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To calculate the percentile rank for grouped data, you need to add up the frequencies of all of the values before the one you are interested in, divide by the total number of observations, and then multiply by 100. This will give you the percentile rank for the value that you are interested in.
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.
The following tutorials provide additional information for working with grouped data: