Quartile & Percentiles Questions - Answers by Alex

[alexbib]

I have a few questions about distributing values into quartiles:

1.must all equal values be in the same quartile, even if that makes you create (sometimes very)unequal groups?

2.what do you do when your number of values cannot be divided by 4? Say I have 10 values, do I make the quartiles 3-2-3-2, 2-3-3-2, or something else?

About percentiles, what do you do when you have less than 100 values?


I know stats isn't meant to be used on small numbers of values, but I am tutoring two high school students and couldn't answer these questions.

Thanks,

Alex

 

[Damned charming :)]

I teach at 4 unis and also privately teach students. Unfortunately for you I have seen at least 4 similar ways of doing this. The most common way is that the upper quartile is the median of the upper half of the numbers. so the upper quartile of
12,13,15,19,100,102 is the median of 19,100,102 so the upper quartile is 100.

note that if the data set is odd the middle number is used in both the lower half and upper half of the numbers.

so the lower quartile of 13,15,19,100,102 is the median of 13,15,19
so lower quartile is 15.

so the upper quartile of 13,15,19,100,102 is the median of 19,100,102
so lower quartile is 100.


if you want a formula that works quartiles it the
lower quartile is the (n+1)*0.25th number.

the xth percentile would be (n+1)*x/100th number

What do you when you want the 5.25th number? take the 5th number or use linear interpolation, it depends on their skill.

 

[tacman]

Hi Alex,

Thank you for your questions. Here are some answers to help you better understand quartiles and percentiles:

1. In general, equal values should be placed in the same quartile. However, if you have a large number of equal values, it is okay to divide them evenly among the quartiles. For example, if you have 100 values and 20 of them are equal, you can place 5 in each quartile.

2. When the number of values cannot be divided by 4, it is best to use the nearest whole number for each quartile. In your example of 10 values, you can create quartiles of 3-3-2-2, as this would be the closest approximation to dividing them evenly.

3. When dealing with less than 100 values, you can still calculate percentiles by using the formula (n+1)/100, where n is the number of values. This will give you the position of the value in the data set, and you can then use that position to determine the corresponding percentile.

I hope this helps. Remember, it is always important to consider the context and purpose of your data when using quartiles and percentiles. Good luck with your tutoring!