The Five Number Summary | CodeSignal Learn

The Five Number Summary | CodeSignal Learn

Introduction

Welcome back to Measuring Spread with Range and IQR! This is lesson three of five, and we have officially crossed the halfway point of the course. In the first lesson, we computed the range from the minimum and maximum. In the second, we moved inside the data to find Q1, the median, and Q3, and used them to compute the interquartile range . Each of those measures tells us something valuable, but each one works alone. In this lesson, we bring all five values together into a single, organized package called the five-number summary .

From Separate Pieces to One Snapshot

So far, we have been collecting individual landmarks of a dataset: the minimum, the maximum, the median, Q1, and Q3. Each one answers a specific question about where values fall, but looking at them in isolation is like checking five weather stations one at a time instead of viewing the whole forecast map. The five-number summary simply lines up these landmarks from smallest to largest, giving us a compact profile of the entire distribution. No new formulas are needed beyond what you already know. The real value lies in reading the five numbers together and understanding what each one contributes to the overall picture.

What Is the Five-Number Summary?

\text{Max} - \text{Min}

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Let's build one from scratch. Suppose we recorded the daily number of customer orders at a small bakery over 11 days:

15, \; 22, \; 9, \; 30, \; 18, \; 25, \; 12, \; 20, \; 27, \; 35, \; 14

Step 1 — Sort the data.

9, \; 12, \; 14, \; 15, \; 18, \; 20, \; 22, \; 25, \; 27, \; 30, \; 35

Step 2 — Identify the minimum and maximum. The minimum is $9$ and the maximum is $35$ . These are simply the first and last values in the sorted list.

Step 3 — Find the median. There are $11$ values, so the median sits at position 6. That value is $20$ .

Step 4 — Find Q1 and Q3. Using the median-exclusive method from the previous lesson, we set the median aside and work with the remaining halves.

Lower half: $9, \; 12, \; 14, \; 15, \; 18$ — five values, so Q1 is the middle one: $\mathbf{14}$
Upper half: $22, \; 25, \; 27, \; 30, \; 35$ — five values, so Q3 is the middle one: $\mathbf{27}$

The completed five-number summary:

Min	Q1	Median	Q3	Max
9	14	20	27	35

Five values, one clean row, and a surprisingly complete portrait of 11 days at the bakery.

Number line showing bakery order data with five-number summary markers and the shaded IQR

One of the most useful things about the five-number summary is what the gaps between consecutive values reveal about how the data is distributed. Let's compute those gaps for our bakery data:

Segment	Calculation	Gap
Min to Q1	$14 - 9$	5
Q1 to Median	$20 - 14$	6
Median to Q3	$27 - 20$	7
Q3 to Max	$35 - 27$	8

Each of these four segments contains about 25% of the data. When the gaps are roughly equal, the data is spread fairly evenly. Here the gaps grow slightly from left to right (5, 6, 7, 8), which means the upper portion of the data stretches out a bit more than the lower portion. In plain language, the busiest days are more spread apart from each other than the slowest days are.

If one gap were dramatically larger than the others, it would signal that values in that quarter are more dispersed, or that an extreme value is pulling the boundary outward. This kind of quick shape reading is exactly what makes the five-number summary so practical — and it will become even more visual in the next lesson when we turn these numbers into a box plot.