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5. Data and Displays
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Year 11

5.04 Dot plots and stem plots

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Lesson

Dot plots

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.

  • To correctly display the distribution of the data, the dots must be evenly spaced in columns above the line
  • The scale or categories on the horizontal line should be evenly spaced
  • A dot plot does not have a vertical axis
  • The dot plot should be appropriately labelled

 

Practice questions

Question 1

Here is a dot plot of the number of goals scored in each of Bob’s soccer games.

  1. How many times were five goals scored?

  2. Which number of goals were scored equally and most often?

    $1$1

    A

    $0$0

    B

    $4$4

    C

    $3$3

    D

    $2$2

    E

    $5$5

    F

  3. How many games were played in total?

Question 2

The goals scored by a football team in their matches are represented in the following dot plot.

  1. 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 $\editable{}$

 

Stem plot

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 right-most 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.

  • The stems are arranged in ascending order, to form a column, with the lowest value at the top 
  • The leaf values are arranged in ascending order from the stem out, in rows, next to their corresponding stem 
  • A single vertical line separates the stem values 
  • There are no commas or other symbols between the leaves, only a space between them 
  • In order to correctly display the distribution of the data, the leaves must line up in imaginary columns, with each data value directly below the one above
  • A stem plot includes a key that describes the way in which the stem the leaf combine to form the data value 

 

Practice questions

Question 3

Which of the following is true of a stem-and-leaf 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
 
Key: $1$1$\mid$∣$2$2$=$=$12$12
A stem-and-leaf plot is displayed. The plot is divided into two columns: "Stem" on the left, and "Leaf" on the right. The "Stem" column lists the digits in the order 0, 1, 2, 3, 4, 5, and 6, starting with 0 at the topmost column. Each digit in the "Stem" column is paired with aligned with a group of digits in the "Leaf" column. For stem 0, the leaf is 7. For stems 1 and 2, there are no leaves. For stem 3, the leaves are 1, 3, 3, and 3. For stem 4, the leaves are 1, 2, 3, 4, and 9. For stem 5, the leaves are 1, 2, 4, 5, and 5. For stem 6, the leaf is 0. Below the plot is a row named "Key," which explains the notation. On the "Key" row, it is written that 1 | 2 = 12.

  1. The scores are ordered.

    A

    A stem-and-leaf plot does not give an idea of outliers and clusters.

    B

    It is only appropriate for data where scores have high frequencies.

    C

    The individual scores cannot be read on a stem-and-leaf plot.

    D

QUESTION 4

The stem-and-leaf 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
 
Key: $1$1$\mid$∣$2$2$=$=$12$12
years old

  1. How many people passed through the gates in the first $5$5 seconds?

  2. What was the age of the youngest person?

    The youngest person was $\editable{}$ years old.

  3. What was the age of the oldest person?

    The oldest person was $\editable{}$ years old.

  4. What proportion of the concert-goers were under $20$20 years old?

Outcomes

1.2.2.2

display numerical data as frequency distribution tables, dot plots, stem-and-leaf plots and histogram

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