Modified Boxplot vs Boxplot

A modified boxplot is the version you normally draw, because it shows outliers instead of burying them at the end of a long whisker. You first set the fences at $Q_1 - 1.5 \times \text{IQR}$ and $Q_3 + 1.5 \times \text{IQR}$, where $Q_1$ is the first quartile and $Q_3$ is the third quartile, taking both by the median-excluded (TI-84) rule this site uses, then mark every value beyond a fence with its own dot. Suppose $Q_1 = 20$ and $Q_3 = 32$, so the IQR is 12 and the fences sit at $20 - 18 = 2$ and $32 + 18 = 50$: a value of 61 becomes a plotted point, and the upper whisker stops at the largest value at or below 50. The box is unchanged either way, still running from $Q_1$ to $Q_3$ with the median marked inside it.

A boxplot turns the five-number summary into a picture: a box spans $Q_1$ (the first quartile) to $Q_3$ (the third quartile), a line inside marks the median, and whiskers reach the smallest and largest non-outlier values. For example, a longer right whisker signals a right-skewed distribution. Points more than $1.5 \times \text{IQR}$ beyond the nearer quartile are drawn separately as outliers. Boxplots make it easy to compare center and spread across several groups side by side.