Displaying Data

Different displays answer different questions:

• Bar chart: compares categories. Bars have gaps.
• Histogram: shows the shape of numerical data in intervals. Bars touch.
• Line graph: shows change over time.
• Dot plot: small data sets, one dot per value.
• Box plot: shows the median, the quartiles and the spread at a glance.
• Scatter plot: shows the relationship between two variables.

Bar chart and histogram look similar but are not interchangeable: bar charts are for categories, histograms for number ranges.

When reading any chart, check the axis. A vertical axis that starts at 90 instead of 0 makes a tiny difference look enormous.

Display choice follows data type. Categorical data uses bar charts and, when parts of a whole matter, pie charts. Univariate numerical data uses histograms, dot plots and box plots. Bivariate numerical data uses scatter plots.

A histogram bins continuous data, so bin width is a real analytical choice: too wide hides structure such as bimodality, too narrow turns the display into noise. Bars touch precisely because the underlying variable is continuous.

A box plot encodes the five-number summary (minimum, Q1, median, Q3, maximum) and shows the interquartile range as the box. The usual outlier rule marks points beyond Q1 − 1.5·IQR or Q3 + 1.5·IQR separately.

Truncating the vertical axis exaggerates differences, and truncation is legitimate for time series of small variation only when clearly marked. This is the most common technique for making a chart technically accurate and practically misleading, which is a reason to read the axis before the picture.