mathematics

Wide and narrow data

Wide and narrow data is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Wide and narrow data rather than just read about it. In short: Wide and narrow are terms used to describe two different presentations for tabular data. Terminology The terms used vary by community and software: Wide and long: Common in modern data science and time-series analysis (e.g., pandas, R).

Key takeaways

Wide and narrow data belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Wide and narrow data to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Wide and narrow data from memory before moving on to harder problems.

Reference excerpt

Wide and narrow are terms used to describe two different presentations for tabular data.

Terminology The terms used vary by community and software:

Wide and long: Common in modern data science and time-series analysis (e.g., pandas, R). Un-stacked and stacked: Common in statistical software and spreadsheet operations. Pivoted and unpivoted: Common in SQL and data preparation tools like Power Query, where "unpivoting" refers to transforming wide data into a long format. Wide and narrow: Common in database modeling.

Wide Wide, or unstacked data is presented with each different data variable in a separate column.

Narrow

Narrow, stacked, or long data is presented with one column containing all the values and another column listing the context of the value

This is often easier to implement; addition of a new field does not require any changes to the structure of the table, however it can be harder for people to understand.

Implementations Many statistical and data processing systems have functions to convert between these two presentations, for instance the R programming language has several packages such as the tidyr package. The pandas package in Python implements this operation as "melt" function which converts a wide table to a narrow one. The process of converting a narrow table to wide table is generally referred to as "pivoting" in the context of data transformations. The "pandas" python package provides a "pivot" method which provides for a narrow to wide transformation.

See also Abstract data type Pivot table Table (information) Information graphics Row (database) Table (database) Table (HTML)

References

External links

https://tidyr.tidyverse.org/articles/pivot.html https://cran.r-project.org/web/packages/reshape

Worked examples

Example 1 — a first encounter with Wide and narrow data

Start with the simplest possible case. Write down what Wide and narrow data claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Wide and narrow data before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Wide and narrow data ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Wide and narrow data

In research: Wide and narrow data appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Wide and narrow data in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Wide and narrow data is common in secondary-school and first-year university syllabi. It links to neighbouring topics Data modeling, Descriptive statistics, Statistical data types, so understanding it makes those chapters shorter.
In everyday life: Look for Wide and narrow data outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Wide and narrow data in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Wide and narrow data means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Wide and narrow data out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Wide and narrow data in simple terms?

Wide and narrow are terms used to describe two different presentations for tabular data. Terminology The terms used vary by community and software: Wide and long: Common in modern data science and time-series analysis (e.g., pandas, R).

Why does Wide and narrow data matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Wide and narrow data?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Wide and narrow data.