# 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 lesson 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.

The idea of using the box as a container which holds the most representative data helps to understand box plots and whisker diagrams. We then discussed the median as the average 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 compare the two sets noting 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.

I would love to hear how other teachers have taught Box and Whisker diagrams so please leave a comment.

### Mr Mathematics Blog

#### Teaching Mathematics for a Growth Mindset

Inspiring students to enjoy maths and feel the success that comes with attempting a difficult challenge is why I teach.  The feeling of success is addictive.  The more students experience it the more they want it and the further out of their comfort zone they are willing to go to get more of it.  Teaching […]

#### Equation of Straight Line Graphs

To find the equation of straight line graphs students need to calculate the gradient using two pairs of coordinates and the intercept which is the y value of where it crosses the vertical axis.  Examiner’s reports of past exam questions show students are more able to find the intercept of a straight line than they […]

#### Arithmetic and Geometric Sequences

Students learn how to generate and describe arithmetic and geometric sequences on a  position-to-term basis.  Learning progresses from plotting and reading coordinates in the first quadrant to describing geometric sequences using the nth term. This unit takes place in Term 4 of Year 10 and is followed by the equations of straight line graphs. Arithmetic […]