Statistics and Core Maths
Have you ever asked yourself (or your teacher) the age old question... When will I use Maths?
These two courses are designed to help you answer that question! We look at how Mathematics and Statistics are used in all sorts of scenarios in the real world.
Core Maths focuses on topics like: Personal Finance, Estimation, Critical Analysis, and Statistics. It can help you answer questions like: How do I calculate how much tax I will have to pay? Which bank is best to borrow or invest with? How much will I have to repay each year on my student loans? Is the data in this article unbiased? How can I estimate this? How confident are we that this particular estimate is correct? Is there a relationship between these two events?
A Level Statistics focuses on topics like: Probability, Hypothesis Testing, Statistical Diagrams, and much more. It can help you answer questions like: How can we determine whether this new vaccine is more effective than a previous one? What's the probability that we convict an innocent person... or let a guilty person go free? What conclusions can we draw from this data and how confident are we in them?
Have you ever read a news article or watched a news report and wondered how accurate it was? Have you ever seen a number or percentage being quoted and questioned its reliability?
A key skill in both Core Maths and Statistics is the ability to critically analyse and discuss real-world news articles which quote statistics and use statistical diagrams.
To give you a sense of what that might look like, watch the two short clips below, then check out this article from The Guardian which outlines how to spot when Statistics is being misused in the media. Then have a look at The New York Times articles below to see how Maths and Statistics are being used in the fight against Coronavirus!
David Spiegelhalter is the Winton Professor of the Public Understanding of Risk at the University of Cambridge and president elect of the Royal Statistical Society. Check out his other articles (including several about the Statistics of Coronavirus) on The Guardian here: https://www.theguardian.com/profile/david-spiegelhalter
TASK: Look at the graphs in these articles below and try to answer the critical analysis questions posed in the article. Explore the solutions offered at the end of each article.
Interested in the Personal Finance aspect of Core Maths? Did you know that more than two thirds of 18-24 year olds have some form of debt in the UK?
Watch this clip below to find out more!
Interested in the Estimation aspect of Core Maths? Have you ever tried to guess how many pieces of candy there are in a jar? Or tackled a mindbender like: “How many piano tuners are there in Chicago?”
Physicist Enrico Fermi was very good at problems like these -- learn how he used the power of 10 to make amazingly fast estimations of big numbers. Watch this clip from TEDEd below to find out more!
Interested in the probability of convicting an innocent person or letting a guilty person go free in Statistics?
This concept is known as the probability of committing Type I and Type II errors.
Type I errors are also known as "false positives" and would describe the conviction of an innocent person.
Type II errors are also known as "false negatives" and would describe the situation where a guilty person is found innocent.
Have you ever wondered why airlines sometimes overbook their flights? Did you know that Statistics plays a huge role in this?
Check out the video clip from TEDEd about how airlines use a Statistical Distribution called the Binomial Distribution to determine whether they should overbook their flights. Learn how they calculate the optimal amount of seats to overbook so that they maintain maximum profits. Then try the multiple choice quiz by clicking the THINK button to the right of the video to see if you understood the concept!
The Binomial Distribution is a key topic covered in A Level Statistics. It appears in lots of real - world scenarios.
Want to know more? Check out this article from Plus Maths Magazine: https://plus.maths.org/content/overbooking