How to Draw and Read a Box Plot

A box plot shows five key values from a sorted dataset: the minimum (smallest value), the lower quartile Q1, the median Q2, the upper quartile Q3, and the maximum (largest value). You read each one straight off the scaled number line beneath the box plot.

Sort your numbers from smallest to largest, then take the two middle values and find their average. For a list of 10 numbers, the median sits between the 5th and 6th values, so you add those two together and divide by 2 to get the median.

The interquartile range is the difference between the upper quartile Q3 and the lower quartile Q1, so IQR = Q3 − Q1. First split your sorted data into a lower half and an upper half, find the median of each half, then subtract Q1 from Q3 to get the IQR.

The range is the gap between the maximum and minimum value, so it covers the full spread of the data. The interquartile range only covers the middle 50%, calculated as Q3 minus Q1. The range uses the two ends; the IQR uses the two quartiles.

A larger interquartile range means the middle 50% of the data is more spread out, suggesting less consistency in the values. A smaller IQR means the middle half is tightly clustered, so the dataset is more consistent and the typical values stay closer together.