You can use the following formula to calculate percentile rank for grouped data:
Percentile Rank = L + (RN/100 – M) / F * C
where:
- L: The lower bound of the interval that contains the percentile rank
- R: The percentile rank
- N: The total frequency
- M: The cumulative frequency leading up to the interval that contains the percentile rank
- F: The frequency of the interval that contains the percentile rank
- C: The class width
The following example shows how to use this formula in practice.
Example: Calculate Percentile Rank for Grouped Data
Suppose we have the following frequency distribution:
Now suppose we’d like to calculate the value at the 64th percentile of this distribution.
The interval that contains the 64th percentile will be the 21-25 interval since 64 is between the cumulative frequencies of 58 and 70.
Knowing this, we can find each of the values necessary to plug into our formula:
L: The lower bound of the interval that contains the percentile rank
- The lower bound of the interval is 21.
R: The percentile rank
- The percentile we’re interested in is 64.
N: The total frequency
- The total cumulative frequency in the table is 92.
M: The cumulative frequency leading up to the interval that contains the percentile rank
- The cumulative frequency leading up to the 21-25 class is 58.
F: The frequency of the interval that contains the percentile rank
- The frequency of the 21-25 class is 12.
C: The class width
- The class width is calculated as 25 – 21 = 4.
We can then plug in all of these values into the formula from earlier to find the value at the 64th percentile:
- Percentile Rank = L + (RN/100 – M) / F * C
- 64th Percentile Rank = 21 + (64*92/100 – 58) / 12 * 4
- Percentile Rank = 21.293
The value at the 64th percentile is 21.293.
Additional Resources
The following tutorials provide additional information for working with grouped data:
How to Find Mean & Standard Deviation of Grouped Data
How to Find the Mode of Grouped Data
How to Find the Median of Grouped Data
Grouped vs. Ungrouped Frequency Distributions
I believe this is only correct if your data set has 100 observations. Cumulative % is how I would determine the correct interval. In this case, the end result is the same for the 64th percentile, but it would fail if you were calculating the 90th or 95th percentile.
Hi Zach,
So useful, thanks. Thank you for this.
I have an issue with finding the C, for my 75th percentile. My final data band does not have a class width because it says 16,000 and above, and the range before it is 13,000 – 15,999. How do I find the class width with this number. I also made the L 16,000 will this still work?
Thank you in advance for your help .
Gillian
So interesting
Thank you so much
Your publications helped me a lot
Keep doing the good work