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Autograph Activities Free Dynamic Mathematics Resources
6. Statistical Diagrams
Welcome to the sixth Autograph Newsletter! Each jam-packed edition will look at a specific topic in mathematics and how Autograph can help engage students and enable them to understand the key concepts better.
Hope you enjoy it!
Craig Barton
Craig Barton
Advanced Skills Teacher, creator of and TES Secondary Maths Adviser. Follow me on Twitter: @TESMaths
Diagnostic Question
Free Online Autograph Activity
Ideas for Extension
Video Tutorials
Handy Autograph Tip
There are two things that students need to be able to do with statistical diagrams; to construct them and to interpret them. Once the basic skills of construction have been learnt, there is little point wasting valuable class time asking students to create more diagrams which they can then interpret. This is where Autograph comes in! Using its statistical functions, we can easily import interesting data sets from anywhere and instantly create a whole host of diagrams. This allows us to focus teaching time on helping students develop those higher level interpreting skills. In this newsletter we take a look at how to import data and create basic statistical diagrams, including cumulative frequency, box and whisker, histograms and scatter diagrams.
Diagnostic Question
Diagnostic questions are ideal to use at the start of the lesson to enable you to get a quick and accurate picture of your students' levels of understanding. They are designed in such a way that common misconceptions that your students may hold should steer them to one of the incorrect answers, thus allowing you to learn where the problems lie from their responses. Typically I give my class 30 seconds thinking time and then ask them to hold up their fingers: 1 for A, 2 for B, etc.
Reflection Diagnostic Question
Free Online Autograph Activity
Wages of Footballers
This strange looking cumulative frequency diagram and box and whisker plot show the weekly wages of a group of 50 football players. Can you change the data to fit the seven tricky challenges?
Cumulative Frequency and Box Plots Together
These Autograph activities do not require the full version of Autograph to run them. You just need to install the free Autograph Player (you will be guided through how to do this), which means you can use these activities in the classroom or set them for your students to do at home.
Ideas for Extension
The following ideas for extending this topic require the full version of Autograph.
Baby Weight Data.xls
We will be using the above data set for the next three activities. It gives data about babies and their mothers, and also includes information about if the mother smoked or not. I have split the data into separate worksheets for Smokers and Non-Smokers (click on the tabs at the bottom), or you can use the filters on the first worksheet.
To import data from Excel into Autograph, follow these steps:
Select and copy the column you want (it does not matter if it has a header).
Open a new Statistics page.
Click on Raw Data and paste the data into the appropriate cells.
Or click on Grouped Data, click on Use Raw Data, Edit and then paste the data as above.
Top Tip: If your data has commas in it, these will need to be removed before you import it. Just select the cells, right-click and choose Format Cells, Number and remove the tick by Use 1000 separator.
Idea 1 – Cumulative Frequency Diagrams
Download  1. Cumulative Frequency.agg
The Autograph page shows a cumulative frequency diagram of the birth weights of babies from non-smoking mothers.
Use the C.F.D Measure tool to get an estimate for the median and quartiles.
How will the cumulative frequency diagram for the Smokers differ? Select the birth weight column for the Smokers and paste it in as Grouped Data as described above or in the video below.
Select the new data set from the key at the bottom of the page, create a cumulative frequency diagram and calculate the median and quartiles.
How do they differ?
Can you explain this?
What would the two box plots look like?
Use the Scribble Tool to mark on your students' predictions.
Select the Data set and then click on Box Plot to find out!
Investigate Cumulative Frequency Diagrams and Box Plots for some of the other columns of data.
Idea 2 – Frequency Diagrams/Histograms
Download  2. Histograms.agg
The Autograph page shows a frequency diagram of the gestation period (in days) of babies from non-smoking mothers.
Which group contained the most people, and approximately how many were in this group?
Use the Animation Controller to adjust the group sizes until you find one you are happy with.
Select the gestation period column for the Smokers and paste it in as Grouped Data as described above or in the video below.
Select the new data set from the key at the bottom of the page and create a Histogram
How do they differ?
Double-click on your new frequency diagram and choose Plot Down.
Edit the y-axis so it has a minimum value of −400.
What would the diagrams look like if we used Frequency Density instead of Frequency? Double-click on them and select Frequency Density to find out!
Investigate Frequency Diagrams and Histograms for other columns of data.
Experiment by changing the group widths so they are not uniform (see the video).
Idea 3 – Scatter Diagrams
Download  3. Scatter Diagram.agg
What is the relationship between a mother's weight and the weight of their babies?
Will it be positive or negative correlation? Strong or weak?
Select and copy the Birth Weight column, and paste it into the x column of the Enter XY Data Set.
Repeat for Mother Weight (kg) in the y column and click OK.
Click Default Scales to make your graph look a bit nicer.
You may need to drag the page into a better position.
Does the relationship match your predictions?
Scribble on your estimate for the line of best fit.
To check your answer, make sure the dots are selected, right-click and choose Line of Best Fit from the menu.
Investigate how the relationship changes if you separate Smokers and Non-Smokers.
Video Tutorials
The following video takes you through, step-by-step, some of the ways you can use Autograph to look at grouped data.
Handy Autograph Tip
Autograph can calculate all the statistics you could possibly want, and it's really easy to paste this as text!
Open a new Statistics page.
Create a Grouped Data set as described above.
Click on View Statistics Box to get a nice summary of useful statistics.
Click on Table of Statistics and the Results Box should open. If not, click on View > Results Box. This text can now be copied and pasted into any application you like so you can work with it further!
Curriculum Coverage
Not teaching statistics today? No problem, Autograph covers much more including probability, graphing, vectors, coordinate geometry, shapes and transformations, numerical methods, cartesian equations, parametric equations, polar equations, differential equations, calculus, trigonometry and all in two- and three-dimensions.
List of Autograph Activities
Douglas Butler's series of 7 Autograph Tutorial Videos provide a perfect overview of curriculum coverage.
Free Autograph Activities
If you need free Autograph Activities that can be used without Autograph installed try Mr Barton's Autograph Activities.
Getting Started
If you are just getting started with Autograph try the Video Training Series and the Training Manual with step-by-step instructions.
Autograph trainer Alan Catley has created an impressive collection of student worksheets which can all be downloaded and used for no charge.
Video Tutorials
Watch videos by Craig Barton, Douglas Butler, Hassan Lakiss and Janet Smith.
Past Newsletters
Read other newsletters in this series by visiting the newsletters page.
Prefer printed material? Download sample chapters from the Autograph Activities books.
Autograph Activities Books
New this month: Dynamic Statistics with Autograph and Dynamic Algebra with Autograph by Dr James Kett.
Courses and Trainers
If you prefer face-to-face training attend a training course or book a trainer to come to your school.
Be Inspired
Been using Autograph for a while and looking for new ideas? For inspiration try Owen Elton's Matheminutes blog, and the blog from Autograph's creator Douglas Butler.
Jonny Griffiths has three resources sites which make use of Autograph: Rich Starting Points for A Level Core Mathematics, Making Statistics Vital and Carom Maths.
More Resources
A complete list of useful websites can be found on Douglas' TSM Resources website.
You can find many of these resources on the Autograph TES page.
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