# What are Box-and-Whisker Plots?

Jul 28, 2018

A box-and-whisker plot is a type of graph that has statistics from a five-number summary.

#### Explanation:

Here's an example:

The five-number summary consists of:

• Minumum: lowest value/observation
• Lower quartile or Q1: "median" of the lower half of data; lies at 25% of data
• Median: middle value/observation
• Higher quartile or Q3: "median" of the upper half of data; lies at 75% of data
• Maximum: highest value/observation

The interquartile range (IQR) is the range of the lower quartile (Q1) and upper quartile (Q2).

Sometimes, there are also outliers. Outliers occur when outside the range of $Q 1 - 1.5 \left(I Q R\right)$ or $Q 3 + 1.5 \left(I Q R\right)$.

If an outlier occurs, it is graphed on the box-and-whisker plot as a dot. For example, the outlier here is at the data value $95$:

NOTE : An outlier is not a minimum or maximum. If an outlier is the lowest point, then the 2nd lowest point will become the minimum. If an outlier is the highest point, then the 2nd highest point will become the maximum.

Hope this helps!
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