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Math Help - Calculating Quartiles answer explanation

  1. #1
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    Exclamation Calculating Quartiles answer explanation

    Question: Calculate Q1 (lower quartile)

    There are 50 data entries so im not going to type them all.

    Answer:
    n = 50, so (n+3)/4=13.25
    Therefore Q1 is a quarter of the distance between the 13th an 14th sorted data values.


    I dont understand why we add three to our number of data values. Can sombody please explain this. PLease please please!
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  2. #2
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    Quartiles

    Hello Mandi_Moo
    Quote Originally Posted by Mandi_Moo View Post
    Question: Calculate Q1 (lower quartile)

    There are 50 data entries so im not going to type them all.

    Answer:
    n = 50, so (n+3)/4=13.25
    Therefore Q1 is a quarter of the distance between the 13th an 14th sorted data values.


    I dont understand why we add three to our number of data values. Can sombody please explain this. PLease please please!
    Sadly, statisticians can't agree about how to find the quartiles. Some add 3, some add 1. See, for example, Quartile -- from Wolfram MathWorld.

    The method I've always thought the best is to add 1; then

    • take a quarter of the result to get the position of the first quartile;
    • take a half to get the position of the median;
    • and take three-quarters to get the third quartile.

    For example, if there are 11 items, n = 11, n+1 = 12.

    Then, using the method I've just described, the median (which is sometimes called the second quartile) is in \tfrac{1}{2}\cdot 12 = 6^{th} position. This makes sense as the middle item, because there are then 5 items on either side (5 + 1 + 5 = 11).

    The first quartile (which I think of as the median of the lower 5 of these items) is in \tfrac{1}{4}\cdot 12 = 3^{rd} position. Within the lower 5 items, then, the third one has two either side - so it's their median.

    And the third quartile (the median of the top 5 items) is in \tfrac{3}{4}\cdot 12  = 9^{th} position.

    This gives the following picture: \cdot \quad\cdot \quad\odot \quad\cdot \quad\cdot \quad\odot \quad\cdot \quad\cdot \quad\odot\quad\cdot \quad\cdot where the circled dots represent the quartiles. You'll see these are evenly spaced with two dots between each.

    Grandad
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