# Percentiles

• May 12th 2009, 07:35 PM
redpack
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.
• May 13th 2009, 09:08 AM
CaptainBlack
Quote:

Originally Posted by redpack
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
• May 13th 2009, 02:38 PM
redpack
$(1-a/b)y_{r}+(a/b)y_{r+1}$ 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?
• May 13th 2009, 03:06 PM
CaptainBlack
Quote:

Originally Posted by redpack
$(1-a/b)y_{r}+(a/b)y_{r+1}$ 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
• May 13th 2009, 04:28 PM
redpack
That is the answer I got, 21.0, but all my answers were marked wrong. Is there a different formula I should be using?
• May 14th 2009, 12:01 AM
CaptainBlack
Quote:

Originally Posted by redpack
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