Histogram Activity

HISTOGRAM ACTIVITY

After my GCSE students found histograms difficult, I decided to try a practical approach. I gave each group of four a set of axes (see the file Graph axes for histograms) and a sheet of sticky- backed red squares.

They were told to construct histograms for the given data tables (pages 3 to 6) by sticking squares onto the axes. Each square represents ten people, thus, when they reach the histogram with unequal class intervals, they have to think in terms of area, not just heights of bars.

Action research

After meeting with Marie Hart and Chris Smith at the Network meeting on 16th November 2007 I offered to gear this activity towards something that all three of us wanted to achieve: namely, getting learners to write observations about their graphs/charts.

So the instructions I gave to the groups were as on page 7, and required them to write two statements which I hoped they would model on the ones I had given them.

Reflections on the activity

 There was some delight by at least one learner at the prospect of placing sticky squares! Though of course these took a fair amount of preparation time (red card, sprayed on one side with Spray Mount and sliced with a craft knife into 2.5cm squares). Perhaps an alternative would be to print the axes with faint gridlines and ask them to shade the squares in pencil.

 It wasn’t clear which histogram the questions were about, so it’s important to explain, at least verbally, that they refer to the one with unequal class intervals.

 I asked them to think carefully about what to write on the vertical axis, and I had to engage with the groups to draw out the idea of Frequency Density, and explain the “width x height” concept for the columns.

 When I pushed them, they did come up with two more questions per group, as the instructions asked. Someone from each group presented them to the rest. I was running short of time, and would have preferred to get them to swap and answer each other’s questions.

I would welcome any comments, positive or negative, from anyone, whether or not you are able to try out the activity.

Graph 1: Age distribution of a group of 300 people

Age (a) Frequency 0 ≤ a < 10 10 10 ≤ a < 20 30 20 ≤ a < 30 40 30 ≤ a < 40 60 40 ≤ a < 50 50 50 ≤ a < 60 50 60 ≤ a < 70 40 70 ≤ a < 80 20

Age (a) Frequency 0 ≤ a < 20 60 20 ≤ a < 30 60 30 ≤ a < 40 50 40 ≤ a < 50 30 50 ≤ a < 60 40 60 ≤ a < 90 60

HISTOGRAM ACTIVITY

 Using the red squares construct two histograms on the graph paper given. Each red square represents 10 people.

 The first histogram has equal class intervals, and is similar to a bar chart. This one is the same for every group.

 The second histogram has unequal class intervals and each group has slightly different data.

 Choose one statement from the four below that applies to your histogram.

 Write two more statements about your histogram.

There were as many below the age of 36 as above.

An estimate of the median age is 46.

There are approximately 90 people over 55.

There are approximately 104 people over 48.