ShmoopTube

00:04

Here's the boring, unshmoopily-voiced question...

00:06

The lengths, in centimeters, of ten different types of pencils and pens are listed below.

00:13

What is the median length of these writing utensils?

00:17

Here are the potential answers.

00:24

So... what is this question really asking?

00:26

Well, it's really two things.

00:28

First, it's testing our vocabulary... do we know what a median is?

00:33

Uh, no, that's a mediUM.

00:34

A median is the center value of a data set.

00:39

That is, if we took all our numbers and organized them low to high...

00:42

...and started throwing out one high for every low

00:45

'til we were left with only the middle number...

00:48

we would have our median.

00:51

Okay... first we have to order the numbers.

00:54

00:54

We want to organize our data set in terms of length from shortest to longest.

00:59

Cross out the high, cross out the low... Cross out the high, cross out the low...

01:06

Kind of sounds like a camp song we'd sing around the lake, no?

01:09

Anyway, when we're done crossing out numbers, we're left with 13.6 and 14 in the middle.

01:14

We're too competitive to settle for a tie.

01:17

Our median has to have a single answer.

01:20

But... freeze... and go back to the answer set offered to us.

01:24

Note that 14 isn't even listed as a choice.

01:28

So even if we didn't know that we're supposed to average the numbers,

01:32

we know that we don't just pick... any ol' number.

01:35

But also notice that 13.6 is there as a choice.

01:38

Ooh... curveball.

01:39

Let's not get hit in the head by it. The answer isn't 13.6.

01:44

To get the median, we have to average the remaining 2 numbers.

01:49

Average? Uh oh, what does that mean?

01:51

All we have to do is add our two middles numbers...

01:54

in this case we add 14 and 13.6 to get 27.6...

01:58

...then, since there are 2 numbers, we divide 27.6 by 2 to get the magic number... 13.8.

02:05

And voila!

02:05

There is our answer...

Full Transcript