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- 4.1 Sampling.
- 4.2 Presentation of data.
- 4.3 Central tendency and dispersion.
- 4.4 Correlation.
- 4.10 Regression Line.

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Here are some related resources in alphabetical order. Some may only be appropriate for high-attaining learners while others will be useful for those in need of support. Click anywhere in the grey area to access the resource.

- Box Plots Video Box plots, sometimes called box and whisker diagrams, are a useful way of visualising data.
- Averages Video Revise how to calculate the mean, median, mode and range from lists and frequency tables.
- Averages Test your understanding of averages with this self marking quiz about mean, median and range.
- Histograms Practise drawing and reading information from histograms displaying grouped data
- Choose Your Average This is a game for two players. You should know how to find the mean, median and range of a set of numbers.
- Cartoon Scatter Graph Place the cartoon characters on the scatter graph according to their height and age.
- Correlation Arrange the given statements in groups to show the type of correlation they have.
- Reading Graphs and Charts Answer real-life problems from different types of graphs and charts including piece-wise linear graphs.
- Human Scatter Graphs Pupils move to positions in the room according to their data relative to the walls as axes.
- The Beauty of Data Visualization Complex data sets (like military spending, media buzz, Facebook updates) are turned into beautiful, simple diagrams.
- Cumulative Frequency Online exercises on cumulative frequency for discrete and grouped data with exam-style questions.
- Standard Deviation Find how 'spread out' data is by estimating and calculating this measure of dispersion.
- Box Plots An exercise on reading and drawing box-and-whisker diagrams which represent statistical data.

Here are some exam-style questions on this topic:

- "
*The number of visitors to a cycle track and the number of drinks sold by a café at the location are recorded in the table below.*" ... more - "
*The grouped frequency table gives information about the times, in minutes, that 90 commuters take to get home from work.*" ... more - "
*The table shows information about the heights of 85 stalagmites.*" ... more - "
*The scatter graph shows the maximum temperature (*" ... more^{o}C) and the number of bowls of soup sold at a sandwich shop on twelve randomly selected days last year. - "
*Kevin recorded the heights, in centimetres, of some cows.*" ... more - "
*155 people were asked how much money they would pay for particular three-course meal in a special restaurant.*" ... more - "
*Jimmy is ordering the t-shirts for the community choir which has 240 members.*" ... more - "
*The scatter graph gives information about the marks earned in a Statistic exam and a Mathematics exam by each of 13 students.*" ... more - "
*Here is some information about the length of time children spent in a swimming pool at a holiday resort during a heat wave.*" ... more - "
*The table shows the marks earned by 200 students taking a Maths exam.*" ... more - "
*The following table shows the time taken by fifty people to answer their emails one day.*" ... more - "
*The table shows the amount of time, in months, taken to sell houses on the Happyland housing estate.*" ... more - "
*This histogram shows information about the ages of 317 people attending a charity concert. The cost of tickets for children under 15 years of age are half price. If a full price ticket was £18, estimate the total income of all 317 ticket sales.*" ... more - "
*The following table shows the relationship between the number of workers and the amount of time in minutes it takes them to harvest the sugar cane in a particular field.*" ... more - "
*The distribution of daily average wind speed on an island over a period of 120 days is displayed on this box-and-whisker diagram.*" ... more - "
*The following grouped frequency table shows the length of time, \(t\), in minutes, visitors watched an octopus swimming around a tank at an aquarium.*" ... more - "
*Derek has put together a fantasy football squad and has recorded the heights of all the players in the squad rounded to the nearest centimetre. The data is illustrated in the following box and whisker diagram.*" ... more - "
*The charts below show the results of pupils in a Year Group answering twenty mental arithmetic questions.*" ... more - "
*Poppy Pringle recorded the heights in centimetres of the sunflowers growing in her brother's and sister's gardens.*" ... more - "
*The histogram gives information about the distribution of the heights of some shrubs grown by a garden supplier.*" ... more - "
*The following table shows the amount of diesel required by a train to travel certain distances.*" ... more - "
*The following table shows the mean weight in kilograms of members of a group of young children of various ages.*" ... more - "
*The following table contains data collected from an experiment.*" ... more - "
*The following table shows the number of days families spend in a particular seaside hotel in August last year.*" ... more - "
*The following table shows the average number of hours per night sleeping by seven men and their youngest child.*" ... more - "
*The following table shows the average weights for given heights in a population of men.*" ... more - "
*The Student Council in a large school conducted a survey to find out how many classes assigned homework for students to complete.*" ... more - "
*The times taken in seconds by a group of students to complete an online exercise are listed as follows.*" ... more - "
*As part of a conservation project, Darren was asked to measure the circumference of trees that were growing at different distances from a beach.**His results are shown in the following table.*" ... more - "
*The Farang Parkour Team hosted a Free Running event. The judges, Anan and Jason awarded 7 competitors a score out of 10. The scores are shown in the following table.*" ... more - "
*The personal trainer collected data from a randomly selected sample of days. From this he found that the number glasses of water he drank in a day had a mean of 4.35.*" ... more - "
*In a survey of insect life near a stream, a student collected data about the number of different insect species \((y)\) that were found at different distances \((x)\) in metres from the stream.*" ... more - "
*A pair of twins, Percy and Patsy, take Maths assessment tests each week. Their teacher records their scores in this table:*" ... more - "
*A TV company surveyed 88 of its employees to find out how much time they spend travelling to work on a given day. The results of the survey are shown in the following cumulative frequency diagram.*" ... more - "
*This cumulative frequency graph shows the speeds in kmh*" ... more^{-1}of cyclists passing a certain point on a race track. - "
*The table below shows the scores for 12 students on two Mathematic exam papers. For the first paper calculators were allowed and for the second paper they were not.*" ... more - "
*Gringe Hull Secondary School has students from Year 7 to Year 13. A group of 138 students in Year 9 were randomly selected and surveyed to find out how long it takes them to travel to school each morning. Their results are represented by the following cumulative frequency graph.*" ... more - "
*A data set has \(n\) items. The sum of the items is 650, the mean is 13 and the standard deviation is 5.*" ... more - "
*A number of organically-grown carrots were measured (in centimetres) and the results recorded. The following box and whisker diagram shows a summary of the results where L and U are the lower and upper quartiles respectively. The diagram is not drawn to scale.*" ... more

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

- Averages "Average" is a very general term that is used commonly in everyday English and most people have an idea what it means. Mathematicians like to be a little more precise however and have come up with a number of different ways of finding a measure of central tendency. Pupils at school should develop their understanding of averages so that they can more precisely communicate information to others and are not misled by statistics presented in a way to distort the facts. Pupils should understand and use the mean of discrete data. They should be able to compare two simple distributions using the range and one of the mode, median or mean. See also the topics called Data Handling and Statistics.
- Data Handling Data is talked about more this decade than ever before. Whether it be how social media companies deal with your personal data or how analysing data can improve algorithms for systems that make everyday life easier or more profitable. Pupils are first introduced to small, familiar data sets and learn to visualise them in many different ways. They may produce their own data from experiments, observations or games and will then describe their data in different ways. Pupils will calculate averages and other summary measures (mean, median, mode range) and produce bar charts, pie charts and box plots. Older pupils will use technology to help analyse larger data sets and will be introduced to inter-quartile range and standard deviation. They will draw conclusions from scatter diagrams, and have a basic understanding of correlation. They will learn how to apply statistical information to calculate probabilities. See also the topics called Statistics, Averages and Probability.
- Graphs This topic includes algebraic and statistical graphs including bar charts, line graphs, scatter graphs and pie charts. A graph is a diagram which represents a relationship between two or more sets of numbers or categories. The data items are shown as points positioned relative to axes indicating their values. Pupils are typically first introduced to simple bar charts and learn to interpret their meaning and to draw their own. More sophisticated statistical graphs are introduced as the pupil's mathematical understanding develops. Pupils also learn about coordinates as a pre-requisite for understanding algebraic graphs. They then progress to straight line graphs before learning to work with curves, gradients, intercepts, regions and, for older pupils, calculus.
- Live Data One of the big differences between Maths from a textbook and Maths from the web is the possibility of using live data. This possibility gives problem solving real context and allows investigating statistical connections to be far more meaningful.
- Statistics Statistics is the study of the collection, organisation, analysis, interpretation and presentation of data. It deals with all aspects of data, including the planning of data collection in terms of the design of surveys and experiments. It also includes describing mathematical relationships between variables and presenting these to an audience in a way that best conveys meaning. See also the topics called Data Handling, Probability and Averages.

This Scheme of Learning was produced by White Rose Maths and is used here with permission granted on 30th June 2021.