What is a box and whisker plot?

A crate and stubble plot—additionally called a container plot—shows the five-number synopsis of a lot of information. The five-number synopsis is the base, first quartile, middle, third quartile, and most extreme.

In a case plot, we draw a case from the principal quartile to the third quartile. A vertical line experiences the crate in the middle. The stubbles go from every quartile to the base or greatest.

Model: Finding the five-number outline

An example of 101010 boxes of raisins has these loads (in grams):

2525, 282828, 292929, 292929, 303030, 343434, 353535, 353535, 373737, 383838

Make a box plot of the data.

Step 1: Order the data from smallest to largest.

Our data is already in order.

252525, 282828, 292929, 292929, 303030, 343434, 353535, 353535, 373737, 383838

Step 2: Find the median.

The median is the mean of the middle two numbers:

252525, 282828, 292929, 292929, \large{30}3030, \large{34}3434, 353535, 353535, 373737, 383838

\dfrac{30+34}{2}=32

2

30+34

=32start fraction, 30, plus, 34, divided by, 2, end fraction, equals, 32

The median is 323232.

Step 3: Find the quartiles.

The first quartile is the median of the data points to the left of the median.

252525, 282828, \large{29}2929, 292929, 303030

Q_1=29Q

1

=29Q, start subscript, 1, end subscript, equals, 29

The third quartile is the median of the data points to the right of the median.

343434, 353535, \large{35}3535, 373737, 383838

Q_3=35Q

3

=35Q, start subscript, 3, end subscript, equals, 35

Step 4: Complete the five-number summary by finding the min and the max.

The min is the smallest data point, which is 252525.

The max is the largest data point, which is 383838.

The five-number summary is 252525, 292929, 323232, 353535, 383838.

Model (kept): Making a container plot

We should make a container plot for the equivalent dataset from above.

Step 1: Scale and label an axis that fits the five-number summary.

Stage 2: Draw a container from Q_1Q  Q, start subscript, 1, end subscript to Q_3Q

Recall that Q_1 =29Q, start subscript, 1, end subscript, equals, 29, the median is 32, and Q_3=35.

Draw a whisker from Q1, start subscript, 1, end subscript to the min and from Q3​, start subscript, 3, end subscript to the max.

Recall that the min is 25 and the max is 38

Translating quartiles

The five-number rundown isolates the information into areas that each contain around 25\%25%25, percent of the information in that set.