How to Calculate Percentile Rank for Grouped Data

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.