The answer is D. Charles Babbage was a founder member in 1834 of the then Statistical Society of London. Harold Wilson was not only a Royal Statistical Society member he was the Society’s president from 1972 to 1973. Florence Nightingale was the first woman to become a member – known as a Fellow – in 1858. She used statistical information and diagrams to illustrate her reports to MPs and civil servants on the causes of deaths in military hospitals in the Crimean War, helping change the approach to sanitary care.

The answer is B – 25 per cent. There are four possible outcomes from tossing a coin twice: tails followed by tails, tails followed by heads, heads followed by tails and heads followed by heads. Only one of these four is two heads, so the probability is 1 in 4 or 25 per cent. As the outcome of tossing a coin is independent of any previous toss there is a simple rule we can use mathematically: we multiply the probability of the first toss coming up heads by the probability of the second toss coming up heads. That is ½ times ½ which equals ¼ or 25 per cent.

The answer is B – 1801. There has been a Census across the whole UK every ten years since, except for 1941 during the Second World War and 1921 in Northern Ireland. The Census provides an enormous amount of information that is used by government to decide how much to spend on services and how that might change. Census information is also widely used by the private sector to inform their business planning. The Census cost about £500 million – although a lot of money the information is used for 10 years and affects all 60 million plus people living in the UK. So that works out to less than £1 for each of us per year.

The answer is D – all of them. That’s because there are different types of average. Each is used in different circumstances but for the same reason – to help us summarise lots of figures in a single useful number. The average we’re most used to is the arithmetic mean where you add all the numbers up and divide by how many there are. So the total of our numbers is 5+500+1+4+1+3+200+1+5=720. There are 9 numbers so this particular average is 720 divided by 9 which equals 80. Another average is the median. We get this by putting all the numbers in ascending order. The middle one is the median. So in order our numbers are 1, 1, 1, 3, 4, 5, 5, 200, 500. The middle number is 4 and this is the median. For an even number of figures we would pick the two middle numbers and find their mean. Yet another type of average is the mode. This is the number that appears more often than any other. In our case there are more of the number 1 than any other so that is the mode of these figures.

The answer is C. That is a very big number. But the recent Census gave the population of the UK as about 62 million. So that means the spending is the equivalent to about £2,000 per person for the year. To get a real feel for a big number it can be important to see how much that works out, say, per person or per day.

The answer is B. The median is useful as a guide to average because of the way income distribution is skewed. Imagine you are in a room with ten people all earning about what you earn. Now imagine Bill Gates walks in. Your mean income goes through the roof – Bill Gates is extremely rich. But your median income – the middle value – would hardly change. In this circumstance the median would be seen as representing typical earnings better. Even with Bill Gates in the room, most people are not mega-rich.

The answer is B. So if 23 people – you and 22 others at your party – are in a room the chances are just over half that there will be two people who have the same birthday. By the time you’ve got 57 people in the room the probability is about 99 per cent! To work the figure out start with you in the room. For the next person to come in to NOT share your birthday theirs must be on one of the remaining 364 days (we’ll make things simple by ignoring leap years). That is they have a 364/365 probability of not sharing your birthday. For the next person to not share a birthday with either of you their birthday must be on one of the remaining 363 days. So the chances of three of you not sharing a birthday are 364/365 multiplied by 363/365. We keep letting people in till the multiplication 364/365 x 363/365 x 362/365 x 361/365 and so on comes to less than half. This means there is less than 50 per cent probability of there being no shared birthday – or in other words over 50 per cent probability of there being a shared birthday.