certainly appreciate what you are asking. As mathematicians it makes us cringe but probably Jo public see nothing wrong with it.
    A misleading histogram is certainly one thing I might call the type you were asking about. Perhaps we just need to re-arrange the first 4 letters of histogram to find a better name.
     
  12. "This" ?
     
  13. Thanks mathsteacher1953 and Nazard. The reason I asked was because I'm planning a lesson on histograms and wanted to start out with the misleading chart as a motivation for moving to frequency density/histograms. From the responses so far it seems that there isn't an official name for the chart so I'll stick with misleading!
     
  14. Of course this was what I was thinking. I don't know of any other possibilities.
    A thisogram it is then.
     
  15. Oh come on! It's staring you in the face ...


    Any self-respecting Star Wars fan would know that it is also an anagram of "Sith".
    "Sithogram". Does it for me.

     
  16. Sorry for being slow on the uptake, it's been a long day! Very good with the thisogram!
     
  17. Whenever I see it I want to headbutt something. So you could call it a "Glasgow Kiss-ogram".
    No? Suit yourself then!

     
  18. Sorry, of course it a histogram that has been incorrectly plotted, and therefore misleading, I misunderstood the original question. Doh!
     
  19. Interesting aside:


    In the US (*) Histograms have frequency on the vertical axis not frequency density so they don't ever have unequal class widths. This is as sane and sensible as what we do, just different :)


    (*) IME, I'm happy to be corrected
     
  20. thanks for posting this, cleared up stuff for me too! two birds with one stone!
     

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