Quantile vs. Quartile — What's the Difference?
Edited by Tayyaba Rehman — By Maham Liaqat — Updated on March 11, 2024
Quantiles are cut points dividing the range of a probability distribution into continuous intervals with equal probabilities, while quartiles divide data into quarters.
Difference Between Quantile and Quartile
Table of Contents
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Key Differences
Quantiles refer to points taken at regular intervals from the cumulative distribution function of a random variable, effectively dividing the distribution into equal-sized, contiguous intervals based on the population or sample values. Whereas, quartiles are a special case of quantiles that specifically divide a dataset or distribution into four equal parts, representing the 25th (first quartile), 50th (median or second quartile), and 75th (third quartile) percentiles.
Quantiles are useful in statistics for assessing the spread and center of distributions and can be used to compare against theoretical distributions or between datasets. On the other hand, quartiles are particularly useful for describing the spread and center of a dataset, providing a simple, intuitive measure of variability, and identifying outliers.
While quantiles can be of any number, allowing for a detailed division of the data (deciles, percentiles, etc.), quartiles are fixed in their division, providing a more generalized view. This difference makes quantiles more flexible in statistical analyses where detailed divisions of data are needed.
Quantiles are typically used in a broader range of applications, from financial risk assessment to machine learning models, where precision in data segmentation is crucial. Whereas quartiles are often used in more descriptive statistical analyses, such as in box plot visualizations to summarize data distributions.
The calculation methods for quantiles and quartiles can differ slightly depending on the statistical software or the specific context in which they are used. However, both concepts fundamentally rely on sorting data and determining values that divide the dataset into the desired number of groups.
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Comparison Chart
Definition
Cut points dividing the range of a distribution into intervals with equal probabilities.
Specific quantiles that divide data into four equal parts.
Division
Can be of any number (e.g., deciles, percentiles).
Fixed at four (25%, 50%, 75%, 100%).
Use Case
Broad application in statistical analysis for detailed data segmentation.
Often used for descriptive statistics and data visualization.
Flexibility
Highly flexible, allowing for detailed data division.
Less flexible, fixed to four divisions.
Calculation
Depends on the distribution and desired intervals.
Based on dividing the sorted dataset into four equal parts.
Compare with Definitions
Quantile
A measure that divides a distribution into intervals with equal probabilities.
The 90th quantile of exam scores shows the threshold below which 90% of the scores fall.
Quartile
A type of quantile that divides data into four equal parts.
The third quartile marks where 75% of the data falls below.
Quantile
Flexible in application, suited for various statistical needs.
Quantiles are crucial in financial risk management to assess portfolio performance under extreme conditions.
Quartile
Calculation involves dividing the sorted dataset into quarters.
To find the second quartile (median), the data is sorted and divided into two halves.
Quantile
Used in statistical analysis to assess distribution properties.
Quantiles helped identify the distribution's skewness by comparing mid-range quantiles.
Quartile
Commonly used in box plots for data visualization.
Quartiles are used to create box plots, highlighting the median and variability.
Quantile
Dependent on the cumulative distribution function for its calculation.
Calculating quantiles involves understanding the distribution's CDF.
Quartile
Fixed division makes it less flexible than quantiles.
Quartiles provide a generalized overview of the data distribution.
Quantile
Can be any number, allowing detailed data segmentation.
The 20th quantile divides the dataset into twenty equal parts.
Quartile
Specifically represents the 25th, 50th, and 75th percentiles.
The first quartile is the same as the 25th percentile of a dataset.
Quantile
In statistics and probability, quantiles are cut points dividing the range of a probability distribution into continuous intervals with equal probabilities, or dividing the observations in a sample in the same way. There is one fewer quantile than the number of groups created.
Quartile
In statistics, a quartile is a type of quantile which divides the number of data points into four parts, or quarters, of more-or-less equal size. The data must be ordered from smallest to largest to compute quartiles; as such, quartiles are a form of order statistic.
Quantile
Each of any set of values of a variate which divide a frequency distribution into equal groups, each containing the same fraction of the total population.
Quartile
Each of four equal groups into which a population can be divided according to the distribution of values of a particular variable
In the highest quartile, the mean age was 72
Quantile
(statistics) One of the class of values of a variate which divides the members of a batch or sample into equal-sized subgroups of adjacent values or a probability distribution into distributions of equal probability.
Quartile
Any of the groups that result when a frequency distribution is divided into four groups of equal size.
Quartile
Any of the values that separate each of these groups.
Quartile
(statistics) Any of the three points that divide an ordered distribution into four parts, each containing a quarter of the population.
Quartile
(statistics) Any one of the four groups so divided.
This school is ranked in the first quartile.
Quartile
Same as Quadrate.
Quartile
(statistics) any of three points that divide an ordered distribution into four parts each containing one quarter of the scores
Common Curiosities
What are quantiles?
Points that divide the distribution of a dataset into equal-sized intervals based on the data values.
What are quartiles?
Special quantiles that divide a dataset into four equal parts, representing the 25th, 50th, and 75th percentiles.
How do quantiles differ from quartiles?
Quantiles can represent any division of the data into equal intervals, while quartiles are specifically the division into four equal parts.
Can quantiles be used for all types of data?
Yes, quantiles can be used for any continuous or discrete data distribution.
What is the difference between quartiles and percentiles?
Quartiles are a subset of percentiles, specifically the 25th, 50th, and 75th percentiles.
How are quartiles used in descriptive statistics?
They are used to describe the distribution, identify outliers, and summarize the data through box plots.
Why are quartiles less flexible than quantiles?
Because they are fixed at dividing the data into four equal parts, while quantiles can divide the data into any number of equal parts.
Why are quantiles important in statistics?
They help in understanding the distribution, spread, and central tendency of data.
Are quartiles always the same for a given dataset?
Yes, once a dataset is sorted, the quartiles are fixed based on the 25th, 50th, and 75th percentiles.
How do quantiles help in data analysis?
They provide a way to segment the data into equal parts, helping in the analysis of distribution and trends.
Can the calculation of quantiles vary?
Yes, the method of calculation can vary slightly depending on statistical conventions and the distribution of the data.
How are quantiles calculated?
The calculation depends on the desired number of divisions and the cumulative distribution function of the data.
Is the median the same as the second quartile?
Yes, the median of a dataset is equivalent to the second quartile.
How does the concept of quantiles extend beyond quartiles?
Quantiles include any division of the data, such as deciles or percentiles, allowing for more detailed analysis than quartiles.
What role do quartiles play in box plots?
They are used to create the box and whiskers, showing the median, spread, and potential outliers in the data.
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Written by
Maham Liaqat
Edited by
Tayyaba RehmanTayyaba Rehman is a distinguished writer, currently serving as a primary contributor to askdifference.com. As a researcher in semantics and etymology, Tayyaba's passion for the complexity of languages and their distinctions has found a perfect home on the platform. Tayyaba delves into the intricacies of language, distinguishing between commonly confused words and phrases, thereby providing clarity for readers worldwide.
