Announcements:
- Everyone has been doing their homework, it looks good, I am happy!
- I notice some of you have trouble spelling. However, you spell phonetically, and I get what you mean, so that's fine. Don't worry about spelling during math because I need you to focus on the math, and not get self-conscious about spelling.
- Also, about a word I may use: set. It just means a collection. If I say a set of numbers, I just mean a group of them. Nothing fancy. Sometimes I will show things, like numbers, are related by grouping them together with these grouping symbols: {}. Again, it just means they all go together, like so: {2, 3, 4, 10}.
- Also, for today's lesson I mention "salary." That is how much someone gets paid in one year for working.
Questions for you: How is class going so far? How is doing homework this way, with the surveys online?
[Note to self: really listen and don’t just think about what you are going to say]
Today: Graphs are about groups of numbers. But do we always need to draw pictures to talk about groups of numbers? That seems like a lot of work. “Hey how did your class do on the test?” “Oh well... do you have a minute? I have to grab some pens.”
Sometimes, numbers are the best way to communicate: if someone asks how tall you are, I hope you don’t have to pull out a life-sized poster of yourself. Today, we will talk about three numbers that let you communicate about a group of numbers. They are different ways of “measuring” the group of numbers, and they are called mean, median, and mode. But first, we need some numbers.
Measure everyone’s:
heights
hair length
foot size
(all measured in inches)
Then we put them in a spreadsheet (we’ll talk about spreadsheets later, they are magic). Well, you fill out a form and it magically puts them in the magical spreadsheet:
Then we will take all these numbers and try to answer questions like
"How tall is this class?"
"How long is the class' hair?"
"How long are the class' feet?"
We will answer these questions naively, and also by introducing some concepts.
Given a list of the classes measurements, how can we answer those questions?
You probably mentioned a lot of good ways, some of which being the range, mean, median, and mode (I know many, if not all of you, are familiar with this, but maybe I will present it in a different light).
The range is the difference between the biggest and smallest number in a group. In this group {5, 10, 12, 20, 99, 105} the range is biggest - smallest = 105 - 5 = 100.
The mode is the most common number in a collection. It is not used too much "in the wild" (really, people use math in the real world), because it doesn't tell you too much, except in certain situations. Example: in this collection: {2, 2, 2, 3, 4, 5, 6, 7, 8, 9, 9}, the mode is 2, because there are three 2s, and only one of every other number, except the two 9s, but there are more 2s so it is the mode.
The median is the middle number in a set. It is a very common measurement for large sets of numbers. For example, if you want to know how much a preschool teacher makes, you google "preschool teacher salary", and it says "$27,130" and you think:
"Really? That is very low, considering how important preschool is. Why do they make half as much as every other kind of teacher?" (The reason is that they are not unionized like other teachers, and almost all preschools are private, and private schools pay less because their money comes from tuition, and private schools would have to charge unaffordable amounts to have as much money as private schools).
Then you think some more and you are like "So... do they all make exactly $27,130? Is there some sort of law? That seems weirdly specific..."
And the answer there is "No, that would be weird." $27,130 is the median salary, which means if you take every preschool teacher, and line them up by salary - least-paid on the left, highest-paid on the right, the one in the MIDDLE would make $27,130.
The mean of a set of numbers is the sum of the numbers, divided by how many numbers there are. Examples here if you need them. It's usually a lot like the median, but sometimes, if the numbers are clumped together in bunches, the mean shows that, but the mode doesn't.
Your homework:
Finish the mean median and mode and range practice from class.
You know what? Why should I force you to do something? I don't know if you get this or not, or what parts you need practice on and what parts you totally get. Maybe you:
- Want to practice it just to make sure you get it?
- Totally need help adding and dividing before you can start running around finding means?
- You understand all this and are frankly a little insulted I would think you didn't know this?
- Try reading this discussion on the mean vs median age of the world
- Not deep enough? First off, wow, second, give this a shot!
Do you have to do all? DEFINITELY NOT! Do you have to do some? Well, I don't want to waste your time, but I am pretty confident that one of those is the right thing for you. So give it a shot.
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