What is the correct method for finding the 60th percentile of grouped data?

[tzx9633]

Homework Statement

I am asked to find the 60th percentile of this question , so i found that 30 x 0.6 = 18 ,

So , the 60th percentile is the 18th term ? Or 19th term ? I am confused . I know whether it's 18th or 19th , it's still the same . I just want to get my concept correct

Homework Equations

The Attempt at a Solution

 

[.Scott]

To be within the 60th percentile among 30, you would need to be at 18 or more.

 

[tzx9633]

To be within the 60th percentile among 30, you would need to be at 18 or more.

So , i should take the 19th term , am i right ?

 

[.Scott]

So , i should take the 19th term , am i right ?

For your data set, taking 18 or 19 is the same. But normally you would take 18.

You're asking about a case that is unusual in two ways:
1) The "curve" is not continuous - it is a step function.
2) One of the "steps" occurs at the percentile you are looking for.

A simpler example would be: 10 students get a mark of 20 and 10 students get a mark or 21, what is the 50th percentile?
The step falls on the 50 percentile mark. In such a situation, you would need to know how that 50th percentile figure was going to be used.
In most cases, it would be reasonable to use 20.5 as the 50th percentile mark - as it provides a dividing line.
But since all of the students who got the 21 are in the 50th percentile and none of those who received 20 are, then the value 21 also works.
Finally, if you are asking the question: what is the minimum mark I would need to get to make it into the 50th percentile, the answer would be 20.000001 - just more than the 10 who got 20.

 

[tzx9633]

For your data set, taking 18 or 19 is the same. But normally you would take 18.

You're asking about a case that is unusual in two ways:
1) The "curve" is not continuous - it is a step function.
2) One of the "steps" occurs at the percentile you are looking for.

A simpler example would be: 10 students get a mark of 20 and 10 students get a mark or 21, what is the 50th percentile?
The step falls on the 50 percentile mark. In such a situation, you would need to know how that 50th percentile figure was going to be used.
In most cases, it would be reasonable to use 20.5 as the 50th percentile mark - as it provides a dividing line.
But since all of the students who got the 21 are in the 50th percentile and none of those who received 20 are, then the value 21 also works.
Finally, if you are asking the question: what is the minimum mark I would need to get to make it into the 50th percentile, the answer would be 20.000001 - just more than the 10 who got 20.

is it wrong to take (18th term + 19th term) /2 ? Assuming the 18th term and 19th term has different value , then should i just take the 18th term or (18th term + 19th term) /2 ??

 

[Ray Vickson]

is it wrong to take (18th term + 19th term) /2 ? Assuming the 18th term and 19th term has different value , then should i just take the 18th term or (18th term + 19th term) /2 ??

How does your textbook say you should do it? What do your course notes have to say about it?

There is not really any "officially correct" answer---different books and websites do it in different ways. All you can do is adopt a particular convention and stick to it; it would be wise to choose a convention which is the same as the one used by your teacher, especially on a written test. If you are dealing with a case not covered in your textbook or course notes, go to your teacher and ask for clarification.