How to use the PERCENTRANK.INC function

What is the PERCENTRANK.INC function?

The PERCENTRANK.INC function calculates the percent rank of a given number compared to the whole data set. PERCENTRANK.INC stands for "PERCENTRANK Inclusive". This includes the value of the score in the ranking. This function was introduced in Excel 2010 and has replaced the PERCENTRANK function.

1. Introduction

What is the percent rank?

The percent rank (or percentile rank) indicates the percentage of scores that fall at or below a given score in a dataset. It provides a way to evaluate the standing of a score relative to others.

What is relative standing?

Relative standing refers to how a particular score compares to the distribution of scores within a group or population. It allows you to understand where a score ranks in relation to others.

When is the PERCENTRANK.INC function useful?

Use the PERCENTRANK.INC function to evaluate the standing of an aptitude test score among all scores for the test.

What is an aptitude test score?

An aptitude test is a standardized test designed to measure a person's ability or skills in a specific topic. An aptitude test score is the performance measurement on such a test.

Evaluating an aptitude test score's percentage ranking allows understanding its standing compared to other test takers. Higher percentiles indicate better relative performance on the aptitude test.

2. Syntax

PERCENTRANK.INC(array, x, [significance])

3. Arguments

array	Required. The array or range of data with numeric values that defines relative standing.
x	Required. The value for which you want to know the percent rank.
[significance]	Optional. Lower bound, default value is 3.

What are significant digits?

The PERCENTRANK.EXC function does not round the output number to the specified number of significant digits. If the specified number is 3 then 0.1875 becomes 0.187 which means that the remaining digits are simply removed.

4. Example 1

In a class of 15 students, the scores on a final exam were recorded. What is their percentage rank among all the students if a student scored 75 using PERCENTRANK.INC? The data is:

Values
2
9
11
16
18
19
24
27
32
35
36
39
65
67
84

Here are the arguments:

• array = B23:B37
• x = 75

Formula in cell B17:

The formula calculates a value of 0.904 (or 90.4%) when a student scores 75, based on the data range B23:B37. The third argument, [significance], is optional and has a default value of three significant digits. The function performs interpolation to determine the appropriate value when the input value (x) does not directly correspond to a value in the data array.

The chart in the image visually represents this interpolation process, displaying the calculated value of 0.905 as an interpolated value falling between the data points 67 and 84.

To understand this graphical representation, locate the value 75 on the y-axis. From that point, draw an imaginary horizontal line until it intersects with the black line, which represents the interpolated line connecting the data points. Then, follow the point of intersection vertically downwards towards the x-axis. The corresponding value on the x-axis is approximately 90%.

The PERCENTRANK.INC function employs this interpolation technique to provide the correct value when the input value (x) does not match any value in the data array.

What is interpolate?

Interpolate means to estimate or infer a data point within a range of known data points. In statistics, interpolation refers to estimating the percentage between existing data points in a distribution.

5. Example 2

A company has 15 sales representatives, and their monthly sales figures are recorded. If a representative sold $40,000 worth of products, what is their percentage rank among all the representatives using PERCENTRANK.INC?

Here are the arguments:

• array = B30:B44
• x = 40000
• significance = 3

Formula in cell B17:

The formula returns 0.407 (40.7%) if a sales representative sold for 40, 000 based on all sales representatives in B30:B44. The function interpolates in order to return the correct value if x doesn't match a value in the array. This is the case in this example, there is no data point equal to 40,000.

In the image above, locate value 40,000 on the y-axis. From that point, draw an imaginary horizontal line until it intersects with the blue line which represents the interpolated line between data points. Then, follow the point of intersection vertically towards the x-axis below. You will find that the corresponding value on the x-axis is approximately 41%.

6. Example 3

In a marathon race with 25 participants, the finishing times of all runners are recorded. If an athlete finished the race in 3 hours and 20 minutes, what is their percentage rank among all participants using PERCENTRANK.INC?

Here are the arguments:

• array = B30:B54
• x = 3:20:00 (0.138888888888889)
• significance = 4

Formula in cell B17:

The formula returns 0.3737 (37.37%) if an athlete finished the race in 3 hours and 20 minutes, based on all data points in B30:B54. The function interpolates in order to return the correct value if x doesn't match a value in the array. This is the case in this example, there is no data point equal to 3:20:00.

In the image above, locate value 3:20:00 on the y-axis. From that point, draw an imaginary horizontal line until it intersects with the blue line which represents the interpolated line between data points. Then, follow the point of intersection vertically towards the x-axis below. You will find that the corresponding value on the x-axis is approximately 37%.

7. How is the function calculated?

1. Sort the scores from lowest to highest.
2. Determine the rank of the given score in the ordered list.
3. Calculate the percent rank using the formula:
   Percent rank = (Rank - 1) / (Total number of scores - 1)

(3-1)/(15-1)

becomes

2/14 = 0.142 (approx. 3 digits)

8. Function not working

The PERCENTRANK.INC function returns

• #NUM! error value if:
  • array is empty
  • [significance] < 1
• #NAME? error if you misspell the function name.
• propagates errors, meaning that if the input contains an error (e.g., #VALUE!, #REF!), the function will return the same error.

8.1 Troubleshooting the error value

When you encounter an error value in a cell a warning symbol appears, displayed in the image above. Press with mouse on it to see a pop-up menu that lets you get more information about the error.

1. The first line describes the error if you press with left mouse button on it.
2. The second line opens a pane that explains the error in greater detail.
3. The third line takes you to the "Evaluate Formula" tool, a dialog box appears allowing you to examine the formula in greater detail.
4. This line lets you ignore the error value meaning the warning icon disappears, however, the error is still in the cell.
5. The fifth line lets you edit the formula in the Formula bar.
6. The sixth line opens the Excel settings so you can adjust the Error Checking Options.

Here are a few of the most common Excel errors you may encounter.

#NULL error - This error occurs most often if you by mistake use a space character in a formula where it shouldn't be. Excel interprets a space character as an intersection operator. If the ranges don't intersect an #NULL error is returned. The #NULL! error occurs when a formula attempts to calculate the intersection of two ranges that do not actually intersect. This can happen when the wrong range operator is used in the formula, or when the intersection operator (represented by a space character) is used between two ranges that do not overlap. To fix this error double check that the ranges referenced in the formula that use the intersection operator actually have cells in common.

#SPILL error - The #SPILL! error occurs only in version Excel 365 and is caused by a dynamic array being to large, meaning there are cells below and/or to the right that are not empty. This prevents the dynamic array formula expanding into new empty cells.

#DIV/0 error - This error happens if you try to divide a number by 0 (zero) or a value that equates to zero which is not possible mathematically.

#VALUE error - The #VALUE error occurs when a formula has a value that is of the wrong data type. Such as text where a number is expected or when dates are evaluated as text.

#REF error - The #REF error happens when a cell reference is invalid. This can happen if a cell is deleted that is referenced by a formula.

#NAME error - The #NAME error happens if you misspelled a function or a named range.

#NUM error - The #NUM error shows up when you try to use invalid numeric values in formulas, like square root of a negative number.

#N/A error - The #N/A error happens when a value is not available for a formula or found in a given cell range, for example in the VLOOKUP or MATCH functions.

#GETTING_DATA error - The #GETTING_DATA error shows while external sources are loading, this can indicate a delay in fetching the data or that the external source is unavailable right now.

8.2 The formula returns an unexpected value

To understand why a formula returns an unexpected value we need to examine the calculations steps in detail. Luckily, Excel has a tool that is really handy in these situations. Here is how to troubleshoot a formula:

1. Select the cell containing the formula you want to examine in detail.
2. Go to tab “Formulas” on the ribbon.
3. Press with left mouse button on "Evaluate Formula" button. A dialog box appears.
   The formula appears in a white field inside the dialog box. Underlined expressions are calculations being processed in the next step. The italicized expression is the most recent result. The buttons at the bottom of the dialog box allows you to evaluate the formula in smaller calculations which you control.
4. Press with left mouse button on the "Evaluate" button located at the bottom of the dialog box to process the underlined expression.
5. Repeat pressing the "Evaluate" button until you have seen all calculations step by step. This allows you to examine the formula in greater detail and hopefully find the culprit.
6. Press "Close" button to dismiss the dialog box.

There is also another way to debug formulas using the function key F9. F9 is especially useful if you have a feeling that a specific part of the formula is the issue, this makes it faster than the "Evaluate Formula" tool since you don't need to go through all calculations to find the issue..

1. Enter Edit mode: Double-press with left mouse button on the cell or press F2 to enter Edit mode for the formula.
2. Select part of the formula: Highlight the specific part of the formula you want to evaluate. You can select and evaluate any part of the formula that could work as a standalone formula.
3. Press F9: This will calculate and display the result of just that selected portion.
4. Evaluate step-by-step: You can select and evaluate different parts of the formula to see intermediate results.
5. Check for errors: This allows you to pinpoint which part of a complex formula may be causing an error.

The image above shows cell reference C19 converted to hard-coded value using the F9 key. The PERCENTRANK.INC function requires numerical values in the second argument which is not the case in this example. We have found what is wrong with the formula.

Tips!

• View actual values: Selecting a cell reference and pressing F9 will show the actual values in those cells.
• Exit safely: Press Esc to exit Edit mode without changing the formula. Don't press Enter, as that would replace the formula part with the calculated value.
• Full recalculation: Pressing F9 outside of Edit mode will recalculate all formulas in the workbook.

Remember to be careful not to accidentally overwrite parts of your formula when using F9. Always exit with Esc rather than Enter to preserve the original formula. However, if you make a mistake overwriting the formula it is not the end of the world. You can “undo” the action by pressing keyboard shortcut keys CTRL + z or pressing the “Undo” button

8.3 Other errors

Floating-point arithmetic may give inaccurate results in Excel - Article

Floating-point errors are usually very small, often beyond the 15th decimal place, and in most cases don't affect calculations significantly.

9. What is the difference between the PERCENTRANK.EXC and PERCENTRANK.INC functions?

The image illustrates the distinction between the calculations performed by the PERCENTRANK.EXC function (displayed in columns C19:C33) and the PERCENTRANK.INC function (displayed in columns D19:D33).

The formulas used for these calculations are:

PERCENTRANK.EXC = Rank / (Total number of values + 1)
PERCENTRANK.INC = (Rank - 1) / (Total number of values - 1)

To determine the rank, the following steps are followed:

1. Sort the values in ascending order from lowest to highest.
2. Assign a rank of 1 to the lowest value.
3. Assign a rank of 2 to the second-lowest value.
4. Continue this process, incrementing the rank for each subsequent value until all values have been ranked.

It's important to note that the PERCENTRANK.INC function always returns 0 for the lowest value and 1 for the highest value in the dataset.

Functions in 'Statistical' category

The PERCENTRANK.INC function function is one of 73 functions in the 'Statistical' category.

Excel function categories

Excel categories

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