Reading Histograms, Box Plots and Scatter Plots

Numbers summarise data, and charts show how the values are arranged. Each of the three charts below answers a different question.

Histogram

A histogram groups values into ranges called bins and draws a bar showing how many values land in each bin. The overall shape carries the most information:

• Symmetric: both sides look alike, and the mean and median are close.
• Right-skewed: a long tail stretches toward high values, pulling the mean above the median.
• Left-skewed: a long tail stretches toward low values, pulling the mean below the median.
• Two peaks: often a sign that two different groups are mixed in the same column.

Bin width changes what you see. Very wide bins hide detail, and very narrow bins make the chart look noisy.

Example: A histogram of food delivery times shows most deliveries between 20 and 40 minutes, with a thin tail reaching past 90 minutes. This is a right-skewed shape. The mean delivery time is higher than the median, so the median better describes a typical order.

Box Plot

A box plot condenses the quartiles into one picture. The box spans Q1 to Q3, and a line inside it marks the median. The whiskers reach the furthest values still inside the fences from the previous lesson, and points beyond them are drawn individually as outliers.

Placing several box plots side by side, such as delivery time by city, makes it easy to compare groups.

Scatter Plot

Each point is one observation, with one variable on the horizontal axis and the other on the vertical axis. Four things are worth checking:

• Direction: points rising from left to right suggest a positive relationship, and points falling suggest a negative one.
• Strength: the tighter the points cluster around a pattern, the stronger the relationship.
• Shape: the pattern may be a straight line, a curve, or no pattern at all.
• Odd points: isolated points far from the rest deserve a closer look.

A scatter plot of advertising spend against weekly sales that slopes upward shows the two move together. It does not, on its own, show that the spend caused the sales.