Data Visualization

Choose the graph for the question

A graph should expose a pattern the reader needs to evaluate. Start with the unit of observation and variables, then decide whether the question concerns counts, a distribution, a relationship or change over time.

Question	Useful starting graph	Check
How frequent are categories?	Bar chart	Denominator and missing categories
How is a numerical variable distributed?	Histogram or dot plot	Bins, skew, clusters and extremes
How do groups differ?	Side-by-side distributions	Spread and group sizes, not just averages
How do two measurements relate?	Scatter plot	Curves, subgroups and influential points
How does a measure change over time?	Time plot	Regularity, seasonality and missing periods

Bar charts leave gaps between categories; histogram bars describe numerical intervals. A connected line implies an ordering that unordered categories do not have.

Worked example: look beyond the mean

Two hypothetical teams have completion times in minutes:

• Team A: 4, 5, 5, 6.
• Team B: 1, 1, 9, 9.

Both means are 5 minutes. A bar chart of means alone makes the teams look identical. A dot plot shows that A is tightly grouped while B has two clusters. Their ranges are 2 and 8 minutes. With four observations per group, showing all points is clearer than suggesting a precisely estimated smooth distribution.

If you add an error bar, label exactly what it represents: standard deviation, standard error, confidence interval or another quantity. These answer different questions. An interval around a mean does not show the distribution of individual times.

Histograms need thoughtful bins

Bin width and boundaries can reveal or conceal clusters. Explore more than one reasonable width and label units. With equal-width bins, counts or relative frequencies can be shown as heights. With unequal-width bins, use frequency density so the area represents frequency; otherwise wide bins can be misleading.

A density estimate is a smoothed description, not proof that the population is normal. For small samples, dots or a rug plot keep the underlying observations visible.

Axes, denominators and subgroup structure

Start bar-chart quantity axes at zero because bar length represents magnitude. A line chart can use a narrower range to show movement, but make the scale explicit and avoid implying a huge change. Avoid 3D effects that distort comparisons.

Rates need denominators: 10 completions among 20 users differs from 10 among 200. Plot comparable time windows and state whether repeated observations belong to the same person. A pooled scatter plot may hide different patterns within groups; examine plausible subgroups without selecting only those that support a preferred conclusion.

Use clear labels, accessible colors and shapes, and a short text statement of the main finding. Color should not be the only signal. A descriptive graph alone does not establish causation or generalize beyond the collected data.

Practice

Which graph should you inspect before summarizing a relationship with Pearson correlation?

Show the explanation

A scatter plot of matched numerical observations. Check for curves, influential points, clusters and restricted ranges. A correlation coefficient compresses the pattern and can miss these features.

Continue

Use scatter plots and correlation or frequency tables. NIST’s exploratory data analysis handbook provides graphical methods and their purposes.