## GCSE Statistics and Probability

GCSE Statistics and Probability refers to the **collection of data** and interpreting this data in different forms using tables, charts, graphs and diagrams.

To revise this topic successfully, there are a number of areas you need to cover including **sampling, averages,** calculating the standard deviation as well as representing and analysing data in various ways. GoConqr can help you create, share and discover Mind Maps, Flashcards, Quizzes and more to help you study this topic. Start practicing exam papers to help you get the grade you want.

Keep reading below to find some useful study resources to improve your revision of GCSE Statistics and Probability

## Averages & Standard Deviation

There are 3 main types of average:

**Mean:**Adding a group of numbers and diving by the number of numbers**Mode:**The number in a set of numbers which occurs most often**Median:**The number in the middle of a group of numbers

One of our GoConqr members in our Maths Chat group shared this handy rhyme to remember these:

*“Hey diddle diddle, the median’s the middle, You add then divide for the mean.*

*The mode is the one that you see the most, And the range is the difference between.”*

You should also be able to calculate the average from grouped data and the range which is the highest number minus the smallest.

Standard deviation measures how spread out the numbers are. It is the square root of variance. Variance is calculated this way:

- Work out the Mean (the simple average of the numbers)
- Then for each number: subtract the Mean and square the result (the
*squared difference*). - Then work out the average of those squared differences.

## Sampling Data

Sampling simply refers to selecting a sample from a population to **test a hypothesis**. It would be impossible to test an entire population, instead a representative sample should be chosen and tested.

There are several methods of sampling, including **random and stratified samples**. Random sampling means that members of a population have equal chances of being selected. Stratified sampling is a more complex than this as a population is divided into different groups before being selected, so that you make sure certain populations are represented, which might not happen if you sampled at random. So instead of taking 60 people at random from a school with 4 grade levels, you would select 15 from each grade.

## Representing Data

There are multiple ways which data can be displayed for GCSE Statistics and Probability, here are some examples:

- Histograms
- Stem and Leaf Diagrams
- Bar and Pie Charts
- Box and Whisker Plots
- Scatter and Cumulative Frequency Graphs

As part of this section of your GCSE Maths revision, you need to be able to plot and interpret data in this way.

## Probability

Probability is the **likelihood of an event happening**. In GCSE Maths, you are required to calculate how likely an event occurs. Simple probability estimations such as the chance of a coin landing heads up can be calculated by dividing the ways an outcome can happen by the total number of possible outcomes.

As with all topics in GCSE Maths, it’s best to **get the basics right** before moving on. Exam questions can be tricky so understanding how probability works at its core will help you breakdown any problem you will face.

## Tree Diagrams

Probability Trees help you devise the chance of two or more events occurring by using a **visual representation** of the data. Each branch in a tree diagram represents a possible outcome.

Calculating probabilities can get quite complex so this type of** table simplifies the process**. It’s used when two events are independent of each other, meaning that the outcome of one does not affect the outcome of the other. Drawing the tree out **in your maths exam** is a good way to show your reasoning and get some marks even if you don’t fully work out the solution.

## The AND and OR Rules

As mentioned above, when two events are independent, the outcome of each does not have an effect on the other. However, when two events are mutually exclusive, they cannot happen at the same time. This is where the **AND** and **OR** rules come in.

When two events, A and B, are **independent**, we use the formula *P(A and B) = P(A) x P(B)*. We use this when the questions ask for the probability of A and B occurring. When two events are **mutually exclusive**, we use *P(A or B) = P(A) + P(B)*. This means that it isn’t possible for two events to occur.

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