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S1 - finding the lower quartile question, I have the answer, just don't get something watch

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    Here is the question:
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    When finding the lower quartile, I get why they have used 100/4. They got the 100 from 100 pieces of data, and divided it by 4 to find the lower quartile. 100/4=25.

    In a past example I had done, there were 11 pieces of data,I added 1 to make it an even number, and then divide it by 4 to find the lower quartile. So I had 12/4=3, so the answer was the 3rd piece of data. The mark scheme also got this answer, just rounding up instead of adding 1 to the 11. (See here: http://imgur.com/a/IDVYI)

    However, in the example I posted in this thread, 100/4=25, so I thought it should have been the 25th piece of data. However, the mark scheme says it is the average value between the 25th and 26th piece of data. Why is this? I don't understand why the answer lies between the 25th and 26th pieces of data when 100/4=25, not 25.5

    Can you explain this to me please?
    Thank you!
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    First let me say that the method Edexcel want you to use is completely whacko and sometimes you won't actually get the same answer as you would by finding the median first then going half way to that from the minimum value. But just do it the way they want you to You don't have to but it makes the numbers easier.

    For continuous or grouped data only:
    \mathrm{Q}_1 = \frac{n}{4}^\mathrm{\ th\ }\mathrm{value}
    \mathrm{Q}_2 = \frac{2n}{4}^\mathrm{\ th\ }\mathrm{value}
    \mathrm{Q}_3 = \frac{3n}{4}^\mathrm{\ th\ }\mathrm{value}
    Where n is the number of pieces of data. Then just find the value with interpolation.

    For discrete data only, do the same process as above and then:
    If you get an integer (eg. 11th value) go half way between it and the next value (eg. 11.5th value).
    If you don't get an integer (eg. 13.5th value) you must round up (!) to the next integer (eg. 14th value) even if you would not normally round up. (eg. 17.25th value -> 18th value). Hold up your five fingers. The median finger is the third right? (not the 2.5th)

    Just follow those rules and you'll get the right answer. Totally strange right? But that's what the text book says. If something's not clear, do say.
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    (Original post by Tommy59375)
    First let me say that the method Edexcel want you to use is completely whacko and sometimes you won't actually get the same answer as you would by finding the median first then going half way to that from the minimum value. But just do it the way they want you to You don't have to but it makes the numbers easier.

    For continuous or grouped data only:
    \mathrm{Q}_1 = \frac{n}{4}^\mathrm{\ th\ }\mathrm{value}
    \mathrm{Q}_2 = \frac{2n}{4}^\mathrm{\ th\ }\mathrm{value}
    \mathrm{Q}_3 = \frac{3n}{4}^\mathrm{\ th\ }\mathrm{value}
    Where n is the number of pieces of data. Then just find the value with interpolation.

    For discrete data only, do the same process as above and then:
    If you get an integer (eg. 11th value) go half way between it and the next value (eg. 11.5th value).
    If you don't get an integer (eg. 13.5th value) you must round up (!) to the next integer (eg. 14th value) even if you would not normally round up. (eg. 17.25th value -> 18th value). Hold up your five fingers. The median finger is the third right? (not the 2.5th)

    Just follow those rules and you'll get the right answer. Totally strange right? But that's what the text book says. If something's not clear, do say.
    Wow, holy crap, thank you so much! You answered my question as simply as possible and covered it all.

    Where you talked about continuous data in terms of like n/4 for the Q1, is there a way to talk about discrete data in terms of an expression?
    So for discrete data:

    After following the process for continuous or grouped data, can you talk about it in terms of like (n+1)/4? ie, if you had 100 data pieces and wanted the first quartile, instead of getting 100/4=25 and then half way to 26th term afterwards, can you talk about it as something such as (100+1)/4 and then round it up because it's a decimal?

    Am I just over complicating this? I am trying to think of expressions for doing the discrete data, so you add 1 to n then divide by, say 4 for the first quartile, 2 for the second quartile, etc. Am I just over complicating this and over thinking it way too much?

    If I am, please tell me that it's pointless what I am trying to work out and I should just use the method you said. I completely understand what you said to me, I think I am just overcomplicating it for no reason with what I am trying to do. If this is the case, let me know please - I overthink the simple stuff way too much in maths and it gets me so confused when I don't need to be.
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    (Original post by blobbybill)
    Wow, holy crap, thank you so much! You answered my question as simply as possible and covered it all.

    Where you talked about continuous data in terms of like n/4 for the Q1, is there a way to talk about discrete data in terms of an expression?
    So for discrete data:

    After following the process for continuous or grouped data, can you talk about it in terms of like (n+1)/4? ie, if you had 100 data pieces and wanted the first quartile, instead of getting 100/4=25 and then half way to 26th term afterwards, can you talk about it as something such as (100+1)/4 and then round it up because it's a decimal?

    Am I just over complicating this? I am trying to think of expressions for doing the discrete data, so you add 1 to n then divide by, say 4 for the first quartile, 2 for the second quartile, etc. Am I just over complicating this and over thinking it way too much?

    If I am, please tell me that it's pointless what I am trying to work out and I should just use the method you said. I completely understand what you said to me, I think I am just overcomplicating it for no reason with what I am trying to do. If this is the case, let me know please - I overthink the simple stuff way too much in maths and it gets me so confused when I don't need to be.
    If it were possible, I would have told you that in the first place unfortunately. What I wrote is both what my teacher told me and what it says in the textbook, so I think there's just not a better way to explain it.

    You certainly would think you could do (n+1)/4, 2(n+1)/4, 3(n+1)/4 and as far as I am aware if you do this you will get the marks for it in the exam (there are always 2 or 3 valid answers on the mark scheme). The real problem seems to stem from the fact that you round up, even when you have 0.25. If that wasn't a rule, I think the two methods would actually be identical in results.

    It's a bit like skewness. There seem to be lots of different ways to calculate it... statistics is funny like that!

    But I would just recommend accepting the method I outlined, as much as it really makes no sense... just because the numbers are usually easier with it. Sorry!
 
 
 
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