Welcome to **statistics**! Statistics is a tool for quantifying information and can reveal patterns and truth about the world in surprising ways. To get you warmed up, this quiz has some puzzles on the most common of statistical measures: that of mean, or average.

The **mean** or **average** of a set of numbers is
\[ \frac{\text{the sum of the numbers}}{\text{how many numbers are in the set}} .\]
For example, the mean of the numbers 3, 5, and 10 is \( \frac{3+5+10}3 = \frac{18}3 = 6 .\)

The visualization below will automatically show the mean (as the dot above the number line) given four numbers \(a,\) \(b,\) \(c,\) and \(d.\) For example, what is the mean of \[ 5, 11, 19, 21 ?\]

**must** it be the case that the mean of \(a, b, c,\) and \(d\) together is 15?

According to World Bank data, if you take the percentage of energy consumption that is renewable energy between the years 1990 and 2015,

- Of 100 countries that had their percentage of use go up, there was an average increase of
**7.6%**per country; - Of 100 countries that had their percentage of use go down, there was an average decrease of
**11.5%**per country.

If we look at the percentage of renewable energy use across the world (using just the countries from the data above), is it appropriate to conclude the average change is \( \frac{7.6 + (-11.5)}{2} = -1.95 \) percent?

In reality, world renewable energy use **increased** from roughly 17% to 18%, although it should be noted there is volatility in the data:

As the previous question illustrates, statistics can be deceptive when presented in a particular way. One of the themes of this introduction (and this course) will be grappling with the issue and bolstering your ability to spot bad statistics.

First, though, let's look at something very important: the difference between statistics and probability.

×

Problem Loading...

Note Loading...

Set Loading...