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Math Help - Percentiles

  1. #1
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    Percentiles

    I have 81 scores as shown below followed by the frequencies

    20.5 - 1
    20.6 - 2
    20.7 - 2
    20.8 - 2
    20.9 - 2
    21.0 - 5
    21.1 - 2
    21.2 - 5
    21.3 - 8
    21.4 - 7
    21.5 - 8
    21.6 - 12
    21.7 - 11
    21.8 - 6
    21.9 - 5
    22.0 - 3

    I had to find the 15th, 25th, 50th, 60th and 75th but my answers (below) weren't correct and I am wondering what I did wrong.

    15th=(.15)(21.0)+(.85)(21.0)=21.0
    since (n+1)*.15=82(.15)=12.3 and 21.0 is in the 12th and 13th position. I used the same formula for the following and got it all wrong.

    25th=(.25)(21.2)+(.75)(21.2)=21.2

    50th=(.50)(21.5)+(.50)(21.5)=21.5

    60th=(.60)(21.6)+(.40)(21.6)=21.6

    75th=(.75)(21.7)+(.25)(21.7)=21.7

    Thank you for any help.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by redpack View Post
    I have 81 scores as shown below followed by the frequencies

    20.5 - 1
    20.6 - 2
    20.7 - 2
    20.8 - 2
    20.9 - 2
    21.0 - 5
    21.1 - 2
    21.2 - 5
    21.3 - 8
    21.4 - 7
    21.5 - 8
    21.6 - 12
    21.7 - 11
    21.8 - 6
    21.9 - 5
    22.0 - 3

    I had to find the 15th, 25th, 50th, 60th and 75th but my answers (below) weren't correct and I am wondering what I did wrong.

    15th=(.15)(21.0)+(.85)(21.0)=21.0
    since (n+1)*.15=82(.15)=12.3 and 21.0 is in the 12th and 13th position. I used the same formula for the following and got it all wrong.

    25th=(.25)(21.2)+(.75)(21.2)=21.2

    50th=(.50)(21.5)+(.50)(21.5)=21.5

    60th=(.60)(21.6)+(.40)(21.6)=21.6

    75th=(.75)(21.7)+(.25)(21.7)=21.7

    Thank you for any help.
    What definition of percentiles are you using?

    CB
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  3. #3
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    (1-a/b)y_{r}+(a/b)y_{r+1} where r is the integer attained from (n+1)p and a/b is the fraction leftover and y is the value in position r or r+1. For example (82*.25)=20.5 so r=20 and a/b=1/2 Since 20.5 is r=20 and r+1=21, y_{r} and y_{r+1} are 21.2 and 21.2?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by redpack View Post
    (1-a/b)y_{r}+(a/b)y_{r+1} where r is the integer attained from (n+1)p and a/b is the fraction leftover and y is the value in position r or r+1. For example (82*.25)=20.5 so r=20 and a/b=1/2 Since 20.5 is r=20 and r+1=21, y_{r} and y_{r+1} are 21.2 and 21.2?
    OK, so lets work the 15-th percentile according to this recipe.

    81*0.15=12.15

    so r=12, r+1=13, Now y_{12}=21.0, and y_{13}=21.0, and the interpolation will give a 15th percentile of 21.0.

    However I don't like this method as your data is (probably) grouped and the 15th percentile should be more like 20.95

    CB
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  5. #5
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    That is the answer I got, 21.0, but all my answers were marked wrong. Is there a different formula I should be using?
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by redpack View Post
    That is the answer I got, 21.0, but all my answers were marked wrong. Is there a different formula I should be using?
    Look at the Wikipedia page on "percentile".

    CB
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