Statistics Fundamentals

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.

Riddles on Averages


The mean (or average) of a set of numbers is:

the sum of the numbershow many numbers are in the set \frac{\text{the sum of the numbers}}{\text{how many numbers are in the set}}

For example, the mean of the numbers 3,5,3, 5, and 1010 is:

3+5+103=183=6 \frac{3+5+10}3 = \frac{18}3 = 6

In the visualization below, the purple dot above the line automatically shows the mean of a,a, b,b, c,c, and d.d.

What is the mean of 5,11,19,215, 11, 19, 21?
Hint: use the sliders above for some help!

Riddles on Averages


If the mean of aa and bb is 1010 and the mean of cc and dd is 20,20, does the mean of a,b,c,a, b, c, and dd have to be 15?15?

Riddles on Averages


If a<b<c<d a < b < c < d, is it possible for the mean of the four numbers to be between aa and b?b?

Hint: what if aa is extremely small, and all other values are large?

Riddles on Averages


What is the average of all integers from 11 to 100,100, inclusive?

{1,2,3,,98,99,100}\left \{ 1, 2, 3, \ldots , 98, 99, 100 \right \}

Riddles on Averages


Let's say that in the past decade:

  • 100100 countries in the world have had their energy consumption increase by 8%8\% per country.
  • 100100 countries in the world have had their energy consumption decrease by 10%10\% per country.

The International Energy Association is interested in the percent change across all 200200 countries. Is it accurate to say that energy consumption decreased by 8+(10)2=1%\left | \frac{8 + (-10)}{2} \right | =1\% per country?

Riddles on Averages


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.

Riddles on Averages


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