# Frequency Diagrams

For KS3, our SoW starts with a Data module and after spending a fair amount of time with my Year 8 group ensuring we had nailed Mean, Median, Mode and Range (yes, the hardest bit is remembering which is which, apparently) we embarked on a few lessons learning about frequency diagrams.

Our starter was a picture of this frequency diagram, with the words “Mean, Median, Mode, Range?” written beneath. I also verbally, carefully, said “If possible, calculate the mean, median, mode and range.”

We discussed their answers, many of which were incorrect (“the mode is 7!”) initially, but by the end of the discussion, most had realised where they had gone wrong. I then showed them this frequency diagram, and asked them to tell me what was wrong with it.

They identified all the problems easily. Poor title, no labelling of the axis, unequal bar widths, uneven spacing of gaps. The students then answered some questions interpreting data from frequency diagrams.

The following lesson, I projected a list of ages (of people visiting a shop) and asked how they might draw a frequency diagram. Some suggested simply plotting the values in the order they appear and joining them up like a line graph. I hadn’t expected this, but drew what I thought this graph might look like, and asked if it told us anything? We agreed the graph told us very little – in which case, what’s the point in drawing it? I also mentioned that type of graph is generally used when time is involved and drew an example of rainfall per day over a week.

So what can we do with this data? Cue one bright spark: “Could we count how many are between 10 – 20, 20 – 30, …” We spent a bit of time discussing groups (where would I put 20?) and discrete and continuous data, and then we grouped the data together and I asked them to draw the frequency diagram.

So surely after our previous lesson during which they had attentively listened and worked hard (they looked like they had?), I would be presented with 28 perfect frequency diagrams, right?

This class and I have got in to a habit of them coming to me while I’m sat at my desk. This isn’t usually my teaching style… I like to pace around and talk to the students and correct any mistakes I might spot and challenge any students to see if they know what they are doing – if they really know what they are doing. But instead, this Year 8 group have decided they like coming to see me, and I haven’t stopped them. The queue seems to self-regulate (I don’t want to wait for more than 6 people ahead of me… maybe I’ll ask my friend?) and it gives me a nice view of the class to ensure they stay on task while I intervene with anyone who needs my feedback. My classroom this year is also really quite cramped and not as easy to get round (particularly without turning my back on someone).

So I have my queue forming, and I cannot wait to see all the perfect frequency diagrams.

I think most students took three attempts to get it nailed. I wrote comments on each diagram that wasn’t perfect (I could see their hearts breaking) but backed this up with verbal feedback that told them all the things they had got right. All of them forgot a title. And then many gave me a title that just said “bar chart”. Many scaled poorly (from 0 – 20, but then only needed a max of 4) and labelled unclearly. Many ran out of room so had to squeeze their last bar in at the end. It was interesting to watch. So they did them again. Some students once, twice, some four. I think most students took three attempts.

I then showed them what the bar chart should look like. I briefly discussed (again) how we leave gaps for discrete data (look at the groups… there seems to be a gap between 20 and 21, so we leave a gap on our chart) and not for continuous data, and said I’d prefer larger gaps than those on this diagram, but the important thing is that they were evenly spaced.

But, by the end of the lesson, there was no confusion about what was an acceptable bar chart. Every student knew (at least one day later) exactly what I expected from them in order for them to not have to re-do the work. Additionally, they also knew that I had told them, before hand, exactly what I expected of them in order to not have to re-do the work – so hopefully, they may now focus that little bit harder? Perhaps.

The next lesson the students worked in pairs with half a pack of smarties to tally and draw an appropriate frequency diagram. This was what one student produced:

Then we considered pie charts, but perhaps that’s another blog post…