Year 7AC9M7ST02

Data Displays and Stem-and-Leaf Plots

Create different types of numerical data displays including stem-and-leaf plots; describe and compare the distribution of data, commenting on the shape, centre and spread including outliers.

A display should make the shape of the data obvious at a glance. A stem-and-leaf plot does that while still keeping every original value.

Method

Column graph for categories

Bars separated by gaps. Good for comparing groups.

Dot plot for small numerical sets

One dot per value. Repeats stack up, so the mode is visible.

Stem-and-leaf keeps every value

The stem is the tens, the leaf is the units. Nothing is lost.

Always include a key

3\ |\ 4 = 34

Without a key the plot means nothing.

Worked example

e.g.

\text{Draw a stem-and-leaf plot for } 23,\ 31,\ 25,\ 42,\ 38,\ 27,\ 31

Find the smallest and largest to decide the stems. $23 \ldots 42 \ \Rightarrow\ \text{stems } 2,3,4$
Write the stems in a column. $2 \ |\ \quad 3 \ |\ \quad 4 \ |$
Add each unit digit as a leaf beside its stem. $2\,|\,3\ 5\ 7 \quad 3\,|\,1\ 8\ 1 \quad 4\,|\,2$
Put the leaves in order. $2\,|\,3\ 5\ 7 \quad 3\,|\,1\ 1\ 8 \quad 4\,|\,2$
Add a key. $3\ |\ 1 = 31$
Read the shape. Most of the data sits in the twenties and thirties. $\text{median} = 31$

Practice

Choose a display, or read one.

\text{Best display for favourite sport?}

Answer

\text{column graph}

\text{In } 4\,|\,7 \text{ with key } 4\,|\,7 = 47, \text{ what is the value?}

Answer

47

\text{A stem-and-leaf has 12 leaves. How many data values?}

Answer

12

\text{Why keep a key on every plot?}

Answer

\text{The stems could mean tens, hundreds or units.}

\text{What does a long tail on one side show?}

Answer

\text{The data is skewed that way.}