I’ve used word length analysis for years as a source of comparative statistics. The concept is easy – you take a children’s book and a grown up book and compare the word lengths of the first 20, 40, 80 words. After you collect the information in a table, you can use this data to compare averages and the range.
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But what texts to use? Well – you can’t beat a bit of Dr Seuss, but what grown up text could you use. I can highly recommend this extract from ‘Pride and Prejudice and Zombies’:
Not only will you be investigating mathematical concepts, but you might just be inspiring a student to pick up a book and read.
Update: If you use the first chapter (say thirty words) of ‘Pride & Prejudice & Zombies’ you get some interesting data. The range is wide, but the highest frequency word length is just two. It’s a great conversation piece – why does this happen? The language is a very precise parody of 19th prose with all the correct connectives and no contractions eg ‘it is’ not ‘it’s’.
Here’s a problem on averages that has been used by many teachers over the years. I like the additional ‘sting in the tail’ as it really makes pupils think about real life and it is an instant use of calculating the mean from an ungrouped frequency table.
A job advert says that the average worker at OfficesRUs earns over £30 thousand pounds.
Sales Person £35,000
Clerical Assistant £22,000
Is the advert true?
If pupils calculate the mean they will find it is £44,400 – this makes the advert true
But why would a company have the same number of employees at each pay grade?
OfficesRUs is a clerical agency, offering temporary clerical staff for other businesses. Their staff numbers are:
1 Director £100,000
4 Managers £50,000
8 Sales People £35,000
200 Clerical Assistants £22,000
4 Trainees £15,000
Is the advert still true?
My class worked out how much each pay grade would get and added them to find the total salary cost. Some pupils then divided by 5, but discovered that the mean would be far greater than the Director’s salary. They then realised they had to total up the employees too. The mean turned out to be less than £30,000. This then leads to a discussion of which measure of average is best in this situation.
This is the working out from my board. The original problem is in black, with the sting and working in red. We linked the individual pay grade calculations to the work we had done on means from ungrouped frequency tables. The layout of the calculations is very similar to our tables.
This was a really good investigative starter to bridge between a theory and problem solving lesson. You could get pupils to see if they can find any examples of job adverts with average salaries in and make up their own problems.
This is my favourite activity for introducing different measures of average. You can do this in a corridor or outside, no special equipment required.
Line up the class in height order
Ask the shortest and tallest students to stand back to back. The difference in height is the range.
Tell the first and last student to make a half turn. Ask the second and second to last student to make a half turn. Repeat until only one or two students are facing forward.
One pupil = median height.
Two pupils = halfway between their heights is the median.
Imagine everyone is the same height. Tell the students to try to be the same height by bending knees or standing on tiptoes. Explain the mean is about sharing out equally.
Ask students to put themselves into groups of the same height. The biggest group is the mode.
This activity links a numerical calculation with a physical activity, which makes it more memorable.