# Box Plots and Whisker Diagrams

Earlier this week the school I work at was inspected. This caused a mixture of reaction amongst the staff. As a teacher of mathematics with a number of GCSE classes I was pretty confident I could expect to be observed. Box plots and whisker diagrams was my observation lesson.

##### Beginning the Lesson

As the students entered the room they were given a past exam question about interpreting cumulative frequency curves from grouped data. Although the lessonÂ was to plot and interpret box plots I felt it important for students to recap their prior learning with grouped data. Plus, this helped to draw their attention from the Headteacher and Inspector.

The students marked their partner’s work using the mark scheme. We also used the examiner’s report to address potential misconceptions. Students were asked to feedback to their peer. This activity took approximately 5 minutes to complete at which point we had a quick discussion about the most common misconceptions.

##### Sharing the Learning Objectives

I shared the learning objective and success criteria that were written on the main whiteboard.

To give greater context to these aims I displayed the dot plot and asked the students to work in pairs to make two comparative statements about the boys and girls IQ.

While I gave no explicit details about the content of the comparison I did wave my hand over the area that contained the greatest density of dots as well as the length of the spread of data.

A number of the students worked really well in pairs and came up with one statement about girls having a higher IQ and another about the boys having the greater spread. It was clear from listening to their discussions that while some had shown great insight into the dot plots.

I asked different pairs to show each other their whiteboards and discuss the range of comments each group had made. Listening into these conversations highlighted to me need to review the median and interquartile range definitions I introduced the previous lesson.

### The Need for Box Plots and Whisker Diagrams

The point of this activity was to identify how much detail is lost when data is grouped.Â

The idea of using the box as a container which holds the most representative data helps to understandÂ box plots and whisker diagrams. We then discussed the median as the averageÂ height and the interquartile range as the measure of spread for the most representative data.

To consolidate this point I asked the class to draw on their whiteboards a picture of the people who lie at given points along the box and whisker diagram. The most typical response is shown.

At this point we’re about 25 minutes into the lesson so I go back to the success criteria board and mark off our progress.

### Consolidation

I gave out the sheet showing two cumulative frequency curves and asked the class to calculate the upper and lower quartiles as well the median to draw the box plot for both sets of data. Then compareÂ the two sets notingÂ the median and interquartile range.

Another quick trip to the success criteria board to show our progress followed. At this point the Inspector and Headteacher thanked me for the lesson and left.

### Independent Learning

The remainder of the lesson consisted of students working through similar problems in their exercise book. The plenary extended their learning by commenting on how a series of box plots illustrate the change in a person’s height during the puberty years.

### Feedback

Shortly after the lesson I received an email from my Headteacher who wanted to feedback at the end of the day. I duly accepted this invitation with just a little nervousness. The feedback I received reflected what they saw as a very nice lesson where all students were enjoying their learning, made excellent progress and felt challenged. Phew!!

If you like the ideas behind this lesson it is available as a download by clicking here.

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