Learning About Probability and Statistics

This chapter is about two things.
One is called statistics.
Statistics means looking at facts and numbers.
The other is called probability.
Probability means how likely something is to happen.

Kids will collect information.
This is called data.
They will make pictures of the data.
These pictures are called plots and graphs.
Kids will look at the middle of a group of numbers.
They will look at how spread out the numbers are.
Kids will also guess chances of things happening.
Some things happen together.
These are called compound events.
Kids will use lists, tables, and tree pictures to study them.

A Story About Statistics

A long time ago, there was a war.
It was called the Crimean War.
A nurse named Florence Nightingale worked there.
She saw many soldiers dying in the hospital.
They were not dying from their hurts.
They were dying from something else.

Florence thought the hospitals were not clean.
She collected data from clean hospitals.
She collected data from dirty hospitals.
She wanted to find a fix.

She found one big answer.
Doctors should wash their hands!
She told the leaders. They did not listen fast.
So she told the Queen instead.
She made a new kind of picture called a bar graph.
It showed the Queen why hand-washing mattered.
The Queen said, "Doctors must wash their hands!"
This helped start the study of statistics.
It also helped start modern medicine.

A Story About Probability

Probability comes from games of chance.
Long ago, gamblers made up rules for games.
Some rules were right. Some were wrong.

A man named Chevalier de Méré played a dice game.
His rule did not work.
He asked a mathematician named Blaise Pascal for help.
Pascal talked with another mathematician, Pierre Fermat.
Together, they figured out how probability works.
Today, this helps us understand many things.
It helps with living things and with money too.

What Kids Will Learn

Part 1: Probability Basics
Kids will use dice and cards.
They will find probability as fractions and decimals.
Some probabilities are hard to know for sure.
Kids can guess them by trying many times.
This is called the Law of Large Numbers.
Kids will toss a chocolate kiss candy many times.
They will count how often it lands on its bottom.

Part 2: Gathering Samples
Kids will learn about samples.
A sample is a small part of a big group.
The big group is called a population.
Populations are often too big to study fully.
So, we study a sample instead.
Then we guess about the whole population.
The sample must be picked in a fair, random way.
Kids will collect samples, make plots, and do math with them.

Part 3: Comparing Groups
Kids will compare two or more populations.
They will look at their plots side by side.
They will compare the middle and the spread of each group.

Is It a Fair Game?

A game has players.
It has a playing space, called a tableau.
It has moves and outcomes.
It has a rule to pick the winner.

A game is fair if every outcome has the same chance.

Example: The Spinner Game
Two players each spin a spinner.
Numbers 0 to 9 are split between the spinners.
The higher number wins.

Is this fair?
If one spinner has 0,1,2,3,4 and the other has 5,6,7,8,9,
the second player always wins.
That is not fair!

What if one spinner has all odd numbers?
The other has all even numbers?
There are 25 possible outcomes.
25 cannot split evenly into two equal groups.
So this is still not fair.

What if one spinner has {0,2,4,6,8,10}?
The other has {1,3,5,7,9}?
There are 30 possible outcomes.
Each player wins 15 times.
This game IS fair!

Another Game: Four Spinners
There are four spinners: Red, Blue, Green, Yellow.
Each has three numbers on it.

Player A picks a spinner first.
Player B picks a spinner next.
The higher number wins.

If Player A picks Blue and Player B picks Yellow,
Player A wins more often.
This game is not fair.

But there is a trick!
Player B can always win more.
Player B should pick the spinner that comes right after
the one Player A picked.
If A picks Yellow, B should pick Red.
Then B has the better chance to win.