How do you make a Box and Whisker plot with the numbers: 60, 90, 90, 92, 100, 100, 100, 100?

1 Answer
Aug 8, 2017

See below.

Explanation:

To create a box-and-whisker plot, you need five values: the minimum, the "Q1", "Q2" (also known as the median), "Q3" values, and the maximum.

  • The minimum value is 60.
  • The median can be calculated by finding the middle number out of the set. You must first arrange the numbers in order from least to greatest, but here they are already in this order.

In this case, there are two middle numbers: 92 and 100. To find the middle number, find the average of them.

(92+100)/2 = 96

So, the median or "Q2" value is 96.

  • The maximum value is 100.

  • The "Q1" and "Q3" values are simply the medians of the two halves of our data.

"Q1" value (first quartile)

Find the median of the lower half of the data, which is 60, 90, 90, 92.

The two middle numbers are 90 and 90; the average of these is 90.

"Q1" = 90

"Q3" value (third quartile)

Find the median of the upper half of the data, which is 100, 100, 100, 100.

The two middle numbers are 100 and 100; the average of these is 100.

"Q3" = 100

Now that we have the five values we need, make a number line and draw lines where each value occurs.

Connect the middle three lines to form a box. This "box" is called the interquartile range because it consists of the "Q1", "Q2", and "Q3" values, along with everything in between.

Finally, draw lines extending out from the box and connect them to the minimum values. These are the "whiskers".

In the end, a box-and-whisker plot looks something like this:

![https://statsmethods.wordpress.com/tag/box-and-whisker-plot/](useruploads.socratic.org)

However, since our "Q3" and maximum value were the same, there is no right whisker. Our box plot looks like this:

![http://www.imathas.com/stattools/http://boxplot.html](https://useruploads.socratic.org/gsSyR0tTWAjBz7nQnVtA_boDMBfN.png)