Dot plots are a graphical way of displaying the distribution of numerical or categorical data on a simple scale with dots representing the frequency of outcomes. They are best used for small to medium size sets of data and are good for visually highlighting how the data is spread and whether there are any gaps in the data or outliers. We will look at identifying outliers in more detail in a latter lesson.
In a dot plot, each individual value is represented by a single dot, displayed above a horizontal line. When data values are identical, the dots are stacked vertically. The graph appears similar to a pictograph or column graph with the number of dots representing the total count.
Here is a dot plot of the number of goals scored in each of Bob’s soccer games.
How many times were five goals scored?
Which number of goals were scored equally and most often?
$1$1
$0$0
$4$4
$3$3
$2$2
$5$5
$1$1
$0$0
$4$4
$3$3
$2$2
$5$5
How many games were played in total?
The goals scored by a football team in their matches are represented in the following dot plot.
Complete the following frequency distribution table.
Goals scored  Frequency 

$0$0  $\editable{}$ 
$1$1  $\editable{}$ 
$2$2  $\editable{}$ 
$3$3  $\editable{}$ 
$4$4  $\editable{}$ 
$5$5  $\editable{}$ 
A stem plot, or stem and leaf plot, is used for organising and displaying numerical data. It is appropriate for small to moderately sized data sets. The graph is similar to a column graph on its side, an advantage of a stem plot over a column graph is the individual scores are retained and further calculations can be made accurately.
In a stem plot, the rightmost digit in each data value is split from the other digits, to become the 'leaf'. The remaining digits become the 'stem'.
The values in a stem plot are generally arranged in ascending order (from lowest to highest) from the centre out. To emphasise this, it is often called an ordered stem plot.
The data values $10,13,16,21,26,27,28,35,35,36,41,41,45,46,49,50,53,56,58$10,13,16,21,26,27,28,35,35,36,41,41,45,46,49,50,53,56,58 are displayed in the stem plot below.
Which of the following is true of a stemandleaf plot?
Stem  Leaf  
$0$0  $7$7  
$1$1  
$2$2  
$3$3  $1$1 $3$3 $3$3 $3$3  
$4$4  $1$1 $2$2 $3$3 $4$4 $9$9  
$5$5  $1$1 $2$2 $4$4 $5$5 $5$5  
$6$6  $0$0  

The scores are ordered.
A stemandleaf plot does not give an idea of outliers and clusters.
It is only appropriate for data where scores have high frequencies.
The individual scores cannot be read on a stemandleaf plot.
The scores are ordered.
A stemandleaf plot does not give an idea of outliers and clusters.
It is only appropriate for data where scores have high frequencies.
The individual scores cannot be read on a stemandleaf plot.
The stemandleaf plot below shows the age of people to enter through the gates of a concert in the first $5$5 seconds.
Stem  Leaf  
$1$1  $1$1 $2$2 $4$4 $5$5 $6$6 $6$6 $7$7 $9$9 $9$9  
$2$2  $2$2 $3$3 $5$5 $5$5 $7$7  
$3$3  $1$1 $3$3 $8$8 $9$9  
$4$4  
$5$5  $8$8  

How many people passed through the gates in the first $5$5 seconds?
What was the age of the youngest person?
The youngest person was $\editable{}$ years old.
What was the age of the oldest person?
The oldest person was $\editable{}$ years old.
What proportion of the concertgoers were under $20$20 years old?
display numerical data as frequency distributions, dot plots, stem and leaf plots, and histograms