Companies frequently use Excel to organize statistics in order to better understand their data. The quartiles function, which divides data into four categories in a range, is one function that some people may use in their spreadsheets. Understanding quartiles can help you decide whether this calculation can provide new insight into your numerical data. In this article, we will explain what a quartile is, a simplified example, how it’s calculated, and its purpose among other basic facts you need to know. Let’s proceed!
What is a Quartile?
A quartile is a statistical term that refers to the division of observations into four defined intervals based on data values and how they compare to the entire set of observations.
Quartiles are Excel values that divide numeric values into four sections. People prefer quartiles to percentiles, such as the top 25% of highest-spending customers. The four quartiles are as follows:
- First quartile: The first quartile includes the lowest 25% of a data range.
- Second quartile: The second quartile includes the next lowest grouping of numbers. This group includes numbers through the median of a data set.
- Third quartile: The third quartile is the second-highest grouping of numbers higher than the median.
- Fourth quartile: The fourth quartile includes the highest 25% of numbers in a data range.
For example, if the data ranges from one to eight, each falls into one of the following quartiles:
- First quartile: 1 and 2
- Second quartile: 3 and 4
- Third quartile: 5 and 6
- Fourth quartile: 7 and 8
How Quartiles Work
Quartiles divides the data into quarters, so that 25% of the measurements are less than the lower quartile, 50% are less than the median, and 75% are less than the upper quartiles, just as the median divides the data in half so that 50% of the measurements are below the median and 50% are above it.
The data set is divided into four ranges, each containing 25% of the data points, using three quartile values: lower, median, and upper. The lower quartile, or first quartile, is denoted as Q1 and is the middle number between the dataset’s smallest and median values. The median is also in the second quartile, Q2. The upper or third quartile, denoted as Q3, is the central point of the distribution that lies between the median and the highest number.
We can now map out the four groups formed by the quartiles. The first set of values includes the smallest number up to Q1; the second set includes Q1 to the median; the third set includes the median to Q3; and the fourth category includes Q3 to the highest data point in the entire set.
What Is the Purpose of Quartiles?
Quartiles are surprisingly useful and can serve for a purpose in a variety of contexts. One good purpose of quartiles is that they can help you understand your dataset’s central tendency and variability and even help you find outliers. Graphing them with a boxplot can help you understand the distribution of your data.
Q2 is the median, and it divides the dataset in half. For skewed distributions, it is a useful measure of central tendency. The interquartile range (IQR) is a variability measure. The interval between the first and third quartiles.
IQR = Q3 – Q1
Larger IQRs indicate a wider range of values. Regardless of the shape of the distribution, half of the observations fall within the interquartile range.
The median and interquartile range are more robust measures than the more familiar mean and standard deviation. Outliers have little effect on either statistic because they are not dependent on every value. Furthermore, the interquartile range is ideal for skewed distributions such as the median.
Another good purpose of quartiles is that they can also help you find outliers.
How to Find Quartiles in Excel
When looking for quartiles in Excel, you have several options:
#1. Sort your numbers
You can obtain your quartiles by ordering numbers in a data range from lowest to highest. In a spreadsheet, you can sort these by column. For instance, your numbers could be:
| A | B | |
| 1 | 9 | 1 |
| 2 | 1 | 3 |
| 3 | 3 | 3 |
| 4 | 5 | 5 |
| 5 | 7 | 6 |
| 6 | 6 | 7 |
| 7 | 2 | 9 |
Quartiles formula requires two primary values: quarts and arrays. Each quartile represents a different set of values. These are numbered from 0 to 4:
- 0: The smallest value in a number range.
- 1: This is the first quartile or 25th percentile.
- 2: This is the second or median quartile, or the 50th percentile.
- 3: This is the 75th percentile or the third quartile.
- 4: This is the highest value in a range.
#2. Carry out the task
In Excel, the quartile function returns the quartile for any set of data. In Excel, the following formula is used to calculate quartiles:
=QUARTILE(array, quart)
Where:
- The array represents the entire range of values for which you want to find the quartiles.
- Quart is which quartile you want to find.
Tips for using the quartile function in Excel
Here are some hints for using Excel’s quartile function:
#1. Values should be reviewed.
Before running the quartile function, double-check that your numbers are in ascending order in one column and are correct. The function generates an error message if any of the cells are empty or contain text or special characters. If the value of the quart in your command is less than zero or greater than four, you may receive an error message.
#2. Determine the various quarts
Each quart can provide you with unique data that you can use. For example, you might be interested in knowing how much a customer spends in the lowest shopping percentile, as well as the higher quartiles. This can assist you in determining how to create specific business goals to target specific groups. Calculating each quartile for a wide range of data can show you more than the mean or median because it shows the variation within a data set.
#3. Manually check for precision.
To validate your data, you can manually calculate quartiles using the following formulas:
- Lower quartile = (N+1) x 1/4
- Middle quartile = (N+1) x 2/4
- Upper quartile = (N+1) x 3/4
The number N denotes the number of integers in your data set. The outcome indicates which quartile each position represents. For example, if the lower quartile formula yields a result of six, the sixth number in your sequence is the lower quartile. There is no formula for calculating the fourth quartile because it is the maximum value in a range.
What Is Quartile Example?
Consider conducting a small study on language development in children aged 1-6 years. You’re writing a paper about the study and want to include the age quartiles of the children.
| Age (years) | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Frequency | 2 | 3 | 4 | 1 | 2 | 2 |
#Step 1: Count the number of observations in the dataset
n = 2 + 3 + 4 + 1 + 2 + 2 = 14
#Step 2: Sort the observations in increasing order
1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 5, 5, 6, 6
#Step 3: Find the first quartile
n * (1 / 4) = 14 * (1 / 4) = 3.5
3.5 is not an integer, so Q1 is the number at position 4.
1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 5, 5, 6, 6
Q1 = 2 years
#Step 4: Find the second quartile
n * (2 / 4) = 14 * (2 / 4) = 7
7 is an integer, so Q2 is the mean of the numbers at positions 7 and 8.
1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 5, 5, 6, 6
Q2 = (3 + 3) / 2
Q2 = 3 years
#Step 5: Find the third quartile
n * (3 / 4) = 14 * (3 / 4) = 10.5
10.5 is not an integer, so Q3 is the number at position 11.
1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 5, 5, 6, 6
Q3 = 5 years
How to Interpret Quartiles
Quartiles can provide useful information about a particular observation or dataset.
#1. Comparing observations
Quartiles can help you understand an observation in relation to the rest of a sample or population. You can determine whether an observation is in the bottom 25%, middle 50%, or top 25% by comparing it to the quartiles.
#2. Median
The median, or second quartile, is a measure of central tendency. This middle number is a good indicator of the data’s average or most central value, particularly for skewed distributions or distributions with outliers.
#3. Interquartile range (IQR)
The interquartile range (IQR) is a measure of variability. It is the distance between the first and third quartiles. It represents the distribution of the middle 50% of the data.
IQR = Q3 − Q1
The IQR is an excellent measure of variability for skewed or outlier-filled distributions. Because the IQR only includes the middle 50% of the data, it is unaffected by extreme values, unlike the range.
- Skewness: The distance between the quartiles can indicate whether a distribution is skewed or symmetrical.
- Identifying outliers: Outliers can be identified using the interquartile range (IQR). Outliers are observations that are either extremely high or extremely low. An outlier is defined as any observation that is more than 1.5 IQR away from the first or third quartile.
Formulas of Quartiles
There are four basic quartile formulas used to determine the first, second, third, and interquartiles.
#1. For the first quartile, abbreviated Q1.
First quartile = Q1 = ((n + 1) / 4) th term
#2. For the second quartile, abbreviated Q2.
Second quartile = Q2 = ((n + 1) / 2) th term
#3. For the third quartile, abbreviated Q3.
Third quartile = Q3 = (3(n + 1) / 4) th term
#4. For interquartile range.
Interquartile = Q3 – Q1 = (3(n + 1) / 4) th term – ((n + 1) / 4) th term
We can write a general formula to calculate the quartile using the above three formulas for the first, second, and third quartiles.
How Is Quartile Calculated?
Quartiles can be easily calculated using formulas.
#1. Example Quartile 1
Evaluate all quartile parts of the given data set, 2, 9, 7, 29, 34, 61, 25, 19, 16?
Solution
- Step 1: Begin with the given set of numbers.
2, 9, 7, 29, 34, 61, 25, 19, 16
- Step 2: Sort the given set of numbers in ascending order.
2, 7, 9, 16, 19, 25, 29, 34, 61
- Step 3: Count the given set of numbers and multiply by n.
n = 9
- Step 4: Using the quartile general formula, determine the first, second, and third quartiles.
Qk = k (n + 1) / 4) th term
- Step 5: Substitute k = 1, 2, 3 for the first, second, and third quartiles.
For k = 1
Q1 = 1 (9 + 1) / 4) th term
Q1 = 1 (10) / 4) th term
Q1 = (10) / 4) th term
Q1 = (5) / 2) th term
Q1 = 2.5th term
For k = 2
Q2 = 2 (9 + 1) / 4) th term
Q2 = 2 (10) / 4) th term
Q2 = (10 / 2) th term
Q2 = 5th term
For k = 3
Q3 = 3 (9 + 1) / 4) th term
Q3 = 3 (10) / 4) th term
Q3 = (30 / 4) th term
Q3 = (15 / 2) th term
Q3 = 7.5 th term
- Step 6: Take the calculated values from the organized data set of the quartiles
For Q1
Q1 = 2.5th term
Q1 = 2nd term + 3rd term / 2
Q1 = 7 + 9/2
Q1 = 16/2
Q1 = 8
For Q2
Q2 = 5th term
Q2 = 19
For Q3
Q3 = 7.5 th term
Q3 = 7th + 8th / 2
Q3 = 29 + 34 / 2
Q3 = 63/2
Q3 = 31.5
- Step 7: Apply the general formula to calculate interquartile range and enter the values.
Interquartile = Q3 – Q1
Interquartile = 31.5 – 8
Interquartile = 23.5
As a result, the given set’s quartiles are Q1 = 8. Q2 = 19, Q3 = 31.5, and interquartile = 23.5
#2. Example quartile 2
Find the interquartile of the following data set: 23, 19, 3, 12, 22, 18, 11?
Solution
- Step 1: Begin with the given set of numbers.
23, 19, 3, 12, 22, 18, 11
- Step 2: Sort the given set of numbers in ascending order.
3, 11, 12, 18, 19, 22, 23
- Step 3: Count the given set of numbers and multiply by n.
n = 7
- Step 4: Now apply the general interquartile formula.
Interquartile range = Q3 – Q1
- Step 5: Determine the first and third quartiles.
For Q1
Q1 = (n + 1) / 4) th term
Q1 = (7 + 1) / 4) th term
Q1 = (8) / 4) th term
Q1 = 2nd term
For Q3
Q3 = 3(n + 1) / 4) th term
Q3 = 3(7 + 1) / 4) th term
Q3 = 3(8) / 4) th term
Q3 = (24 / 4) th term
Q3 = 6th term
- Step 6: Enter the third and first quartile results into the interquartile formula.
Interquartile = 6th term – 2nd term
Interquartile = 22 – 11
Interquartile = 11
Why is it called a Quartile?
A quartile is a type of quantile in statistics that divides the number of data points into four parts, or quarters, of roughly equal size. To compute quartiles, the data must be ordered from smallest to largest; thus, quartiles are a type of order statistic.
How do you Divide Data into 4 Quartiles?
Click an empty cell somewhere on the sheet in Excel. For instance, select cell B1. Enter “=QUARTILE(A1:A10,1)” after typing it.
What is the 25% Quartile?
The 25th percentile is also referred to as the first, or lower, quartile. The 25th percentile is the value at which 25% of the answers fall below it and 75% of the answers fall above it.
What are the 5 Quartiles?
A summary is made up of five values: the data set’s most extreme values (the maximum and minimum values), the lower and upper quartiles, and the median. These values are presented in the following order: minimum value, lower quartile (Q1), median value (Q2), upper quartile (Q3), and maximum value.
What are the Steps to Find the First Quartile?
We use the following steps to determine the first quartile:
- Make sure to arrange the data points in the order of least to greatest importance.
- Find the median of the entire data set and divide it into two equal parts.
- Take the median of the data set’s lower half.
What is Quartile Formula used for?
A set of observations is divided into four equal parts using the quartile formula. The first quartile is located between the first term and the median. The median represents the second quartile. The third quartile is the value that falls between the median and the last term.
How do we use Quartile?
Quartiles are frequently used in sales and survey data to categorize populations. For example, QUARTILE can be used to find the top 25% of incomes in a population.
Conclusion
You can now grasp all of the fundamental concepts related to the quartile by simply reading this article. This guide has thoroughly and sequentially explained the purpose and everything you need to know about a quartile, including an example and how it is calculated. Please leave a question in the comments section if you require further assistance.
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