Question

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

Answer 1

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:

`{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}`

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

`{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}`

2) Second, we need to find the median value: as we have `17` values in the data set, the median will be the `9^(th)` 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 `{3.9, 4.0, 4.1, 4.2, 4.2, 4.3, 4.4, 4.5}`, we have 8 values, so its median will be the arithmetic mean of the middle values: `Q_1 = (4.2+4.2)/2 = 4.2`

For the second subset `{4.6, 4.6, 4.7, 4.7, 4.8, 4.9, 5.1, 5.2}`, we also have 8 values, so its median will be the arithmetic mean of the middle values: `Q_3 = (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 and Q_3`: `4.2, 4.5 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: