# How do you draw a box and whisker plot of the data: 29, 33, 36, 37, 39, 40, 41?

Jul 29, 2018

#### Explanation:

$29 , 33 , 36 , 37 , 39 , 40 , 41$

The minimum is the lowest number in the data set.
Since it is listed from smallest to largest, we know that the minimum is $29$.


The median is the middle number. Cancel out $3$ numbers from each side and we are left with the median:
$\cancel{29} , \cancel{33} , \cancel{36} , 37 , \cancel{39} , \cancel{40} , \cancel{41}$

Therefore, the median is $37$.

The first quartile (Q1) is the median of the lower half of data which lies at 25% of the data.
Let's look at the lower half of numbers:
$29 , 33 , 36$

The number in the middle is $33$, so that is the first quartile.

The third quartile (Q3) is the median of the upper half of data which lies at 75% of the data.

Let's look at the upper half of numbers:
$39 , 40 , 41$

The number in the middle is $40$, so that is the third quartile.

The maximum is the highest number in the data set; it is $41$.

So here's the five-number summary:
Minimum: 29

First quartile: 33

Median: 37

Third quartile: 40

Maximum: 41

This is what a typical box-and-whisker plot looks like:

So here's the box-and-whisker plot for this data:

Hope this helps!