How to use the RANK.EQ function

What is the RANK.EQ function?

The RANK.EQ function calculates the rank of a number in a list of numbers, based on its position if the list were sorted.  The top rank is returned if more than one number share the same rank.

The RANK.EQ and RANK.AVG function replaces the RANK function.

1. Introduction

What is ranking a number?

Ranking a number means determining its position or order when arranged with other numbers in a dataset. The rank provides information about where a value stands relative to others.

For example,  ten students had the following test scores: 66, 97, 99, 77, 9, 60, 35, 60, 61, and 57

If we sort the numbers from largest to smallest we get: 99, 97, 77, 66, 61, 60, 60, 35, 9 We can now rank the numbers based on size which I have done in cells D3:D11, however, the RANK.EQ function does not rank numbers like the image demonstrates above. Example 3 below shows how to return unique ranks.

When is it useful in statistics to rank a number?

One example is finding out the standing of an exam score in comparison to all students. Determining the rank is needed to find out the standing relative to the other students.

Another examples is that outliers are often ranked at the extremes.

What are outliers?

Outliers in statistics are observations that differ significantly from other observations in a dataset. They are data points that stand apart from the overall pattern.

What are the differences between RANK.AVG and the RANK.EQ functions?

The RANK.AVG function returns the average rank if more than one item share the same rank, the RANK.EQ function returns the top rank if more than one item share the same rank.

2. RANK.EQ Function Syntax

RANK.EQ(number,ref,[order])

3. RANK.EQ Function Arguments

number	Required.
ref	Required. A list of numbers.
[order]	Optional. This argument determines how the RANK.EQ function ranks a number. 0 (zero) - Default value, list in argument ref is sorted in a descending order. 1  - List in argument ref is sorted in an ascending order.

What is descending order?

Descending order refers to arranging values or data points from highest to lowest. For example, sorting numbers in descending order: 12, 10, 8, 6, 4, 2

What is ascending order?

Ascending order refers to arranging values from lowest to highest. For example, sorting numbers in ascending order: 2, 4, 6, 8, 10, 12

4. RANK.EQ Function Example 1

The picture above displays the arguments in C3 and C4, the list of numbers in cell range B7:B13 and the calculation in cell F2. The data is :

ref
79
39
35
21
10
10
32

The arguments are:

• number = C3 (10)
• ref = B7:B13
• order = C4 (0 zero meaning descending order)

Formula in cell F2:

The image below shows the position of number 10 if the list were sorted in an descending order. Descending order refers to the arrangement of values in decreasing order from the largest to the smallest value. For example, the numbers 20, 12, 8, 5, 2 are arranged in descending order.

This list sorted in a descending order shows number 10 in position 6 which is the rank the RANK.EQ function calculates in cell F2 in the top image. Note that the last duplicate (10) also gets rank 6 and not 7.

position	ref	RANK.EQ
1	79	1
2	39	2
3	35	3
4	32	4
5	21	5
6	10	6
7	10	6

The fomrula in cell F2 has relative cell references. A relative cell reference is one that changes when you copy or move the formula or cell reference to another location. For example, if you have a formula =A1+B1 in cell C1 and you copy this formula to cell C2 the formula will automatically adjust to =A2+B2.

5. RANK.EQ Function Example 2

RANK.EQ function ignores non-numeric values in ref argument. The RANK.EQ function calculates the same rank to duplicate identical numbers, however, it also moves the ranks for the following numbers. This example calculates ranks based on a list sorted in an ascending order.

ref	RANK.EQ
10	1
10	1
21	3
32	4
35	5
39	6
79	7

The arguments are:

• number = B3
• ref = $B$3:$B$9
• order = 1 meaning ascending order

Ascending order refers to the arrangement of values in increasing order from the smallest to the largest value. For example, the numbers 2, 5, 8, 12, 20 are arranged in ascending order.

Formula in cell C3:

10 has a duplicate number, both numbers get the same rank. The following number is 21, that number gets rank 3. No number has rank 2.

The first argument is a relative cell reference, the second argument is an absolute cell reference. A relative cell reference is one that changes when you copy the formula or cell reference to another location. For example, if you have a formula =A1+B1 in cell C1, and you copy this formula to cell C2, the formula will automatically adjust to =A2+B2

An absolute cell reference is a fixed reference that does not change when you copy the formula or cell reference to another location. To create an absolute reference, you need to add dollar signs ($) before the row and column coordinates.
For example, if you have a formula =$A$1+$B$1 in cell C1, and you copy this formula to cell C2, the formula will remain =$A$1+$B$1, referring to the same cells A1 and B1, regardless of the new location.

6. RANK.EQ Function - how to return unique ranks

This example demonstrates how to distribute unique ranks using the RANK.EQ and the COUNTIF functions. If you want the to give duplicate numbers a unique rank use the following formula:

The arguments for the RANK.EQ function are:

• number = B3
• ref = $B$3:$B$9
• order = 1 meaning ascending order

The arguments for the COUNTIF function are:

• range =  $B$3:B3
• criteria = B3

Formula in cell C3:

$B$3:B3 contains both a relative and an absolute cell references meaning it expands when the cell is copied to cells below. This makes the COUNTIF function evaluate  the criteria argument in a larger and larger cell range. In fact, the cell range expands at the same pace as the cell formula is copied meaning the expanding cell range grows to the same row as the formula.

Explaining formula

Step 1 - Calculate rank

RANK.EQ(number,ref,[order])

RANK.EQ(B3,$B$3:$B$9,1)

1  -Numbers are ranked in an ascending order.

Step 2 - Calculate count

The COUNTIF function calculates the number of cells that is equal to a condition.

Function syntax: COUNTIF(range, criteria)

COUNTIF($B$3:B3,B3)

returns 1

Step 3 - Add count to rank

RANK.EQ(B3,$B$3:$B$9,1)+COUNTIF($B$3:B3,B3)

becomes

1+1 equals 2

Step 4 - Subtract 1

2-1 equals 1

1 is returned to cell C3.

7. How to rank text uniquely without duplicates

Question: How do I rank text cell values uniquely? If text values were sorted alphabetically from A to Z, the first text value would rank 1 and so on... Duplicate text values rank uniquely.

Answer:

The image above shows random text values in cell range B3:B14. The formula in cell C3 creates numbers that represent the order if the text values were sorted from A to Z.

Formula in cell C3:

Copy cell C3 and paste to cells below as far as needed. I'll explain each number in C3:C14 and how the formula produces that result:

1. Cell C3 corresponds to "DD" and returns 8. There are 7 values less than "DD" (all AAs, BBs, CC). This is the 1st "DD" encountered: 7 + 1 = 8
2. Cell C4 corresponds to "AA" and returns 1. No values less than "AA". This is the 1st "AA" encountered: 0 + 1 = 1
3. Cell C5 corresponds to "AA" and returns 2. No values less than "AA". This is the 2nd "AA" encountered: 0 + 2 = 2
4. Cell C6 corresponds to "BB" and returns 5. There are 4 "AA" values less than "BB". This is the 1st "BB" encountered: 4 + 1 = 5
5. Cell C7 corresponds to "AA" and returns 3. No values less than "AA". This is the 3rd "AA" encountered: 0 + 3 = 3
6. Cell C8 corresponds to "DD" and returns 9. There are 7 values less than "DD" (all AAs, BBs, CC). This is the 2nd "DD" encountered: 7 + 2 = 9
7. Cell C9 corresponds to "EE" and returns 10. There are 9 values less than "EE" (all AAs, BBs, CC, DDs). This is the 1st "EE" encountered: 9 + 1 = 10
8. Cell C10 corresponds to "AA" and returns 4. No values less than "AA". This is the 4th "AA" encountered: 0 + 4 = 4
9. Cell C11 corresponds to "BB" and returns 6. There are 4 "AA" values less than "BB". This is the 2nd "BB" encountered: 4 + 2 = 6
10. Cell C12 corresponds to "EE" and returns 11. There are 9 values less than "EE" (all AAs, BBs, CC, DDs). This is the 2nd "EE" encountered: 9 + 2 = 11
11. Cell C13 corresponds to "CC" and returns 7. There are 6 values less than "CC" (all AAs, BBs). This is the 1st "CC" encountered: 6 + 1 = 7
12. Cell C14 corresponds to "EE" and returns 12. There are 9 values less than "EE" (all AAs, BBs, CC, DDs). This is the 3rd "EE" encountered: 9 + 3 = 12

The formula works by counting how many values are less than the current value (first COUNTIF) and adding that to the count of how many times the current value has appeared so far (second COUNTIF), effectively creating a unique rank for each entry.

How does this formula work?

Let us start with cell C3.

=COUNTIF($B$3:$B$14,"<"&B3)+COUNTIF($B$3:B3,B3)

Step 1 - Calculate rank

The COUNTIF function is an incredibly versatile function, in this case, instead of counting values based on a condition we simply check if a value is smaller or larger than the others.

Remember, we are using text values so the function returns a rank number based on the position if the list were sorted alphabetically.

COUNTIF($B$3:$B$14,"<"&B3) returns 7. 7 values are sorted before DD, as if they were sorted from A to Z.

The problem is that value DD has a duplicate and we need to make sure that the duplicate doesn't get the same number as the first instance.

Step 2 - Count current value and prior instances of current value

COUNTIF($B$3:B3,B3)

becomes

COUNTIF("DD","DD")

and returns 1.

Note that the cell reference $B$3:B3 expands as we copy the cell to cells below.

Step 3 - Add values

COUNTIF($B$3:$B$14,"<"&B3)+COUNTIF($B$3:B3,B3)

becomes

7 + 1 and returns 8 in cell C3.

Final notes

Select B3 and use "evaluate formula" to see how the next cell calculates rank.  Press with left mouse button on "Evaluate" button and excel calculates cell formula step by step.

Get *.xlsx file

Text values uniquely ranked.xlsx

8. How to rank uniquely based on a condition

The following formula ranks text values in column C uniquely based on the category in column B.

• The formula ranks the "Text" values within each unique "ID" group.
• For each "ID" group, it starts the ranking from 1.
• If there are duplicate "Text" values within an "ID" group, they receive consecutive ranks.

This type of ranking is useful for categorizing items within subgroups while maintaining a consistent ranking system across different categories or IDs.

Formula in D3:

Let's break it down by ID:
For ID 7:

• "parta" gets rank 1 (first occurrence)
• "partb" gets rank 3 (first occurrence after "parta")
• Another "partb" gets rank 4 (second occurrence)
• Another "parta" gets rank 2 (second occurrence)

For ID 11:

• "parta" gets rank 1 (first occurrence)
• "partc" gets rank 3 (first occurrence after "parta")
• "partb" gets rank 2 (first occurrence, comes alphabetically between "parta" and "partc")

It counts how many unique text values come before the current one within the same ID group. Adding 1 to that count to get the rank. Handling duplicates by giving them consecutive ranks within their ID group.

Explaining formula in cell D3

Step 1 - Concatenate cell C3 and current row number

The ROW function returns the row number from a cell reference, if a cell ref is omitted then the row number of the current cell is returned.

The ampersand character & concatenates two values.

C3&ROW()

becomes

"parta"&3

and returns parta3.

Step - 2 Concatenate each cell in column C and corresponding row numbers row-wise

$C$3:$C$9&ROW($C$3:$C$9)

returns {"parta3";"partb4";...;"partb9"}

Step 3 - Compare value with array using the larger than sign

(C3&ROW()>$C$3:$C$9&ROW($C$3:$C$9))

returns {FALSE;....;FALSE}.

The number concatenated to each value makes it unique.

Step 4 - Compare categories with current cell

(B3=$B$3:$B$9)

returns {TRUE;... ;FALSE}

Step - 5 Multiply arrays

(C3&ROW()>$C$3:$C$9&ROW($C$3:$C$9))*(B3=$B$3:$B$9)

returns {0;0;0;0;0;0;0}

Step 6 - Sum values in array

SUMPRODUCT((C3&ROW()>$C$3:$C$9&ROW($C$3:$C$9))*(B3=$B$3:$B$9))

becomes SUMPRODUCT({0;0;0;0;0;0;0}) and returns 0.

Step 7 - Add 1

SUMPRODUCT((C3&ROW()>$C$3:$C$9&ROW($C$3:$C$9))*(B3=$B$3:$B$9)) + 1

becomes

0 + 1 equals 1 in cell D3.

Get Excel *.xlsx file

ranking text with condition.xlsx

Functions in 'Statistical' category

The RANK.EQ function function is one of 73 functions in the 'Statistical' category.

Excel function categories

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