How to use the QUARTILE.EXC function

What is the QUARTILE.EXC function?

The QUARTILE.EXC function returns the quartile of a data set, use this function function to divide data into groups. Quartiles split data into fourths, and this function calculates them using the exclusive method, excluding the quartile values from the boundaries.

This function was introduced in Excel 2010 has replaced the old QUARTILE function

1. Introduction

What is QUARTILE.EXC an abbreviation from?

QUARTILE.EXC is an abbreviation of QUARTILE EXCLUSIVE.

What is a quartile?

A quartile is a type of quantile which splits a dataset into four equal parts. The quartiles divide a rank-ordered dataset into four quarters.

There are three quartile values - Q1, Q2, and Q3:

Q1 (first quartile) - 25th percentile
Q2 (second quartile) - 50th percentile (median)
Q3 (third quartile) - 75th percentile

What is the interquartile range (IQR)?

The interquartile range (IQR) is the difference between Q3 and Q1. It indicates the middle 50% spread of the data.

When is it useful to calculate the quartiles?

Quartiles provide quantile-based partitioning of data that reveals distribution, spread, skewness, and outliers. They serve as an important basic statistical summary.

Symmetrical distribution: Q₂- Q₁ =Q₃- Q₂
Positively skewed: Q₂- Q₁ < Q₃- Q₂
Negatively skewed: Q₂- Q₁ > Q₃- Q₂

Learn more about skewness: SKEW function

What is a quantile?

Quantiles are a statistical technique for dividing a dataset into equal-sized groups for analysis. Quantiles split data into equal-sized subsets when ordered from smallest to largest.
The quartiles, percentiles, quintiles, deciles, etc. are examples of quantiles.

• Quartiles split data into 4 equal groups
• Percentiles into 100 groups,
• Quintiles into 5.

Quantiles can show aspects of shape, spread, and concentration.

How to graph quartiles?

The Box and Whisker chart display quartiles.

 

2. Syntax

QUARTILE.EXC(array, quart)

3. Arguments

array	Required. The cell values for which you want to calculate the quartile value.
quart	Required. Indicates which value to return, see table below.

The quart argument allows you to use the following parameters:

Quart parameters
0	Minimum value. (Microsoft documentation is wrong, this argument returns a #NUM value.) Use the MIN function to calculate the smallest value in a data set.
1	First quartile (25th percentile).
2	Median quartile (50th percentile).
3	Third quartile (75th percentile).
4	Maximum value. (Microsoft documentation is wrong, this argument returns a #NUM value.) Use the MAX function to calculate the largest value in a data set..

4. Example 1

This example demonstrates the QUARTILE.EXC function, the image above shows the following values in B3:B11: 66, 97, 99, 77, 9, 60, 35, 60, 61

The arguments are:

• array = B3:B11
• quart = 1

Formula in cell D3:

The function returns 47 which represents the first quartile in B3:B11.

Here is how the QUARTILE.EXC function calculates the first Quartile (Q1).  The median is 61. The first half contains the following numbers: 9, 35, 60, and 60 The median of these numbers is 47.5, here is how: 35+60=95, 95/2 equals 47.5

5. Example 2

A teacher has recorded the scores of 45 students in a test. What are the values of the first quartile (25th percentile), second quartile (50th percentile or median), and third quartile (75th percentile) of the student scores?

Here are the scores:

41	51	75	54	48	24	36	67	79
64	67	53	49	29	69	68	72	53
38	59	42	71	52	45	48	59	54
70	46	45	68	31	41	54	24	62
37	29	86	63	59	63	80	57	44

The arguments are:

• array = B22:B66
• quart = 1

This formula calculates the first quartile meaning 25th percentile (25%). These values are smaller than 43: 24, 24, 29, 29, 31, 36, 37, 38, 41, 41, and 42

Formula in cell D15:

The following formula in D16 calculates the second quartile meaning 50th percentile (50%). The values between the 1st and 2nd quartile are: 44, 45, 45, 46, 48, 48, 49, ,51, 52, 53, and 53.

Formula in cell D16:

This formula calculates the third quartile meaning 75th percentile (75%). These values are larger than or equal to 67: 67, 67, 68, 68, 69, 70, 71, 72, 75, 79, 80, and 86

Formula in cell D17:

6. Example 3

A retail store tracks the daily sales of a particular product over the last 100 days. The store wants to identify the first, second, and third quartiles of the daily sales data to understand the distribution of sales?

Here are the values:

812	1057	711	585	1006
1077	951	828	1143	991
1051	1065	1206	1014	1092
822	1087	689	998	771
966	968	971	733	390
892	506	814	781	1357
489	1312	646	971	327
756	1044	1272	902	736
761	815	723	1332	1058
872	1128	1244	698	1132
721	977	1102	1157	1315
498	1394	778	654	1528
1043	577	731	1108	883
1059	1639	780	1155	566
1236	1300	1639	1415	1167
1128	1246	1303	1109	1119
915	891	856	1298	854
996	1271	1016	896	1144
1218	940	1826	478	1039
825	527	1132	592	663

The arguments are:

• array = B22:B121
• quart = 1

This formula calculates the first quartile meaning 25th percentile (25%). The first quartile is 772.75.

Formula in cell D15:

The following formula in D16 calculates the second quartile meaning 50th percentile (50%). The second quartile is 984.

Formula in cell D16:

This formula calculates the third quartile meaning 75th percentile (75%). The third quartile is 1140.25.

Formula in cell D17:

The image above shows a box and whisker chart, it contains the values that represent the quartiles and also the smallest and largest values.

7. Example 4

A real estate agency has compiled data on the prices of houses sold in a specific neighborhood over the past year. To better understand the market, they want to calculate the first, second, and third quartiles of the house prices.

Here are the values:

298,567	409,478	496,197	265,195	298,445
352,253	473,740	511,783	422,252	370,326
376,678	325,961	489,498	534,916	388,736
333,298	423,778	380,452	517,917	482,795

The arguments are:

• array = B22:B41
• quart = 1

This formula calculates the first quartile meaning 25th percentile (25%). The first quartile is 338.037.

Formula in cell D15:

The following formula in D16 calculates the second quartile meaning 50th percentile (50%). The second quartile is 399,107.

Formula in cell D16:

This formula calculates the third quartile meaning 75th percentile (75%). The third quartile is 487,822.

Formula in cell D17:

The image above shows a box and whisker chart, it contains the values that represent the quartiles and also the smallest and largest values.

8. Function not working

The QUARTILE.EXC function returns #NUM! value if

• quart < 1
• quart > 4

The QUARTILE.EXC function returns the same value as the MEDIAN function if quart is 2.

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 B3:B11 converted to hard-coded value using the F9 key. The numbers seems to be ok, however, the QUARTILE.EXC function requires numerical values between 1 and 4 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. How is the function calculated?

QUARTILE.EXC calculates quartiles using the exclusive method:

Data is sorted lowest to highest. The quartile boundaries exclude the quartile values themselves.

For example, for the data {1, 2, 3, 4, 5}:

Q1 = 1.5
Q2 = 3
Q3 = 4.5

The median of data {1, 2, 3, 4, 5} is 3. The first half  contains 1 and 2, 2+1 = 3 3/2 = 1.5 = Q1
Q2 is the median: 3
The second half  contains 4 and 5, 4+5 = 9 9/2 = 4.5 = Q3

Functions in 'Statistical' category

The QUARTILE.EXC function function is one of 73 functions in the 'Statistical' category.

Excel function categories

Excel categories

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