Visualizing Distributions
Nisha has a full year of daily cold-coffee sales now: 365 numbers. Mean, median and standard deviation squeeze them into three figures, but they cannot tell her whether there are two kinds of day, where the busy days cluster, or how many fair days there were. A picture of the distribution can, in seconds.
The rule
Histogram for the shape, box plot for the summary and the stragglers.
A histogram splits the number line into equal bins and draws a bar for how many values fall in each.
- It shows the shape at a glance: symmetric or skewed, one hump or two, gaps and isolated bars.
- Bin width matters. Too wide and the shape vanishes into two or three blocks; too narrow and it becomes noisy. Try a few widths.
- It is not a bar chart of categories: the bars touch, because the x-axis is a continuous scale.
A box plot (box-and-whisker plot) draws the five-number summary:
- The box runs from Q1 to Q3, holding the middle half of the data. A line inside marks the median.
- The whiskers reach out to the most extreme values still inside the 1.5 × IQR fences.
- Anything beyond the fences is drawn as a separate dot: a flagged outlier.
For the week: box from 38 to 46, median line at 40, whiskers from 36 to 46, and one dot at 95. Because box plots are compact, several fit side by side, which makes them ideal for comparing groups such as weekdays against weekends or branch 1 against branch 2.
Two other useful views: a dot plot, one dot per value, is best for small datasets like a single week; a density curve is a smoothed histogram, handy for overlaying two groups.
The shortcut
Pick by the question: "What does it look like?" → histogram. "How do these groups compare?" → box plots side by side. "Only a few values?" → dot plot.
Shape
Histogram with 10-cup bins: a big hump around 35 to 50 and a smaller one around 55 to 70.
The trap is trusting a single average for a column you have never plotted. Very different datasets can share the same mean and standard deviation.
Drills
Answer fast — trust the rule.
Which chart best shows whether a year of daily sales has two humps?
In the week's box plot, what does the line inside the box mark?
In the week's box plot, where does the upper whisker end?
You want to compare delivery times across three branches. What is the clearest choice?
Why do histogram bars touch while bar-chart bars have gaps?
Remember
- Histogram for the shape, box plot for the summary and the stragglers.
- Shortcut: shape → histogram; compare groups → box plots side by side; few values → dot plot.
- Trap: trusting an average for a column you have never plotted.