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Description:
Statistics, Data, and Probability I: Drill Set 1, Problem 2. What is the median length of these writing utensils?
Transcript
- 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?
Full Transcript
- 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...
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