I was looking at some **TES resources** the other day trying to find new ideas for teaching mean from a frequency table. I found a few good ones so this post is just a collection of ideas for teaching averages, both from the TES (slightly extended or modified) and things I’ve picked up over the years. This was originally just supposed to be private blog post but I decided to make it public just to see if anyone else has more ideas to bring the topic to life or make it relevant.

1. Fun: I read a post recently (but have no idea where?) with an idea based on the hilariously funny “Is it Alan or Steve” youtube video. Show the video to students and ask them to record how often the words Alan and Steve are said. Ask the class for their answers and then discuss how we could obtain a more reliable result with the data we have. Lead them into calculating the mean, median and mode of the class results and discuss which is the most appropriate. (I’ll get rid of this explanation and post the link to the blog post as soon as someone can tell me where it is)

2. Fun: Averages for Ducks – this was my first post over 15 months ago (Funny to look back at it now). It’s a similar idea to the one above, tell the students that you were followed to school by a flock of birds and they keep flying in and out of the room. Duck under the desk and tell the class to get down because you can hear them coming. Flash a sheet with 15-25 ducks on it and ask for class estimates for how many ducks there were on the sheet. Lead again into discussion on mean, median and mode (here’s a quick sheet I made for it).

3. How do you get students to understand that the mean isn’t always the best average to use? You could:

- Look at the average wage of employees at a small business with one manager and 7 employees. Artificially make the manager’s wage high so that it skews the mean to make it non-representative for the sample. Alternatively, discuss ignoring outliers.
- Similar scenario. Look at the average house prices in a small village which has say 10 small houses and a mansion. Again, median may be a better choice here over a skewed mean.
- A silly one. An alien comes down to planet Earth and bombards you with questions about the human species. One of them is: “What’s the average number of arms on a human being?” Giving the mean in this case will result in you giving a number like 1.99999999999 instead of 2. The mode would be a better average to use.

4. Modified from a great TES worksheet: Imagine you work for a big mobile phone company. How could you determine how satisfied your customers are with a new phone? Talk through possibilities with the class before introducing them to the data. Show them a phone on www.amazon.com with viewers ratings – discuss reliability of the data. Then find mean, median and mode from frequency table to get representative figures. Do this for a number of different phone brands to compare. You can see the numbers for the Iphone below.

6. Extended idea from a great TES worksheet: Which Drving Instructor to use? Show students a PowerPoint slide with 3 driving instructors and the prices they charge for a one hour driving lesson. Ask them which instructor they’d pick and why. Lead them into discussing other things they might want to know about driving instructor quality. Show the students information on how many lessons people needed to pass their driving test with different instructors (in the form of a frequency table). Ask the students to find the mean, median and mode number of driving lessons people needed to pass with each instructor and hence estimate how much they would have to pay in total for lessons. Go onto asking which would be the best average for the driving instructors to use to advertise themselves in a newspaper/website.

7. Generating their own data – whilst I did see this on a blog recently, it is also something I did 2 years ago with a class. We set up the question, “Who has quicker reactions, girls or boys?” There’s a great, but very addictive, applet for this on the **nrich site**. First make sure that the whole group are using exactly the same controls to obtain reliable results. Get each student to do 30 trials, record their results and then find the mean of their individual results. Stick the mean scores into a grouped frequency table and find girls and boys averages from there.

As a side note, we used the same data later on in the year to look at whether increased trials affected reaction time, analysing correlation and lines of best fit (regression).

8. Discuss class size averages in different Countries – how might this affect learning? Or alternatively, average life expectancy on www.gapminder.org.

9. Even though it’s barely worth mentioning because it’s so obvious – sport averages are always good to go with. Get students to find averages based on their favorite sports (or books, or films, etc.) for homework. Alternatively, get them to find out some crazy average facts such as the facts from this website – Example – “The average person eats almost 1500 pounds of food a year.” – I’ve found this to be a great way to jaz up units of measurement.

It’d be great to hear more ideas if anyone has any.

I just developed a lesson about doing “Median Regression”. It involves finding the median of slopes to find the “best slope”. The lesson involves talking about what type of average we should use, sort of like you number 3. I will be trying this out in a class next week. Any feedback would be greatly appreciated. http://shethinksifactorsexy.wordpress.com/2013/05/19/linear-regression-by-the-median-of-slopes/

Hey Luke,

I just skimmed over your post – I’ve never seen or heard of this regression technique before, nice to see something different. It also seems like a fairly accurate way to obtain a decent line of regression for a set of data. I’m not 100% sure about how I would feel teaching it – I guess it completely depends on your students. It almost feels like too much work compared to more standard regression techniques which take less time. It’s difficult with regression now that we have so many options to do it easily with a computer – I guess it’s similar to the calculator debate and mental arithmetic only you’re less likely to use regression in your day to day life. Having said all that, I do like it as another interesting option to find a model for a data set.

Thanks for the input. Yes, having the students do this method each time to find the regression would be silly. This will just be a lab to lead into the concept of finding the least distance to then finding the least distance squared. For this particular class, we do a lot of curve fitting. This time I am trying to build their understanding of curve fitting before they have their calculator do it for them. Overall, I hope that the lab will help review the procedures of finding the “average”, and, just as there are different “averages”, there are different best lines of fit.

By the way, thanks for sharing the Alan or Steve video. I think I will use that for an icebreaker on the first day of my summer classes.

Not sure what grade you teach, but here’s a problem that takes the concept of mean and goes in a different direction:

http://fivetriangles.blogspot.com/2013/05/69-weights_8.html

Thanks for sharing the link. Always good to link topics for practice purposes.

Hiya – great site – I’ve used the reaction times idea before – it works well with the BBC sheep reaction time game: http://www.bbc.co.uk/science/humanbody/sleep/sheep/reaction_version5.swf

I’ve also just blogged about finger ratio – and looking at the relationship between this and mathematical ability. I’ve used this before to explore averages, correlation, scatter graphs etc:

http://ibmathsresources.com/2013/05/05/finger-ratio-predicts-maths-ability/

Ha, I never knew finger ratio could predict so much!!! Nice idea.

Also, I’ve got a love-hate relationship with the BBC sheep reaction time game – I keep on clicking before the sheep runs out – funny but frustrating!

Thanks for sharing this stuff!

Thanks Dan

I had to throw something together quickly for a class today and this really helped. I am definitely going to do the create your own data/reaction test. Have downloaded an app (There are lot of free ones on the Google play store) and it will be perfect for my adult LLN class.

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Great ideas. Thanks