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

In summary, when finding the 60th percentile among 30 data points, both the 18th and 19th term would fall within the 60th percentile. However, it is recommended to choose the 18th term as it is the conventional method. In cases where the data set is not continuous and one of the "steps" falls on the percentile being looked for, there may be more than one possible value for that percentile. It is important to clarify with the teacher or follow a specific convention in such cases.
  • #1
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

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  • #2
To be within the 60th percentile among 30, you would need to be at 18 or more.
 
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  • #3
.Scott said:
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 ?
 
  • #4
tzx9633 said:
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.
 
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  • #5
.Scott said:
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 ??
 
  • #6
tzx9633 said:
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.
 

What is the definition of percentile for grouped data?

The percentile for grouped data is a measure of the position of a certain value within a given dataset. It represents the percentage of values that fall below a specific value.

How is the percentile for grouped data calculated?

The percentile for grouped data is calculated by first finding the cumulative frequency of the grouped data. Then, the desired percentile is multiplied by the total frequency and divided by 100 to get the desired position in the dataset. Finally, the corresponding value in the dataset is determined.

What is the purpose of using percentile for grouped data?

The use of percentile for grouped data allows for a quick and easy way to compare values between different datasets. It also helps to identify extreme values or outliers within a dataset.

Can the percentile for grouped data be used for non-normal distributions?

Yes, the percentile for grouped data can be used for any type of distribution, regardless of its shape. It is a useful measure for comparing values within a dataset and does not require the data to be normally distributed.

How does the percentile for grouped data differ from other measures of position?

The percentile for grouped data differs from other measures of position, such as mean or median, in that it takes into account the entire dataset and the frequency of each value. This makes it a more robust measure, particularly for datasets with extreme values or outliers.

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