3. Stem-and-leaf diagrams or stemplots

As the name suggests, this diagram is made up of a main ‘stem’ to which ‘leaves’ of data are attached. Stem-and-leaf diagrams are used to represent numerical datasets; a way of organising and displaying numerical data in a pictorial structure. These diagrams give a nice overview of the ‘shape’ of the data.

Activity 8

Timing: Allow 10 minutes

Here is an image of a stem-and-leaf diagram which represents the monthly pocket money of individuals in a class of pupils.

Figure 14 Pocket money stem and leaf diagram

Add image here

Before you read further about stem-and-leaf diagrams, decide if the following statements are true or false. If you are unsure, just go with your best guess.

True/false options for each There are 20 pupils in the classThe lowest amount of monthly pocket money any one pupil receives is £10 per monthNo two pupils receive the same amount of pocket money The most common (modal) amount of monthly pocket money is £10 per month The range of the pocket money received is £36

Answer

There are 20 pupils in the class – TRUE There are 20 leaves (digits to the right of the line), each leaf represents one data item, in this case, one pupil The lowest amount of monthly pocket money any one pupil receives is £10 per month – FALSE The lowest amount of pocket money shown is £4 represented by the first stem digit, 0, combined with the first leaf digit, 4 No two pupils receive the same amount of pocket money – FALSE There are five pocket money amounts that two or more pupils receive; these are £6 (3 pupils) and then £10, £12, £14, £20 (all received by 2 pupils each) The most common (modal) amount of monthly pocket money is £10 per month – FALSE There are two pupils who receive £10 per month pocket money but three pupils who receive £6 per month as shown by the three sixes in the first row of the diagram The range of the pocket money received is £36 – TRUE The highest amount of pocket money received is £40 and the lowest amount is £4 so the range can be found by calculating £40 - £4 = £36 The mode and range were covered in Week 3. The mode and range were covered in Week 3.

Not sure if this needs to be a quiz/interactive here?

Asking learners to interpret what they think a graph represents before explaining how to interpret the graph is a form of inductive learning. This method whereby examples and problems are shown first and then explained later is akin to how we learn many things, for instance, in language we often learn to say words before fully understanding what they mean.

Figure 15 Key elements of a stem and leaf diagram

Leaves are only ever single digits. Decimal values can be represented as shown in this example key.

Figure 16 Example stemplot key for decimal values

Sometimes data values may need to be truncated for them to be displayed in a stem-and-leaf diagram. Truncating is where the last few digits of a value have been dropped without rounding; it is customary, when drawing a stem-and-leaf diagram, not to round values thus making it easier to vary how the stem is chosen.