How to use the QUARTILE.INC function
What is the QUARTILE.INC function?
The QUARTILE.INC function returns the quartile of a data set, based on percentile values from 0..1, inclusive. Use the Quartiles.inc function to divide numerical values into groups. This function has replaced the old QUARTILE function
Table of Contents
1. Introduction
What is QUARTILE.INC an abbreviation from?
QUARTILE.EXC is an abbreviation of QUARTILE INCLUSIVE.
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: Q_{2}- Q_{1} =Q_{3}- Q_{2}
Positively skewed: Q_{2}- Q_{1} < Q_{3}- Q_{2}
Negatively skewed: Q_{2}- Q_{1} > Q_{3}- Q_{2}
Learn more about skewness: SKEW function
What is 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. QUARTILE.INC Function Syntax
QUARTILE.INC(array, quart)
3. QUARTILE.INC Function Arguments
array | Required.The cell values for which you want to calculate the quartile value. |
quart | Required. Indicates which value to return. |
Quart parameters | |
---|---|
0 | Minimum value. |
1 | First quartile (25th percentile). |
2 | Median quartile (50th percentile). |
3 | Third quartile (75th percentile). |
4 | Maximum value. |
4. QUARTILE.INC Function Example 1
The image above shows a data set in cell range B3:B11 and a formula in cell D3. The data in B3:B11 contains 9 values and they are:
Array |
66 |
97 |
99 |
77 |
9 |
60 |
35 |
60 |
61 |
The formula in cell D3 calculates the 1st quartile (inclusive) based on the values specified in B3:B11.
Formula in cell D3:
The formula returns 60 which represents the first quartile. The first half of numbers are: 9, 35, 60, 60, and 61. The median number is 60 which is the first quartile. 61 is the median and is also included in the calculation hence the name QUARTILE.INC meaning inclusive.
5. QUARTILE.INC Function Example 2
In a manufacturing process, the weight of products is closely monitored for quality control. Is the distribution of weights skewed?
The data set is in cell range B22:B66.
47 | 51 | 43 | 70 | 50 | 49 | 53 | 52 | 43 |
65 | 4 | 68 | 66 | 30 | 43 | 61 | 34 | 25 |
44 | 51 | 67 | 44 | 50 | 55 | 71 | 44 | 43 |
54 | 50 | 61 | 72 | 47 | 59 | 87 | 67 | 40 |
57 | 46 | 49 | 45 | 56 | 54 | 61 | 39 | 40 |
This formula calculates the first quartile (Q1). Formula in cell C15:
This formula calculates the second quartile (Q2). C15 returns 44. Formula in cell C16:
This formula calculates the third quartile (Q3). C16 returns 50. Formula in cell C17:
C17 returns 61.
Positively skewed meets the following condition Q2 - Q1 < Q3 - Q2
Negatively skewed meets the following condition Q2 - Q1 > Q3 - Q2
Symmetrical distribution: Q2 - Q1 = Q3 - Q2
Q2 - Q1 = 50 - 44 = 6
Q3 - Q2 = 61 - 50 = 11
6 < 11 which means that the distribution is positively skewed, however, the frequency table above shows that the distribution is negatively skewed meaning the tail is longer on the left side. This is one of the downsides with calculating the quartile skewness, outliers may create problems. The SKEW function calculates a more accurate skewness value than the quartile skewness value.
6. QUARTILE.INC Function Example 3
A real estate agent wants to analyze the distribution of home prices in a particular neighborhood. How can they use quartiles to understand the spread of prices, identify any skewness in the distribution, and detect any outliers that may represent unusually high or low-priced properties?
This formula calculates the first quartile (Q1). Formula in cell C15:
This formula calculates the second quartile (Q2). C15 returns 450,000. Formula in cell C16:
This formula calculates the third quartile (Q3). C16 returns 510,000. Formula in cell C17:
C17 returns 610,000.
Positively skewed meets the following condition Q2 - Q1 < Q3 - Q2
Negatively skewed meets the following condition Q2 - Q1 > Q3 - Q2
Symmetrical distribution: Q2 - Q1 = Q3 - Q2
Q2 - Q1 = 510,000 - 450,000 = 60,000
Q3 - Q2 = 610,000 - 510,000 = 100,000
60,000 < 100,000 which means that the distribution is positively skewed. The image above shows a chart displaying a frequency table. This distribution is clearly positively skewed, there is a long tail to the right. This means that the spread of prices are wider on the right tail than the left tail. It also means that there are outliers located on the higher side on the distribution.
7. QUARTILE.INC Function not working
QUARTILE.INC returns #NUM! error value
- if array is empty.
- If quart < 0 or if quart > 5
8. How is the QUARTILE.INC Function calculated?
QUARTILE.INC calculates quartiles using the inclusive method:
Data is sorted lowest to highest. The quartile boundaries include the quartile values themselves. For example, for the data {1, 2, 3, 4, 5}:
Q0 = 1
Q1 = 2
Q2 = 3
Q3 = 4
The median of data {1, 2, 3, 4, 5} is 3. The first half contains 1 , 2, and 3. The median of 1,2, and 3 is 2 = Q1 Q2 is the median: 3
The second half contains 3, 4 and 5, The median of 3, 4 and 5 is 4 = Q3
Functions in 'Statistical' category
The QUARTILE.INC function function is one of 73 functions in the 'Statistical' category.
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