• Skip to secondary menu
  • Skip to main content
  • Skip to primary sidebar
  • My Store
  • Glossary
  • Home
  • About Me
  • Contact Me

Statistics By Jim

Making statistics intuitive

  • Graphs
  • Basics
  • Hypothesis Testing
  • Regression
  • ANOVA
  • Probability
  • Time Series
  • Fun

Quartile: Definition, Finding, and Using

By Jim Frost Leave a Comment

What are Quartiles?

Quartiles are three values that split your dataset into quarters.

These values are the following:

  • Q1 First quartile: 25% of the data are below this value.
  • Q2: Second quartile / Median: This value splits the data in half.
  • Q3 Third quartile: 25% of the data are above this value.

Quartiles also correspond to percentiles. Q1 is the 25th percentile, Q2 is the 50th, and Q3 is the 75th.

Distribution plot that displays quartiles.

How to Find Quartiles

The simple method for finding quartiles is to list the values in your dataset in numeric order. Then find the three values that split your data into quarters, as shown below.

Illustrated dataset that shows the three quartiles.

Note that quartiles are the values that make the “cuts” in a dataset.

Depending on the size of your dataset, you might not be able to divide it into even quarters using the data values. When that occurs, you can average two adjacent values or interpolate between them to find the quartile. Learn about these methods in my post about Percentiles.

Using Them

Quartiles are surprisingly useful in a variety of contexts. They can help you understand your dataset’s central tendency and variability and even help you find outliers. Using a boxplot to graph them can help you understand the distribution of your data. For more details, click the links below!

The median is Q2, and it splits the dataset in half. It is a handy measure of central tendency for skewed distributions.

The interquartile range (IQR) is a measure of variability. It is the range between the first and third quartiles.

IQR = Q3 – Q1

Larger IQRs indicate a broader spread of values. Half of the observations fall within the interquartile range regardless of the distribution’s shape.

Unlike the more familiar mean and standard deviation, the median and interquartile range are robust measures. Outliers do not strongly affect either statistic because they don’t hinge on every value. Additionally, the interquartile range is excellent for skewed distributions like the median.

Quartiles can also help you find outliers. After finding Q1 and Q3, calculate the following outlier fences:

  • Lower fence: Q1 – (1.5 * IQR)
  • Upper fence: Q3 + (1.5 * IQR)

Values below the lower fence and above the upper fence are potential outliers that you should investigate. To see an example, read my post about identifying outliers.

Finally, boxplots graph the quartiles and IQR along with the minimum and maximum values. They help you understand the distribution of your data because you can see where your data fall. Frequently, these plots use outlier fences to identify outliers on the graph. Learn more about the Boxplot!

Share this:

  • Tweet

Related

Filed Under: Basics Tagged With: conceptual, distributions

Reader Interactions

Comments and Questions Cancel reply

Primary Sidebar

Meet Jim

I’ll help you intuitively understand statistics by focusing on concepts and using plain English so you can concentrate on understanding your results.

Read More...

Buy My Introduction to Statistics Book!

Cover of my Introduction to Statistics: An Intuitive Guide ebook.

Buy My Hypothesis Testing Book!

Cover image of my Hypothesis Testing: An Intuitive Guide ebook.

Buy My Regression Book!

Cover for my ebook, Regression Analysis: An Intuitive Guide for Using and Interpreting Linear Models.

Subscribe by Email

Enter your email address to receive notifications of new posts by email.

    I won't send you spam. Unsubscribe at any time.

    Follow Me

    • FacebookFacebook
    • RSS FeedRSS Feed
    • TwitterTwitter

    Top Posts

    • How to Interpret P-values and Coefficients in Regression Analysis
    • How To Interpret R-squared in Regression Analysis
    • Multicollinearity in Regression Analysis: Problems, Detection, and Solutions
    • Mean, Median, and Mode: Measures of Central Tendency
    • How to Find the P value: Process and Calculations
    • How to do t-Tests in Excel
    • Z-table
    • Choosing the Correct Type of Regression Analysis
    • One-Tailed and Two-Tailed Hypothesis Tests Explained
    • How to Interpret the F-test of Overall Significance in Regression Analysis

    Recent Posts

    • Slope Intercept Form of Linear Equations: A Guide
    • Population vs Sample: Uses and Examples
    • How to Calculate a Percentage
    • Control Chart: Uses, Example, and Types
    • Monte Carlo Simulation: Make Better Decisions
    • Principal Component Analysis Guide & Example

    Recent Comments

    • Jim Frost on Monte Carlo Simulation: Make Better Decisions
    • Gilberto on Monte Carlo Simulation: Make Better Decisions
    • Sultan Mahmood on Linear Regression Equation Explained
    • Sanjay Kumar P on What is the Mean and How to Find It: Definition & Formula
    • Dave on Control Variables: Definition, Uses & Examples

    Copyright © 2023 · Jim Frost · Privacy Policy