# Statistics and Probability (Mathematics Curriculum)

# Statistics

## What Is Statistics?

Statistics is a branch of mathematics that collects, organizes, presents, analyzes and interprets data.

Imagine a teacher wanted to know how well their mathematics class were doing.

They might collect statistics on the scores the class get on a test, where the test is out of 10. That is, they could count how many of the class got 10, how many got 9, how many got 8 etc.

They might want to present this information in an easily understood way, such as in a table or graph.

They might then be interested in finding the typical, or average, score that a student got in that class.

These are all examples of statistics.

### Dictionary Definition

The Merriam-Webster dictionary defines statistics as " a branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data."

## Where Does the Word Statistics Come From?

Statistics comes from the German word 'Statistik' meaning "of the state" (as in country).

Statistics was first used to collect information useful for a government of a country, such as how many people there were of different sexes and ages, what their incomes were etc. This information would have been useful to raise taxes and armies.

## Data

Data is information that has been collected or measured.

In this mini-curriculum, you will learn about data and its different types.

## Averages

An average is a single value that summarises or represents a set of numbers that are different to each other.

In this mini-curriculum, you will learn about the different types of averages and how to find them.

## Measures of Spread

If the average gives us a typical number from a set of numbers, measures of spread tell us how much the numbers are spread out from each other.

Are they all bunched up close together (like 2, 3, 3, 3, 4)?

Or are they very spread out (like 2, 30, 300, 3000, 4 million)?

In this mini-curriculum, you will learn about different measures of spread.

## Frequency Tables

Frequency tables are a way of showing data. It lets us see how often a number appears in a set of numbers.

In this mini-curriculum, you will learn about frequency tables and how to find averages and the range from them.

## Cumulative Frequency Tables

Cumulative frequency tables are frequency tables that keep a running total of the frequencies.

In this mini-curriculum, you will learn about cumulative frequency tables.

## Grouped Frequency Tables

Grouped frequency tables are frequency tables where the numbers are grouped together.

In this mini-curriculum, you will learn about grouped frequency tables.

## Cumulative Grouped Frequency Tables

Cumulative grouped frequency tables are grouped frequency tables that keep a running total of the frequencies.

In this mini-curriculum, you will learn about cumulative grouped frequency tables.

## Bar Charts

Bar charts are a way of presenting data. The height of each bar shows how often each value appears in the data.

In this mini-curriculum, you will learn about bar charts.