# How do you create box and whisker plots on a graphing calculator?

May 27, 2015

For a procedure similar to the graphing calculator, see this Plot.ly link . Please explore the Data tab, after reading the detailed explanation below.

Explanation . I never used graphing calculators, because in my country they are considered detrimental to actual mathematical reasoning. I know how to do it ~the hard way~.

Suppose we have the following set of data:

$\left\{5.1 , 4.8 , 4.2 , 4.7 , 4.5 , 5.2 , 4.9 , 4.6 , 3.9 , 4.4 , 4.1 , 4.0 , 4.7 , 4.5 , 4.2 , 4.6 , 4.3\right\}$

1) The first step in creating a box-and-whisker plot is ordering your data set:

$\left\{3.9 , 4.0 , 4.1 , 4.2 , 4.2 , 4.3 , 4.4 , 4.5 , 4.5 , 4.6 , 4.6 , 4.7 , 4.7 , 4.8 , 4.9 , 5.1 , 5.2\right\}$

2) Second, we need to find the median value: as we have $17$ values in the data set, the median will be the ${9}^{t h}$ value, that is $4.5$. The median value gives us the second quartile point :

${Q}_{2} = 4.5$

3) Third, we need to find the other two quartile points , ${Q}_{1}$ and ${Q}_{3}$, by finding the median values of the two data subsets separated by the ${Q}_{2}$.

For the first subset $\left\{3.9 , 4.0 , 4.1 , 4.2 , 4.2 , 4.3 , 4.4 , 4.5\right\}$, we have 8 values, so its median will be the arithmetic mean of the middle values: ${Q}_{1} = \frac{4.2 + 4.2}{2} = 4.2$

For the second subset $\left\{4.6 , 4.6 , 4.7 , 4.7 , 4.8 , 4.9 , 5.1 , 5.2\right\}$, we also have 8 values, so its median will be the arithmetic mean of the middle values: ${Q}_{3} = \frac{4.7 + 4.8}{2} = 4.75$

4) Fourth, we'll mark the 5 significant values on a scale:

• the minimum and maximum values: $3.9$ and $5.2$
• the quartiles ${Q}_{1} , {Q}_{2} \mathmr{and} {Q}_{3}$: $4.2 , 4.5 \mathmr{and} 4.75$

5) Fifth, we draw the box , which goes from ${Q}_{1}$ to ${Q}_{3}$, that is from $4.2$ to $4.75$

6) Sixth, we draw the whiskers at the endpoints (minimum and maximum values $3.9$ and $5.2$).

In the end, we'll get something like this: