Statistics and Probability
Statistics and probability are the mathematical tools that help us organise information and make our minds up about what we think is likely to happen. Imagine trying to understand the world without this language of data and chance, without likelihoods of rain, survey analyses, and no idea how feasible it is to win a game.
Needless to say, the ideas of statistics and probability are everywhere in real life, whether you are reading the news, watching sport, or analysing results from a survey. Here we will cover recognising patterns in data, calculating averages, creating and interpreting graphs, and understanding how likely events are to occur in given situations.
What are statistics?
Statistics as a topic is all about data. When we collect numbers, like heights of a group of people, scores in a test, or temperatures over a week, we need sensible ways to summarise and understand them. There are tools and techniques that help with this.
At the heart of statistics are measures of the average and spread of a set of numbers:
- The mean is the ‘typical’ average – found by adding all the numbers in a set and dividing by how many there are.
- The median is the middle value when the numbers in a set are ordered from smallest to biggest. If there is an even number of numbers and therefore no middle number, the mean of the two middle numbers is taken.
- The mode is the number that appears the largest number of times in the set. If two numbers appear in the same frequency, both are ‘modes’ of the set.
- The range shows how far apart the lowest and highest values are.
Statisticians also use charts and graphs to make sense of data visually. Bar charts, pie charts, and scatter graphs all show correlations and trends that numbers alone might hide. You might use a histogram or a cumulative frequency graph to explore data that is grouped into ranges, helping you spot patterns or unusual values.
What is probability?
Branded ‘the mathematics of chance’, probability helps us answer questions like: ‘what are the chances of rolling a six?’ or ‘what is the probability of picking a red marble from a bag?’
Probability is always a number between 0 and 1 – where 0 is ‘impossible’ and 1 is ‘certain’.
Probability can be expressed as fractions, decimals, and percentages, and you can use simple formulae and diagrams to organise and demonstrate your thinking, primarily for the benefit of your examiners. The probability of an event is found by looking at all the possible outcomes and seeing how many of these are what you want.
For example, rolling an even number on a fair dice has three successful results (2, 4, 6) out of six possible outcomes, so the probability is 0.5 (or 1/2).
You will also learn to use sample space diagrams and tree diagrams. These help you organise all the outcomes of one or more events — especially when things get a bit more complex, like when you’re considering two coin tosses or picking two cards.
Bringing data and chance together
Statistics and probability often feel like two parts of a bigger, and more interesting, story: you collect data, summarise it, and then think about how likely different results are. You might look at surveys and decide whether a result was surprising, or you might use probability to make predictions based on patterns in data.
It’s also important to think about how data is collected. A sample that isn’t chosen carefully might give a misleading picture of the whole population. This is where ideas like bias and sampling methods become important in interpreting results reasonably.
Why this is useful
Learning statistics and probability is not just about getting through your exams – it is about building a foundation upon which to make sense of the world. When you see a graph in the news, you’ll be able to read it properly. When someone talks about chances, like in sport or weather forecasts, you’ll know what they mean. These ideas are arguably the most important aspect of in training you to think logically and to back up claims with evidence.
Getting comfortable with practice
Like learning to ride a bike, getting good at statistics and probability, or any other part of maths, takes practice. In lessons you’re likely to spend time working with real data, sketching your own graphs, and trying problems that make you think about outcomes and chance. The more you see these ideas in action, the more natural they will feel on exam day.
By building an understanding of working with data and chance, you’re cultivating a powerful skill for life beyond the classroom, and setting yourself up for an incredibly broad range of career opportunities.