Year 8 Common Task: Changes in the Average Student

A first lesson (after doing some work on Access skills)
'Come and sit at the same computer as last time. Log on. Bags on floor. Get your books out please. I’ll explain what to do in a moment. Sit yourselves down. Settle down. Exercise books out'

Drawn on the board is something like the following, which has been discussed since the beginning of the work on Access as what the class are aiming towards.

2 LESSONS + 2 HOMEWORKS – YOUR TASK IS TO PRODUCE A REPORT IN WORD ABOUT CHANGES IN THE AVERAGE STUDENT IN YEAR 8 BETWEEN 1992 and 2003

Introduction: Write down at least 2 hypotheses about changes you think will have occurred

Methods: Write down how you are going to test these hypotheses.
Results: Copy charts or averages into your Word document
Analysis and Interpretation: What do these charts and averages tell you?

Conclusion: What can you say about your hypotheses? (How strong is the evidence you have found?)

Evaluation and extension: What could you improve about your project? Try to find the students who is most average in 1992 and most average in 2003, compare these two students.

'Turn the screen off and look this way … We have spent some time setting up the work we will do in the next 2 lessons. You will be writing a report in Word on 2 different years. Explain how you will find out the average student in Year 8. We have spent time talking about this and you’ve written something down about how you'll do this – you might need to look in your books to see what you wrote.'

'For each question, what’s the most common value? - How else can we find averages?
Is there a student with all these values? Who is the nearest student?'

'Your task is to open up a Word document and make a report as you go … the report, at least one sheet of A4 … probably more - no cover sheet or fancy title, unless you have time at the end. You’ll need to open Word and Access … get word up and write a short introduction … get going then. You should be able to get both things up at the same time, both Access and Word.'

Where this can go
I would suggest at least two and possibly three lessons to complete the report. Students will probably calculate averages and compare them, but it is also interesting to try and find the student in the year who has 'most' average values. Encourage students to use the headings to structure their report. Introduction and Methods can be done straight away, then they should keep track of what they find out in the Results section (which they should write as they go). The later sections can be completed after you ICT bookings have finished.

Guidelines for notes at the end of the topic
A hypothesis is …
The mode is the only average you can use for non-numerical data.
Mean, median and mode can be used for numerical data. The advantages/disadvantages of each are … (eg mean takes all values in to account, median ignores extreme values if there are any, mode is often unrepresentative).
[Agree on some statements about doing/writing up statistics projects.]

Vocabulary

Typical mathematical content
Forming their own hypotheses and testing them
Using a database to search and sort
Using a database to calculate averages and draw charts
Interpreting averages
Interpreting charts
Using two ICT packages simultaneously

A homework to be done by everyone
Find the mean, median, mode of the following data. In each case write down, with reasons, which average you think best represents the data, ie is the most sensible to use.

i) Scores of a class on a test (out of 100); 95,2,93,91,93,100,90,93,94,99,98,92

ii) Ages in a family; 11,11,13,15,46,53,90

iii) Saturday Lottery Bonus Ball numbers for the last 10 weeks; 48,7,21,13,16,48,32,37,3,20

iv) Cricket scores of a batsmen in seven 20-20 games; 9,44,0,1,3,58,80

[Answers to averages;
i) Mean=86.7, Median=93, Mode=93
ii) Mean=34.1, Median=15, Mode=11
iii) Mean=24.5, Median=20.5, Mode=48
iv) Mean=27.8, Median=9, There is no mode.]