Minds On

Statistics

Explore the following video. Lady Vocab explains that data can be organized in many ways.

Let’s explore why it’s important to understand how to organize the data we collect.

Organizing data

The following set of data represents the number of goals a hockey player scored in each season of their career:

49, 43, 51, 55, 92, 71, 87, 73, 52, 62, 40, 54, 40, 41, 31, 16, 38, 11, 23, 25, 23, 9

Answer the following questions using the tool of your choice:

  • Is a list of numbers a good way to organize this data? Why or why not? Explain your thinking.
  • What is a better way to organize this data?
  • Why is it important to organize data properly and effectively?

Action

Ways to Organize Data

Two ways that data can be organized are frequency tables and stem-and-leaf plots.

Frequency tables

Frequency tables list items and the number of times each item occurs. Frequency tables can also include a column for tally marks to help with counting.

Below is an example of a frequency table that represents a group of students’ favourite animals:

Favourite Animal Tally Frequency
Aardvark 5
Elephant 8
Zebra 11

Stem-and-leaf plots

Stem-and-leaf plots organize numbered data into two parts: a “stem” and a “leaf.” Stems are listed vertically and their leaves are listed beside them horizontally.

The stem is recorded in the left column and lists the first digit (or digits) of a number.
The leaf is recorded in the right column and lists the last digit of the number. Each leaf can have only a single digit.
If there is more than one leaf on a stem the leaves are listed in ascending (increasing) order.
If there are no leaves, nothing is recorded beside the stem.
Stems are listed in order from least to greatest. Even if there aren't any leaves, the stem is still listed.

Explore the following video, “What is a Stem and Leaf Plot?” As you explore the video, think about the following questions:

  • What do you notice about the shape of the data?
  • Is it easier to use images of data rather than looking at a set of numbers?
  • Do you think a stem-and-leaf plot is easier to analyze?
  • When would a stem-and-leaf plot be a better way to represent data than a bar graph?

The following set of data represents the number of hours that students used their television in a month:

8, 12, 15, 19, 20, 20, 20, 32, 31, 29, 21, 21,
10, 41, 42, 44, 35, 21, 8, 7, 40, 33, 55, 52, 50

Review the following stem-and-leaf plot representing the same data set:

Hours of Television Use Per Month
Stem Leaves
0 7, 8, 8
1 0, 2, 5, 9
2 0, 0, 0, 1, 1, 1, 9
3 1, 2, 3, 5
4 0, 1, 2, 4
5 0, 2, 5

Collecting and organizing your own data

We are now going to collect our own data sets by rolling two dice.

Roll your dice 20 times. After each roll record the sum of both dice using the tool of your choice.

Now organize your results into a frequency table and a stem-and-leaf plot.

Complete the Dice Rolling Frequency Table and the Dice Rolling Stem-and-Leaf Plot in your notebook or using the following fillable and printable documents.

Dice Rolling Frequency Table
Sum of dice Tally Frequency

Press the ‘Activity’ button to access Dice Rolling Frequency Table. 

Dice Rolling Stem-and-Leaf Plot
Stem Leaves

Press the ‘Activity’ button to access Dice Rolling Stem-and-Leaf Plot. 

Using the tool of your choice, compare and contrast these two methods of organizing data by answering the following questions:

  1. Review your frequency table:
    • Which numbers came up the most?
    • Which numbers came up the least?
  1. Review your stem-and-leaf plot:
    • How does the stem-and-leaf plot help you understand the data?
    • How might the shape of the data be helpful to someone analyzing the data?
  1. Which method of data collection did you find most useful?

If possible, share your responses with the class.

Consolidation

Reflecting on data organization

Student Success

Think Pair Share

Respond to these questions using a method of your choice.

  • How could using a frequency table help us make predictions about data?
  • When might a frequency table be more suitable than a stem-and-leaf plot to organize data?

Note to teachers: See your teacher guide for collaboration tools, ideas and suggestions.

Reflection

As you read through these descriptions, which sentence best describes how you are feeling about your understanding of this learning activity? Press the button that is beside this sentence.

I feel…

Now, record your ideas using a voice recorder, speech-to-text, or writing tool.