Statistics are everywhere. These videos will help your kids make practical decisions with data. Specifically you kids will learn about how to calculate an average, interpret charts, visualize data, and other practical skills everyone should know. We thank Crash Course for creating the videos below. We selected our favorite videos and provide summaries.
One thing about statistics, is that they can be found everywhere. From your household to your job statistics help us with all of our daily decisions. Statistics helps us find the simple things inside confusing, entangled, and complex webs of data.
A woman once claimed that tea with milk added first tasted different than tea with it added last. People tested the idea by testing the woman with eight different cups of tea in various patterns. But even after seeing the results of the test, it would still be unclear whether or not she could actually tell. She would get half of them right just by guessing randomly. And even if she could tell, she might miss a couple. It turns out that the woman guessed all of them correctly. But, if she didn’t, where would we draw the line to tell us if this woman really could tell or not?
There are two ways of looking at statistics. First, the Field of Statistics, is the study and practice of getting data and interpreting it. So if you are looking at data and understanding it, congrats! You're using the Field of Statistics! And second, Statistics, is facts or summaries of large amounts of data. You can't really use the Field of Statistics without your data sizable to actually able to comprehend!
In order to find what you want to figure out about things, you’ll have to know if your question can even be solved with statistics. And even though statistics can help us get closer to our answer, it can’t do everything for us. We also need to interpret the data and try to see what it means.
Also, your data may be wrong. If you are asking a question that people's true answers may be kind of embarrassing or dampen their pride, they may not answer truthfully. People may also not understand the question, or maybe none of the answers relate to them. An example is asking how much people exercise, some people may not want to admit that they don't exercise that often. Also a confusing question is probably not going to give you the answers you want. Luckily, this can be fixed by rewriting your question to make it easier to understand.
Sometimes to get closer to our answer, we have to answer something called a proxy. A proxy is something related to what we are trying to figure out, but not exactly.
There are many, many components to finding out something with statistics. There are two different ways: descriptive and inferential statistics.
Descriptive statistics describe what data shows. Takes massive amounts of data and compresses it into a summary so we can actually compute what the data is showing. If there are 100 pages of data, you're probably not going to be able to understand it. Descriptive data uses different strategies to help us compute the data.
Inferential statistics allow us to make conclusions that stretch beyond the actual data that is given to us. It allows us to test an idea or hypothesis by using a spoonful of the large amount of data we have. Like when surveying something with an age component, you aren’t going to survey everyone, you are going to only survey a handful of people with lots of different ages.
Statistics is math. And sometimes we have troubles understanding data, because of the really, really big and small numbers that pop up. We need to visualize numbers, but when I give you the number 456,376,893,054, can you really visualize it?
In order to understand statistics, you’ll have to understand numeracy. Numeracy is having the ability to understand and work with numbers. You probably understand literacy judging that you are reading this, so you can understand what I am saying. Statisticians probably understand numeracy, so they can understand data.
Mathematical thinking can help us see and make decisions by looking at data, and all the different aspects of the data. An aspect is a certain part of something. Like when looking at a house to buy, some people may look at certain aspects of the house that are more important.
So, back to the point. When trying to comprehend big numbers, it is helpful to put it in context with something else and then to simplify it. Like instead of looking at how much debt there is in the U.S. we can see how much debt on average per person. Another tip is to put it into a different measurement. For example, instead of using feet to measure everything, why not put it into miles? This can also go vice-versa and instead of a small fraction of a mile, you can put things into feet. Or you can use different reference points. Like 100,000 words is usually around 400 pages.
There is a law called the Law of Truly Large Numbers that states unlikely things are completely likely to happen just because of the immense amount of whatever. The likelihood of you getting jumped on by a skydiver is pretty low, but since there are so many people in the world, these things are likely to happen, just not extremely likely for any given person.
Statistics can also help us to know what we should actually worry about. Often times people are worried about the wrong things and not really looking at the data and seeing the actual probability of something happening. There are plenty of ways people can die. But looking at the actual numbers can help us see that the chance of it being us, is not that big.
Thinking mathematically isn’t just understanding numbers better, it’s also letting the numbers given to us help us answer our questions. Mathematics can help you see the wider and bigger risks in the world, which is why statistics is so important.
In statistics there are three things that help us look at the big picture and doesn’t focus on the individual parts of things. These three things are only slightly affected by the small details. They are the mean, median, and mode.
First, what is the mean? The mean is the same thing as an average. And an average is what we can expect from a group when looking at everything. The mathematical definition is something that takes the sum of all the numbers in a data set and divides them by the number of data points. For example, if I was trying to find the average of these numbers... 2, 3, 5, 6, 9. I would first add them all together, (because they are the data sets) to get 25. Then I would divide 25 by 5 (because that is the amount of data points.) After I do that, I would know that the average is 5.
The mean (or average) tells us something about the data as a whole, but doesn’t tell us anything about the individual aspects of the data. Sometimes the average can be misleading because certain individual aspects are ignored.
There is something called an outlier which is a data point far off from where most of everything is located. These outliers are often ignored when calculating the mean of some data.
Normal, is when the most common number in a chunk of data shows up around the middle. A distribution shows us how often each value shows up inside of a data set.
The median is the middle number when we lined up our data from least to greatest. If there are multiple medians, usually we take the mean of the two numbers in the middle and say that it is our median. For example, the numbers 1, 2, 3, 4, 5 the median would be 3. But if we had the numbers 1, 2, 3, 4, 5, 6 we would get the mean of 3 and 4 (3 + 4 = x and then x / 2.) After that, we would know that the median is 3.5.
The mode is the most popular value, or the one that shows up the most. Bimodal data is an example of “multimodal” data which has multiple values that are common. If we were to get ratings on a book and 19 people gave 5 stars, 3 people 4 stars, 2 people 3 stars, 0 people 2 stars, and 1 people 1 star. The mode would be 5 stars since it had the most people give it that rating. But if a lot of people gave it a 4 star rating and a 2 star rating it would be bimodal and have 4 and 2 be its modes.
The mode is most useful when you have a large sample so the most popular values will be very large.
When the mode and the median are not the same that means that your data set is skewed. Another way of explaining it is saying that if something is skewed, it means there is an unusually high amount of something on one side of the distribution.
In a skewed distribution, most likely, the mode, median and mean would be positioned somewhat similarly to this one.
We should always remember that statistics can help us make decisions, but we also need to use our common sense to look at other aspects that data can't give us.