# Comparing statistical distributions

Students are expected to be able to compare data sets by considering graphs, averages and measures of spread. This list of resources provides students with the opportunity to describe and compare univariate empirical distributions through appropriate graphical representation involving discrete, continuous and grouped data and appropriate measures of central tendency and spread.

Visit the secondary mathematics webpage to access all lists.

### Analysing and Interpreting Data

This resource contains games, investigations, worksheets and practical activities. Relevant activities in pack one are **It's raining** in which students interpret a simple bar chart, **Handspan**, a simple experiment comparing handspans, **Favourite ice-cream**, finding the mode by interpreting bar charts and three worksheets called **Mode, Median, Mean** which calculate averages of discrete data.

Relevant activities in pack two are **Frequency Graphs** in which students draw and interpret frequency graphs and find the modal value, the mean and the median from a frequency graph, **Best Marks **in which students compare the test marks from different classes, **What does average mean?** is a booklet containing a number of ideas useful for teacher inspiration, **Grouping data** explores the effect of grouping the same data differently and **Cumulative frequency and quartiles**, an exercise using cumulative frequency.

### Discussing Data

This resource contains a variety of activities, each of which includes information on the data, discussion guidance, specific questions, extension questions, possible hypothesis and a vocabulary check list.

The activities are split into six areas at three mathematical levels:**Comparing data **contains activities entitled Travelling to school, Comparing Junes and Population pyramids**Interpreting line graphs** has data from activities such as Going to the cinema, Cinema attendance and Households**Interpreting bar graphs **considers Olympic glory, Healthy eating and Spending money**Interpreting pie charts **asks How fit are you?, considers Keeping fit as well as Young and healthy**Displaying data **requires students to Showing it clearly, asks Which is cleaner? and Making sense**Questionnaire design **suggests titles of An average Year Seven student, An average Year Eight student, An average Year Nine student.

### Statistical Diagrams

This resource requires students to perfom some data collection; extract data from tables and use mileage charts and timetables. Students are asked to present data using stem and leaf diagrams, line graphs, tally charts, pie charts and frequency tables. Students then perform statistical measures of mean, mode, median and range. Students move on to plot scatter diagrams, lines of best fit and find the equation of the line of best fit.

The activities file has two useful activities.**Shortest journey** explores the use of mileage charts and **Estimating means **investigates the average distance students live from school.

### Interpreting Bar Charts, Pie Charts, Box and Whisker Plots S5

This resource is designed to enable students to understand and interpret bar charts, pie charts, and box and whisker plots. Students, working in pairs, match pie charts to bar charts and match box and whisker plots to bar charts. Each session starts with a whole group discussion to compare the newly-introduced type of representation, looking at its advantages, disadvantages and practical applications.

### Real Data: Statistics Projects for Key Stage Three

This resource consists of six themed handling data projects. Each project requires students to carry out work planning and collecting data, processing data, representing data, interpreting data and discussing results.

The themes of the projects are: An average student, the Environment, an experiment called Fast hand, in the context of Sport, Transport and World statistics

Each theme has a supporting spreadsheet of data, except Fast Hand which requires students to collect their own data.

Students are expected to use a range of statistics to address each hypothesis, including frequency tables, bar charts, pie charts, stem and leaf diagrams, box and whisker diagrams, scatter diagrams, compound bar charts, multiple bar charts and line graphs. They are also expected to find the mean, mode and median of data.

### Averages

This video is 27mins in length and is probably best used as teacher inspiration when planning lessons. With careful planning, parts of the video could be incorporated into lessons. The video observes mathematics teacher Jonny Heeley, as he inspires a group of gifted and talented year nine students with an interactive lesson on averages.

Using a variety of challenges this masterclass shows how the mean, median, mode and range of a set of numbers can be both helpful and misleading in understanding sets of data.

### Averaging Continuous Data

This video, 21 mins in length, follows on from the video about averages and should be used in a similar way. In this video mathematics teacher Jonny Heeley inspires a group of gifted and talented year nine students with an interactive lesson on averaging continuous data.

The usefulness of class intervals and cumulative frequency graphs are discussed and explored by using the very practical example of what size gloves a glove company should make.

### Census at School

This collection of materials contains twenty one resources. The activities provide opportunities for students to collect data about themselves and improve understanding of a data gathering process, access large and meaningful data sets and make comparisons between the student responses in different countries. Appropriate activities include **A modal pupil** in which students compare the use of mode, mean and median, **Big schools** in which students are required to compare their own school to others by drawing a picture graph, **Box and whisker plots** in which students compare two sets of data of heights by drawing box and whisker plots, **Frogs** in which students calculate statistics from discrete and grouped data in order to determine how many frogs are on the slide.

### Box and Whisker

This excel spreadsheet has a number of interactive activities using box and whisker diagrams. A single box plot can be drawn. The second activity shows two box and whisker diagrams to allow comparison between distributions. The third activity shows a box and whisker diagram for students to read off the lowest value, the median and quartiles and the maximum value. Answers can be revealed and new diagrams shown. The final sheet shows box plots for two distributions so that they can be compared.

There are three more sheets of questions which may be suitable for use in the classroom