What's the use of statistics, data handling and probability?

Statistics is about gaining information from sets of data. Sometimes you want to represent a lot of complicated information from a large data set in a way that is easily understood. This is called descriptive statistics.

An example of this is the so-called worm plot used in cricket: over the cause of a cricket match there can be many hundreds of balls and runs. In the worm plot depicted below, England’s performance is described by the blue line, and the West Indies’ by the green line. You can see at a glance that, although there was variation in the run rate, England consistently scored at a higher rate than the West Indies, and so won the match.

Although some information has been lost - you don't know for instance from which balls in the overs runs were taken - this summary graph clearly displays all of the meaningful information. The human mind is very visual, and this is why graphics, such as graphs or pie charts, are very good for conveying statistical information.

The other branch of statistics is called inference statistics. This used to obtain information about a large set of data from a smaller sample. Think of opinion polls. Here, the statistician randomly selects a group of people, a thousand say, and asks them about their opinion, for example whether or not they like the current government. It is then assumed that the opinion of the sample reflects the opinions of people as a whole.

To be able to do statistics, you first have to learn how to collect, handle and represent data.

Probability theory

Statistics is intimately linked to probability theory. You can use statistics to work out the probability, the chance, that a certain event will occur: if you want to know the chance that your holiday plane will crash, you think of how many planes usually crash within a year. Since this number is very small, you deduce that the chance of your plane crashing is small also. You've done a very simple statistical analysis of the data concerning plane crashes and used it to work out a probability.

But things also work the other way around: you can use abstract probabilities to help you with your stats. Say for example you want to test whether a die that is used in a casino is fair. To do this, you throw the die a great number of times and record the outcomes. You then reason like this: if the die is fair, then each number should be equally likely. There are six numbers, so each number should come up in 1/6 of the cases. If this is the case, you decide that it is fair.

This example shows how the abstract theory of probability can help to evaluate real-life statistics. And this is why probability theory belongs to the basic tool set of a statistician.

So who, apart from opinion pollsters and professional gamblers, uses statistics? Here are a few examples:

Medicine

Stats and probability theory are absolutely essential in medicine as they are used to test new drugs and work out the chance that patients develop side effects from the drugs. Tests are performed on large groups of animals or people and stats is the tool needed to evaluate the tests. It's essential to get it right, for obvious reasons. Even doctors and nurses who don't perform the tests themselves need to be well-versed in stats to understand the results and advise their patients accurately.

Stats and probability theory are also used to assess the risk from things like tobacco and alcohol, and to see how a certain gene affects people. How likely is it that a person with that gene develops a certain illness or characteristic?
Medical research cannot do without statistics.

Social and natural sciences

On the face of it, sciences like psychology, sociology or biology do not seem to have much to do with maths or stats. But all of these have one thing in common: they are based on observations of the world around us. A psychologist might want to observe people with a certain mental illness, a biologist the behaviour of a virus, and a sociologist a possible link between criminality and drug abuse. To evaluate these observations, scientists need descriptive statistics. They need to know how to best collect data and how to represent them in a meaningful way. To interpret the data, they need inference statistics.

The financial world

A very important thing in the financial world is risk assessment: what is the probability, or risk, of a company going bankrupt, or the interest rates going up? What is the risk of investing in a company, or of taking on a mortgage? The insurance industry is based on the idea of risk: the chance of your house burning down is quite small, but if it does happen, you lose everything. The insurance company exactly balances the risk of fire with the cost of a fire. They decide what premium to charge you, so that they still make a profit even though they sometimes pay out huge amounts.

A good understanding of risk, and how it can be described using statistics and probability, is essential for anyone working in the financial world. Employers in this area often value mathematicians and statisticians just as highly as people with an economics background.

Politics

Politics is very much about strategy. How should an election campaign be fought? How should a government deal with other powers? How much money should the health service receive? To find a good strategy, politicians need to understand public opinion, know about the structure of society and assess risks. The government employs many statisticians to help them with this. They can conduct and evaluate a census, and work out the risk of there being an epidemic, or of the world economy plunging.

During the cold war, game theory, which is closely related to probability theory, was used to decide whether the US strategy - arming itself to the teeth to deter an attack from the USSR - was effective.

Reliability theory in manufacturing

When you produce a product, be it a car or a light bulb, you want to know how reliable it is. To find out, you take a sample of your light bulbs or cars and test them. Just as in an opinion poll, you can use statistical methods to gain information about the quality of your product from this sample. Reliability theory has become a very important branch within statistics.

Law

Statistics is often used in the courts. Say a DNA sample has been taken from a crime scene. What is the chance that a defendant matches this DNA even though he or she is innocent?

In fact, the use of statistics in court can be very tricky, because people are easily confused by it. A few years ago, a woman called Sally Clark was jailed for the murder of her two children. She said that they both died of cot death, but the jury was told by an "expert witness" that the probability of two children dying of cot death in the same family is extremely low, so they decided that she must have killed them. But this reasoning is flawed. This was recognised later and the woman was eventually released.

All of us

Everyday life is full of statistics that we need to understand. Politicians and commercial organisations use stats to convince us to vote for them or buy their products. We need stats to understand the risks involved in taking a certain medicine or making financial decisions. A basic grasp of statistics means that you don't have to rely on someone else to make up your mind about these things. You don’t need to be an expert — a little basic knowledge can go a long way in understanding the numbers you are bombarded with every day.