Welcome to statistics! Statistics is a tool for quantifying information. It can help you better understand randomness and uncertainty in the world.
To warm up, let's look at some puzzles about means, one of the most common statistical measures.
The mean (or average) of a set of numbers is:
For example, the mean of the numbers 3, 5, and 10 is:
In the visualization below, the purple dot above the line automatically shows the mean of and
What is the mean of ?
Hint: use the sliders above for some help!
If the mean of and is 10 and the mean of and is 20, does the mean of and have to be 15?
If , is it possible for the mean of the four numbers to be between and
Hint: what if is extremely small, and all other values are large?
What is the average of all integers from 1 to 100, inclusive?
Let's say that in the past decade:
- 100 countries in the world have had their energy consumption increase by 8% per country.
- 100 countries in the world have had their energy consumption decrease by -10% per country.
The International Energy Association is interested in the percent change across all 200 countries. Is it accurate to say that energy consumption decreased by % per country?
As the previous question illustrates, statistics can be deceptive when presented in a particular way. One of the themes of this course will be grappling with this issue and bolstering your ability to spot bad statistics.
First, though, let's look at something very important: the difference between statistics and probability.