Math: Percentile

[kingwinner]

I am kind of confused with the idea of percentile! The example in my textbook is oversimplified and seems to avoid complicated cases...I am stuck with question a)ii) the 95th percentile...

 

1)

 

For a)i) 50% of the data points are less than or equal to the 50th percentile and 50% are greater than or equal to it. Therefore it is the midpoint between the 50th and 51th scores, i.e. (68+68)/2=68

 

a)ii) For the 95th percentile,

50x95%=47.5(not integer!!!)

There are 47.5 scores(not integer!!!) less than or equal to the 95th percentile and 2.5 scores(not integer!!!) greater than or equal to the 95th percentile

 

[47.5 is not an integer, then how can I find out hte 95th percentile? I don't understand how to do it...]

 

1b) How can I find out this?

 

Thank you for helping and explaning! ;)

[kingwinner]

I am really stuck with the concept of percentile...can someone please help?

[infamous]

Try this link:

 

http://psych.rice.edu/online_stat/glossary/percentiles.html

 

Good luck..................Infy

[C1ay]

47.5 is not an integer, then how can I find out hte 95th percentile? I don't understand how to do it...]

 

1b) How can I find out this?

The nth percentile of a data set is that number such that n% of the data is less than that number.

 

Out of a sample size of 50 points, 47.5 points are 95% of the total number of scores in the data set. The half point really doesn't count so count off 47 of the points from the low score and you will find a value; the next value greater is where the 95th percentile begins.

[kingwinner]

The nth percentile of a data set is that number such that n% of the data is less than that number.

 

Out of a sample size of 50 points, 47.5 points are 95% of the total number of scores in the data set. The half point really doesn't count so count off 47 of the points from the low score and you will find a value; the next value greater is where the 95th percentile begins.

But should you round 47.5 up to 48 to make an integer instead of rounding down to 47?

[C1ay]

But should you round 47.5 up to 48 to make an integer instead of rounding down to 47?

No. It is common to see a value of percentile that does not actually correspond with an actual value in the data set. In this case the 47th point has the value 89 and the 48th 91. The point that is halfway between them, 90, the 47.5th point, is not a data point at all but it is the value that is equal to or less than 95% of the values. In your set a value greater than 90 would be in the 95th percentile.

[kingwinner]

No. It is common to see a value of percentile that does not actually correspond with an actual value in the data set. In this case the 47th point has the value 89 and the 48th 91. The point that is halfway between them, 90, the 47.5th point, is not a data point at all but it is the value that is equal to or less than 95% of the values. In your set a value greater than 90 would be in the 95th percentile.

But 47.5 has the deciminal .5 , according to the rule of rounding, it would be rounded to 48......what is the reason of rounding down to 47?

 

This percentile stuff is really confusing...;)

[C1ay]

But 47.5 has the deciminal .5 , according to the rule of rounding, it would be rounded to 48......what is the reason of rounding down to 47?

I didn't round though. The decimal, .5, is the halfway point between the 47th and 48th values, 89 and 91 respectively. The numerical value that is halfway between these points is 90. By this method all data points that are less than 90 are lower than the 95th percentile and the 48th point, value 91, is in the 95th percentile or higher.

 

To check the percentile rank of a given data point you can calculate it's rank in the set as a percentage. The percentile rank (Pr) of any chosen data point is the rank of that point ® over the total number of values (N) times 100, i.e. Pr=R/N*100. From your data the 47th point has a percentile rank of 47/50*100=94. The 48th point has Pr=48/50*100=96. This verifies that the boundary of the 95th percentile is between the points 47 and 48.