What it means
To find quartiles, you first sort the numbers from smallest to largest. The middle value is the median, also called the second quartile or Q2.
The first quartile, Q1, is the middle of the lower half, and the third quartile, Q3, is the middle of the upper half. Quartiles are more helpful than averages when data is uneven.
An average can be dragged upward by a few very large values, such as a handful of huge deals, while the quartiles show what is typical. They are widely used in salary surveys, sales analysis, fund performance tables and customer segmentation.
The gap between Q3 and Q1 is called the interquartile range. It measures the spread of the middle half of the data and is less affected by extreme values than the full range.
Analysts also use it to flag outliers, which are values unusually far from the rest. In investing, funds are often ranked by quartile within a peer group.
A fund in the first quartile sits in the top 25% of its category, while a fund in the fourth quartile sits in the bottom 25%. This is a simple way to compare performance, though a quartile ranking for one year may not predict the next.
A nuance is that several methods exist for computing quartiles, especially with small data sets. Spreadsheets offer more than one function, and the answers can differ slightly.
When the figures are used in a report, it is wise to state which method was used. Quartiles are easy to communicate to a non-technical audience.
A chart called a box plot draws the first quartile, median and third quartile as a simple box, which lets a board see the shape of the data at a glance. This is often clearer than a table of averages and standard deviations.
In practice
Real-world examples.
Example
An HR manager compares staff salaries against a market survey that reports quartiles for each role. The company's analyst pay sits just below the market median, so the manager proposes targeted rises. The survey's Q1 and Q3 show how far pay could reasonably move.
Example
A fund selector reviews three funds in the same category and finds that one has ranked in the top quartile for three years running. She uses this as one input but also checks fees and risk. The quartile ranking helps her shortlist rather than make the final decision.
Example
A retail chain looks at weekly sales per store and finds that the fourth-quartile stores earn less than a third of the first-quartile stores. The operations director visits the bottom group to understand location, staffing and stock issues. The analysis leads to a plan for the weakest ten stores.
Formula
Calculation
Q1 = median of the lower half; Q2 = median of the whole set; Q3 = median of the upper half; interquartile range = Q3 - Q1
Suppose a sales team closed eight deals worth $12,000, $15,000, $18,000, $20,000, $24,000, $28,000, $35,000 and $40,000, already sorted.
Step 1: the median is the average of the 4th and 5th values = ($20,000 + $24,000) / 2 = $22,000.
Step 2: the lower half is $12,000, $15,000, $18,000 and $20,000, so Q1 = ($15,000 + $18,000) / 2 = $16,500.
Step 3: the upper half is $24,000, $28,000, $35,000 and $40,000, so Q3 = ($28,000 + $35,000) / 2 = $31,500.
Step 4: interquartile range = $31,500 - $16,500 = $15,000.Case study
Seen in the real world.
Oakridge Logistics is a fictional delivery company used for illustration. Its finance team reported an average invoice-payment time of 38 days and assumed customers were paying slowly across the board. A junior analyst calculated the quartiles and found that Q1 was 21 days, the median was 28 days and Q3 was 40 days.
The spread showed that most customers paid in around four weeks, while a small group paying very late pulled the average up. The credit controller focused collection efforts on that late group instead of changing terms for everyone. Within two quarters the average came down, and the team added quartiles to its monthly reporting pack.
The analyst also noticed that the late-paying group was made up of just a few large customers, and presented the figures to the sales team in a simple box plot. Sales then agreed to raise payment reminders during contract renewals. The finance team now tracks the third quartile as an early warning figure for collection problems.
Watch out
Common mistakes.
- Confusing quartiles with percentages. A quartile is a cut-off value, not a share, although each quartile group holds 25% of the data.
- Forgetting to sort the data first. Quartiles only make sense on ordered values.
- Using different calculation methods in the same report. Pick one method and state it.
Questions
People also ask.
What is the difference between a quartile and a quintile?
A quartile splits data into four groups, while a quintile splits it into five.
What does it mean to be in the top quartile?
It means your result is in the best 25% of the group being compared.
Why use the interquartile range instead of the full range?
It ignores extreme values at either end, so it gives a steadier picture of the typical spread.
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