# Statistics and Probability

### AIDS-HIV Statistics

Age: 13+ Time:30-40 minutes. Practice interpreting statistics and graphs, percentages and ratio and have a look at some real data about HIV and AIDS worldwide. Students are given eight pieces of information about eight different countries and asked to sort them in to a different group for each country. Statistics tell stories and [Show][Hide]
this exercise is designed to help students learn about some of the stories related to HIV and AIDS over the last 50 years and up to present day. The real activity here is the reasoning that students will have to use to match up the different data cards. They will have to read and interpret carefully and use logical deduction to put the groups together. In doing so they will naturally discover some of the patterns in the data that reveal the impact HIV and AIDS has had in different places around the world.

### Interpreting World Statistics

Age: 14+ Time:1 hr. This activity is about using statistics and graphs from Gapminder World to answer key questions about history. Using real and relevant data, students are asked to interpret it by matching patterns in the data to historical events. This stands alone, but was made as part of a cross-curricular project. [Show][Hide]

The project centred around asking if World War 2 was a crucial period of development for the world and did we emerge a more sophisticated society as a result of it, in spite of it, or not at all? Students start by matching these 15 scattergraphs with the 15 countries given.

### Comparing Data Distributions

Age: 14+ Time:1-2 hrs. Use this fun, fictional set of results on a number of levels! Processing data, calculating averages, quartiles, ranges and more. Most importantly this resource is great for comparing distributions. The data is full of surprises and two sets might have some things in common and other things really quite different!

### Grime Dice

Age: 14+ Time:1-2 hrs. This activity is based around a set of transitive dice (invented by James Grime) which have a rather surprising set of properties. They are NOT the classic 6-faced dice with numbers one through six on each face - they are far more interesting! Played against each other, rather like paper, rock scissors, there is no dominant dice (red dice beats blue dice, blue beats green yet green beats red).  [Show][Hide]

Students find them fascinating to play with (you will not reveal this fact beforehand) and this provides the motivation to analyse the probabilities behind them. You will easily be able to transform a set of normal dice into transitive dice or you may wish to make use of a digital simulation provided. Students are free to solve the problems with whatever probability techniques they have built up, although knowledge of possibility spaces and/or tree diagrams would certainly be helpful.  Full solutions for the teacher as well as instructions how best to exploit the dice are provided.

### Olympic Circles

Age: 14+ Time: 2-3 hrs. Making infographics based on the Olympic Circles emblem. Combining statistics with areas of circles, this activity involves students thinking about relevant statistics to compare the 5 competing Olympic continents. Students process the data and represent it with different circles to make some brilliant infographics.

### Double Spinner

Age: 12+ Time: 1 - 2 hrs. This is another practical probability experiment.  Students compare the theoretical outcomes of two spinners with that of an experiment (some exposure to sample spaces would be helpful).  The teacher can facilitate the sharing of results with a ready prepared spreadsheet. In this activity, students are encouraged to create and program their own digital spinner using Scratch  [Show][Hide]

, a simple piece of programming software which can now be used online without any download.Whilst the activity can be completed using a ready made set of spinners, teachers are strongly encouraged to give students access to this software to give them a flavour of programming.  A partly made scratch file is provided to help.

### Minesweeper

Age: 11+ Time: 1 hour. Minesweeper is an excellent game to encourage students to play. In this activity, students follow up a few games that they could play online with some questions about probability and logical deduction.  They are required to think critically about the information they are given and make judgements about the next move by considering the probabilities of revealing mines.

### The Great Elf Game

Have some great seasonal fun with this probability game. Students play with their understanding of chance, arithmetic, percentages, spreadsheets and business sense in an attempt to be the most successful Christmas tree seller on the block. Lotteries, strikes, income tax and all kinds of risk come in to play. Lots of fun and plenty of thinking. Age: 10+ Time: 1 hour.

### Number Ones

Age: 12+ Time: 1 - 5 hrs. This is a database of UK number one singles since the charts were started. It comes with a number of activities as suggestions for working with averages, bar charts, pie charts, grouped data, cumulative frequency and scattegraphs. Activities can be used in isolation or the whole things can be used for a larger statistical project.

### Wisdom of the crowd

Anyone can take part! Ask 100 people to guess the number of sweets in a jar and then average their answers. How close will it be? This is an experiment to try and collect lots of data from all around the world to test this theory out. The real jars are touring, but you can take part with videos and photos here. Access the live data and use it for teaching statistics at lots of different levels.

### Probability Trees

Age: 14+ Time: 2-3 hours. This activity is about bridging the gap between the intuition of sample space diagrams and the efficiency of tree diagrams. Students will look at a problem from the two points of view, play with multiplying and adding fractions and hopefully see how tree diagrams are a more efficient way of doing the same thing! The activity is good for group work and physical manipulation, although it could be [Show][Hide]

completed on computers by individuals if required. It may well take 2 to 3 hours to complete all of the tasks, but at the end, the hope is that students have a strong understanding of how tree diagrams work that they can apply to different problems.

### Guess My Colour

When we play games of chance we get a more intuitive feel for probability of events happening.  This activity is the first of a series of three probability experiments to carry out before students have considered theoretical probability.  This one gets students to guess the contents of an envelope by randomly drawing from it.  Students love the guessing games! Age: 10+ Time: 30-40 mins.[Show][Hide]

Roll ‘em – A practical probability experiment with dice.  Roll a dice then create lots of trials using Excel.  This is the second in the series of three experimental probability experiments.  In a Spin – A practical probability experiment with an online virtual spinner.  This is the third in the series of three experimental probability experiments.

### Roll 'em

Roll, roll, roll… This carefully structured activity aims to get students to discover that experimental probability approaches theoretical probability as we increase the number of trials.  We often overlook the importance of carrying out games of chance to build up an intuition for probability.  In this case we roll a dice then use a lifelike simulator on Excel to produce up to 2000 rolls. Age: 11+ Time: 1h.[Show][Hide]

This is the second in a series of three probability experiments. Guess My Colour – A practical probability experiment with coloured cubes.  This is the first in the series of three experimental probability experiments.  In a Spin – A practical probability experiment with an online virtual spinner.  This is the third in the series of three experimental probability experiments.

### In a Spin

This is the third in a series of three practical probability experiments.  The aim of this activity is to show that the more times you carry out an experiment, the closer the experimental probability approaches theory.  Students will use a free online virtual manipulative to be able to carry out a spinner experiment hundreds of times and make the important discovery. Age: 11+ Time: 1h.[Show][Hide]

Guess My Colour – A practical probability experiment with coloured cubes.  This is the first in the series of three experimental probability experiments. Roll ‘em – A practical probability experiment with dice.  Roll a dice then create lots of trials using Excel.  This is the second on the series of three experimental probability experiments.

### Scattertastic

This activity makes use of two excellent virtual mainpulatives that are freely available on the web. The activity helps students to begin understanding the concepts of correlation, lines of best fit and degress of correlation through the use of these manipulatives. Age:  13+   Time: 30 mins - 1h

### Sprinter or Endurance Runner?

This activity gives an insight into how statistics are used by Sports Institutes to select talented youngsters and decide which sport/event they are best suited to. A video demonstrates how to use football player's statistics to draw a stem and leaf diagram in Excel. Students then use data from the IAAF to analyse the heights and weights of sprinters versus endurance runners. Age: 12+   Time: 1h

### Dynamic Scatter Graphs

Statistics can be an emotive subject when the data is real and meaningful.  This activity explores dynamic scatter graphs to search for relationships between fertility and life expectancy, HIV rate and income, amongst others. Students will need computers with internet access to use the wonderful gapminder.org website.  Age:  13+   Time: 1h

### Mistigri

There are so many games of chance that catch out our intuition.  Consider the next possible moves when two players approach the end of this card game where the goal is to make pairs and not be left with the odd one out (Mistigri, the cat).  The aim is to work out the probability of not losing and, since the outcome depends on what the previous player has just done, it practises conditional probability.  Age:  15+   Time: 45min

### Predict the Future

This activity explores time-series data and shows how calculating and plotting moving averages can help to iron out fluctuations and spot trends.  Students will critically analyse temperatures since the mid 19th century to investigate global warming and the effect of wars on life expectancy. Age:  13+   Time: 1h