What is a 'Quartile'
A quartile is a statistical term describing a division of observations into four defined intervals based upon the values of the data and how they compare to the entire set of observations.
Try not to confuse a quarter with a quartile.
BREAKING DOWN 'Quartile'
To understand the quartile, it is important to understand the median as a measure of central tendency. The median in statistics is the middle value of a set of numbers. It is the point at which exactly half of the data lies below and above the central value. So, given a set of 13 numbers, the median would be the seventh number. The six numbers preceding this value are the lowest numbers in the data, and the six numbers after the median are the highest numbers in the data set given. Because the median is not affected by extreme values or outliers in the distribution, it is sometimes preferred to the mean.
While the median is a robust estimator of location, it says nothing about how the data on either side of its value is spread or dispersed. The quartile measures the spread of values above and below the mean by dividing the distribution into four groups. Just like the median divides the data into half so that 50% of the measurement lies below the median and 50% lies above it, the quartile breaks down the data into quarters so that 25% of the measurement are less than the lower quartile, 50% are less than the mean, and 75% are less than the upper quartile.
A quartile divides data into three points – a lower quartile, median, and upper quartile – to form four groups of the data set. The lower quartile or first quartile is denoted as Q1, and is the middle number that falls between the smallest value of the data set and the median. The second quartile, Q2, is also the median. The upper or third quartile denoted as Q3 is the central point that lies between the median and the highest number of the distribution. Now, we can map out the four groups formed from the quartiles. The first group of values contains the smallest number up to Q1; the second group includes Q1 to the median; third set is the median to Q3; and fourth category comprises Q3 to the highest data point of the entire set.
Each quartile contains 25% of the total observations. Generally, the data is arranged from smallest to largest with those observations falling below 25% of all the data analyzed allocated within the 1st quartile, observations falling between 25.1% and 50% and allocated in the 2nd quartile, then the observations falling between 51% and 75% allocated in the 3rd quartile, and finally the remaining observations allocated in the 4th quartile.
Quartile Example
Let’s work with an example. Suppose, the distribution of math scores in a class of 19 students in ascending order is:
59, 60, 65, 65, 68, 69, 70, 72, 75, 75, 76, 77, 81, 82, 84, 87, 90, 95, 98
First, mark down the median, Q2, which in this case is the tenth value – 75.
Q1 is the central point between the smallest score and the median. In this case, Q1 falls between the first and ninth score – 68. [Note that the median can also be included when calculating Q1 or Q3 for an odd set of values. If we were to include the median on either side of the middle point, then Q1 will be the middle value between the first and tenth score, which is the average of the fifth and sixth score – (fifth + sixth)/2 = (68 + 69)/2 = 68.5].
Q3 is the middle value between Q2 and the highest score – 84. [Or if you include the median, Q3 = (82 + 84)/2 = 83].
Now that we have our quartiles, let’s interpret their numbers. A score of 68 (Q1) represents the first quartile and is the 25^{th} percentile. 68 is the median of the lower half of the score set in the available data i.e. the median of the scores from 59 to 75. Q1 tells us that 25% of the scores are less than 68 and 75% of the class scores are greater. Q2 (the median) is the 50^{th} percentile and shows that 50% of the scores are less than 75, and 50% of the scores are above 75. Finally, Q3, the 75^{th} percentile, reveals that 25% of the scores are greater and 75% are less than 84.
If the data point for Q1 is farther away from the median than Q3 is from the median, then we can say that there is a greater dispersion among the smaller values of the data set than among the larger values. Same logic applies if Q3 is farther away from Q2 than Q1 is from the median.
If there is an even number of data points, the median will be the average of the middle two numbers. In our example above, if we had 20 students instead of 19, the median of their scores will be the arithmetic average of the tenth and eleventh number.
Quartiles are used to calculate the interquartile range which is a measure of variability around the median. The interquartile range is simply calculated as the difference between the first and third quartile: Q3 – Q1. In effect, it is the range of the middle half of the data that shows how spread out the data is.
For large data sets, Microsoft Excel can be used to calculate quartiles by using the QUARTILE function.

Quintiles
A quintile is a statistical value of a data set that represents ... 
Comparison Universe
A comprehensive grouping of investment managers with similar ... 
Decile
A decile is method of splitting up a set of ranked data into ... 
Variability
The extent to which data points in a statistical distribution ... 
Business Credit Score
A number indicating whether a company is a good candidate to ... 
Runs Test
A runs test is a statistical technique to test the hypothesis ...

Personal Finance
Top 25 Cities Where You Can Live Large on Less Than $70k
Want life to feel more like Easy Street? Head for one of these cities, where you can live like a king (or queen) without a royal salary. 
Managing Wealth
The 10 Most Expensive ZIP Codes in New Jersey
Often overshadowed by its cosmopolitan neighbor New York, the Garden State has a number of towns that offer luxury and space to those with deep pockets. 
Investing
9 Gentrifying Neighborhoods in the Bay Area
There are a number of gentrifying neighborhoods in the Bay Area, which is home to some of the highest rents and home prices in the nation. Here are nine. 
Small Business
Top 10 Most Developed Cities in the U.S
Want to know where to live, work, or play? If so, the following information might be of great value to you. 
Taxes
Top 10 Cities to Invest in Rental Properties
With home ownership out of reach, many Millennials are opting to rent singlefamily homes, which has created an opportunity for investors. 
Personal Finance
What Is the Average Income in the U.S.?
Information about average income and salary in the United States. It's finally on the rise after years of stagnant wages, but large gulfs exist along gender and racial lines. 
Investing
10 Best States to Own a Big House
On top of the low property taxes and average housing costs, these states all tend to have great natural beauty and land worth building on. 
Investing
Alphabet Median Pay Close To $200K
Google's parent Alphabet paid an average salary of around $200,000 last year. 
Tech
Top 10 Careers For Paying Back Your Student Loans
These jobs will help you pay off your education debt quickly. 
Personal Finance
CEO Pay Increased 6.8% in 2016
A report by the Wall Street Journal suggests that CEO pay among American companies rose by 6.8% in FY 2016.

What's the difference between a credit rating and a credit score?
Learn about the differences between credit ratings and credit scores, and review how these expressions of creditworthiness ... Read Answer >> 
What country has the richest middle class?
Learn which country has the richest middle class in the world, as well as the factors that have enabled the middle class ... Read Answer >>