Visualizing Data: Graphical Representation Techniques in Statistics

Raw numbers can hide more than they reveal. A spreadsheet with hundreds of citation counts, journal impact values, or library footfall figures tells you very little at a glance. Patterns, clusters, and unusual values stay buried until you turn those figures into a picture. Graphical representation is the bridge between a column of data and a clear story. For anyone working with informetric or scientometric data, choosing the right chart is not decoration. It decides whether your audience sees the insight or misses it entirely. This post walks through the core techniques, dotplots, stem-and-leaf charts, bar graphs, histograms, box plots, and pie charts, and explains exactly when each one earns its place.

Why graphical representation matters 🔗

A graph translates numerical data into a visual form so that the human eye can spot what calculation alone is slow to find. The three things every analyst wants to read off a dataset are its shape (is it symmetric or skewed?), its centre (where do most values sit?), and its spread (how widely do values vary?). A good graph answers all three almost instantly. It also flags outliers, values that sit far away from the rest and often signal an error or an important exception.

The key principle is matching the method to the data. The first question to ask is always what kind of data you are holding. Is it categorical (named groups like subject fields or document types) or numerical (measured values like page counts or h-index scores)? Within numerical data, you also distinguish discrete data (countable, like the number of authors per paper) from continuous data (measurable on a scale, like average download time). Every chart below is built for a particular answer to that question.

Dotplot: the simplest starting point 🔗

A dotplot is the most basic visual display and a sensible first move with a small dataset. Each observation is shown as a single dot placed above its value on a number line. When two or more values are identical, the dots are stacked vertically, so the height of a stack instantly shows how often that value occurs.

Because every data point appears individually, a dotplot gives a quick glance at the minimum, maximum, and mode without any calculation. You can see clusters where dots bunch together and gaps where values are absent. Dotplots are generally reserved for small datasets, since a large collection of values would produce stacks too tall and crowded to read.

When a dotplot works best 🔗

Reach for a dotplot when you have perhaps a few dozen values and want a fast, honest view of the distribution before committing to anything more elaborate. In a small research sample, say the number of co-authors on twenty papers, a dotplot immediately reveals whether most papers cluster around a typical figure or spread out.

Stem-and-leaf chart: keeping the real values 🔗

A stem-and-leaf plot, or stemplot, displays quantitative data in a form that is similar to a histogram but with one important advantage: it preserves the actual data values. The method evolved from the early work of Arthur Bowley and became widely used after John Tukey popularised it in his 1977 book on exploratory data analysis.

The idea is to split each number into two parts. The leading digit or digits become the stem, and the final digit becomes the leaf. For a value of 47, the 4 is the stem and the 7 is the leaf. All leaves sharing a stem are listed in a row beside it. The result looks like a histogram turned on its side, but because the original digits remain, you can recover the exact values and use them for further calculation.

The importance of the key 🔗

Every stemplot needs a key so readers interpret it correctly. A key showing that 1 | 7 means 17 prevents confusion with 1.7 or 1700. Stemplots are most useful for small to moderate datasets, roughly under a hundred points. With very few values they offer little, and a dotplot may serve better; with very large datasets they become cluttered because every single point must be written out, and a histogram or box plot becomes the wiser choice.

Bar graph versus histogram: a difference that matters 🔗

These two charts look almost identical, yet they are built for different data and confusing them is one of the most common mistakes in data presentation. The single question that separates them is whether your data is categorical or continuous.

The bar graph: for categories 🔗

A bar graph compares distinct categories using rectangular bars, where the height of each bar shows the value or frequency for that category. The defining visual feature is the gap between bars. Those gaps are deliberate. They signal that the categories are separate and unrelated, with no continuous scale connecting them.

Bar graphs suit data such as the number of publications across different subject disciplines, document types held in a collection, or library visits across branches. The bars can even be reordered, largest to smallest, to make comparisons obvious, because there is no inherent sequence to the categories.

The histogram: for continuous ranges 🔗

A histogram shows the distribution of continuous numerical data by grouping values into intervals called bins. Each bar represents the count of values falling within a bin. The crucial visual difference is that the bars touch with no gaps, reflecting the unbroken nature of the underlying scale. Continuous data is anything measured along a range, such as age, time, weight, or test scores.

Forcing categorical data into a histogram, or continuous data into a bar graph, produces a misleading chart. Separated bars imply distinct groups that do not exist on a continuous scale, while touching bars imply a continuity that categories do not have. One practical caution with histograms is the choice of bin width: bins that are too wide can hide important patterns, while uneven bins can exaggerate parts of the data.

The grey area of discrete data 🔗

There is one honest complication. When numerical data is discrete, meaning countable rather than measured, the line between the two charts blurs and either can be defensible. For counts like the number of references per article, you will see both used, and the choice becomes a matter of clarity rather than a strict rule.

Box plot and pie chart: two ways to summarise 🔗

The final pair tackle two very different summarising jobs. One condenses a numerical distribution into five numbers; the other shows how a whole divides into parts.

Box plot: the five-number summary made visible 🔗

A box plot, also called a box-and-whisker plot, is a visual representation of the five-number summary: the minimum, the first quartile (Q1), the median, the third quartile (Q3), and the maximum. The box itself spans from Q1 to Q3, capturing the middle 50% of the data. The length of this box is the interquartile range (IQR), a clean measure of spread. A line inside the box marks the median.

The shape of the box tells you about skew. If the data are symmetrical, the median sits in the centre of the box; if the data are skewed, the median shifts toward the top or bottom. The whiskers extend out to the smallest and largest values that are not outliers. A value is flagged as a potential outlier when it falls more than 1.5 times the IQR below Q1 or above Q3, and is usually plotted as a separate point.

Box plots shine when comparing several groups at once. Placing box plots side by side on the same scale lets you compare the centre and spread of, for example, citation counts across different journals in a single view. The trade-off is that a box plot does not show the fine detail of a distribution the way a stemplot or histogram does. It summarises rather than displays every value.

Pie chart: showing proportions of a whole 🔗

A pie chart divides a circle into slices, where each slice represents a category’s share of the total. Its job is narrow but useful: it shows proportion, how a single whole is split into parts that add up to 100%. A pie chart answers the question “what fraction of the total does each category account for?” rather than “how do the absolute values compare?”

It works well when you have a small number of categories that sum to a meaningful whole, such as the share of a library budget allocated to print, digital, and staffing. The chart becomes hard to read when there are many slices of similar size, since the human eye struggles to compare angles accurately. For precise comparison across many categories, a bar graph is usually the stronger choice.

Choosing the right chart 🔗

The whole skill comes down to matching the method to the data and to the question you are asking. Use a dotplot for a quick look at a small dataset. Use a stem-and-leaf chart when you want a visual shape but need to keep the exact values. Use a bar graph to compare categories and a histogram to show the distribution of continuous data, remembering that the gaps between bars are the giveaway. Use a box plot to summarise and compare distributions through their five-number summary, and a pie chart to show how parts make up a whole. The right graph reveals patterns that a table of numbers would keep hidden; the wrong one can quietly mislead.

What do you think? If you were presenting the spread of citation counts across five different journals to a committee, which chart would communicate the comparison most clearly, and why? And can you recall a chart you have seen recently that used the wrong method for its data?

References

1. https://www.coursera.org/articles/histogram-vs-bar-graph
2. https://online.stat.psu.edu/stat500/lesson/1/1.6/1.6.1
3. https://en.wikipedia.org/wiki/Stem-and-leaf_display
4. https://mathspace.co/textbooks/syllabuses/Syllabus-1007/topics/Topic-20222/subtopics/Subtopic-266179/
5. https://pressbooks.montgomerycollege.edu/statnotes/chapter/2-1-stem-and-leaf-graphs-stemplots-line-graphs-and-bar-graphs/
6. https://www.geeksforgeeks.org/maths/bar-graphs-and-histograms/
7. https://www.domo.com/learn/charts/histogram-vs-bar-graph
8. https://venngage.com/blog/bar-charts-vs-histograms/
9. https://www.storytellingwithdata.com/blog/2021/1/28/histograms-and-bar-charts
10. https://www.jmp.com/en/statistics-knowledge-portal/exploratory-data-analysis/box-plot
11. https://stats.libretexts.org/Courses/Rio_Hondo_College/Math_130:_Statistics/02:_Descriptive_Statistics/2.1.2:_Five_Number_Summary_and_Box_Plots_Part_2
12. https://www.simplypsychology.org/boxplots.html