Minds On

Which graph does not belong?

Examine the following four graphs and decide which one does not belong with the rest. Be prepared to defend your choice! There is no wrong answer, as long as you can explain your decision.

Throughout this learning activity, you can record your thoughts digitally, orally, or in print.

Action

What is a histogram?

A histogram is a type of graph that displays data using bars.

While it is similar to a bar graph, there are major differences between them.

A histogram shows the frequency of discrete or continuous data that falls into ranges or equal-sized intervals (this represents the continuous nature of the data).

Histograms also have no gaps between the bars in the graph.

Bar Graph Histogram
  • Used to display data with specific names or numbers.
  • Gaps between each bar.
  • Used when the data is in categories (i.e. countries, favourite colours, etc.).
  • The x-axis displays the grouped intervals with the values for the range of numbers in the data set.
  • The y-axis shows the number of times (the frequency) the data occurred.
  • The height of each bar displays the frequency of that specific interval.
  • The width of the bar shows what the interval is.
  • There is no space between the bars.

Examine the following histogram and its diverse parts:

Histogram scavenger hunt

Examine the following histogram.

Complete the scavenger hunt by finding the following information from this graph and recording it in a method of your choice.

  • The title of the histogram.
  • The title of the Y axis.
  • The title of the X axis.
  • The bar with the highest number.
  • The bar with the lowest number.
  • How many people take 35 minutes to get to school? How do you know?

When to use a histogram

Histograms are often used to display continuous data.

Here is a list of some example scenarios when using a histogram would be ideal:

  • customer wait time
  • height
  • time
  • length

What are some specific scenarios when using a histogram would be appropriate?

Press ‘Hint’ to reveal an example.

The height of different trees in a forest.

If possible, share your ideas with a partner or record your responses independently.

Pros and Cons of histograms

Consider the benefits to using a histogram. Examine the following chart.

Pros Cons
  • Data can be easily read and compared.
  • Works well for larger ranges of data/information.
  • Can show outliers in the data.
  • As intervals are always equal, it is consistent.
  • Useful for summarizing the data.
  • The data can be misleading.
  • It does not show the actual values, only the number of values within a range.
  • Histograms are not always ideal when comparing different data sets.

Intervals

What are intervals? How do they relate to graphs?

An interval refers to the distance between two endpoints on a graph.

On a histogram:

  • the intervals will usually be displayed on the x-axis
  • the intervals on the graph should be equal
  • the range of the data can help decide the size of the interval

The range is the difference between the highest and lowest number in a data set.

For example, the following list of numbers would be the range for the following data set:

10, 14, 18, 11, 16, 10, 9, 8, 11, 12, 6

Range: 18 − 6 = 12

Range = 12

These are the steps to take when creating your intervals:

  • Determine the range of your data set.
  • Decide on the number of bars you will have in your graph.
  • Choose the size of each interval (they need to be equal!).
  • Make sure that each item in your data set can only fit in one interval.

Example: Blank Interval Graph

A blank interval graph. The x-axis starts at and interval of 0 to 4 and goes up by fives to an interval of 25 to 29. The y-axis starts at 0 and goes up by ones to 6. The 10 to 14 interval is circled and labeled “The end points of this interval are 10 and 14.”

Use the following data on the heart rates of a group of people to choose appropriate intervals that you would use on a histogram of this data.

These are the heart rates of various patients a doctor saw in a week.

  • 60
  • 65
  • 70
  • 63
  • 81
  • 53
  • 78
  • 73
  • 64
  • 69
  • 75
  • 86
  • 71
  • 85
  • 66
  • 85
  • 55
  • 83
  • 54
  • 79

These are the steps to take when creating your intervals:

  1. Determine the range of your data set.

Press ‘Answer’ to reveal the solution for this step.

Our lowest heart rate is 53 and our highest heart rate is 86 so the range is 86−53 = 33.
  1. Decide on the number of bars you will have in your graph.

Press ‘Answer’ to reveal the solution for this step.

I see that there is data in the 50s, all the way to the 80s so I think I will have at least 4 bars.
  1. Choose the size of each interval (kind of like the scale). They need to be equal!

Press ‘Answer’ to reveal the solution for this step.

I will use a scale of 10. My intervals will be 50-59, 60-69, 70-79, 80-89.
  1. Make sure that each item in your data set can only fit in one interval.

Press ‘Answer’ to reveal the solution for this step.

Even though my scale is 10, instead of 50-60, 60-70, I will only go up by 9s otherwise I wouldn’t know where to put 60 because it could go in two places!

Be ready to share your strategies for creating intervals.

Analyzing histograms

Examine the following histogram.

Answer the following questions and record your answers in a method of your choice.

  1. What is the range of this data set?
  2. What population does this data set represent?
  3. What is the most popular pencil length?
  4. What is the least popular pencil length?

Press ‘Answer’ to check your answers.

  1. What is the range of this data set?
    20cm (30cm – 10cm)
  2. What population does this data set represent?
    Our class
  3. What is the most popular?
    20cm
  4. What is the least popular?
    30cm

Creating histograms

It’s time to create a histogram of your own! Use the following data set to create your histogram.

If you would like, you can complete the next activity using TVO Mathify. You can also use your notebook or the following fillable and printable document.

Make Your Own Histogram
Customer Wait Time in Minutes at Metro in a Day
10 12 13 11
18 25 14 17
19 22 23 21
20 18 11 10
22 9 25 18

Press the ‘TVO Mathify’ button to access this resource and the ‘Activity’ button for your note-taking document.

TVO Mathify (Opens in new window) Activity(Open PDF in a new window)
  1. Determine the range of your data set.

Press ‘Answer’ to reveal the solution for this step.

Our lowest wait time is nine and our highest wait time is 25 so the range is 16.
  1. Decide on the number of bars you will have in your graph.

Press ‘Answer’ to reveal the solution for this step.

I will have six bars.
  1. Choose the size of each interval (remember, they need to be equal!)

Press ‘Answer’ to reveal the solution for this step.

I will use a scale of 5.
  1. Make sure that each item in your data set can only fit in one interval.

You will need to also:

  1. Come up with titles and labels for your histogram.
  2. Choose the intervals for your x-axis (by first determining the range of the data set).
  3. Choose the scale for your y-axis.
  4. Create your graph.

Press ‘Answer’ to reveal the solution for this task.

Student Tips

Student tips

Notice that the bars are numbered as intervals, or ranges. Be careful when creating intervals. If you have intervals zero to five and five to 10, where would you put the number five? Make sure where one interval stops, the next continues, like zero to four then five to nine, then 10 to 14, always going up by the same amount.

Consolidation

My histogram

Now it is time to create a histogram using the heart rate data you examined earlier.

These are the heart rates of various patients a doctor saw in a week.

  • 60
  • 65
  • 70
  • 63
  • 81
  • 53
  • 78
  • 73
  • 64
  • 69
  • 75
  • 86
  • 71
  • 85
  • 66
  • 85
  • 55
  • 83
  • 54
  • 79

You will need to:

  • choose your titles and labels for your graph
  • choose the appropriate intervals for your x-axis
  • create your histogram

Think about your learning

Answer the following questions to reflect on what we have learned about histograms.

  • Where might we see histograms in the real-world?
  • How might a histogram change depending on the size of the intervals you use?
  • What questions do you have about histograms?

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.

Connect with a TVO Mathify tutor

Think of TVO Mathify as your own personalized math coach, here to support your learning at home. Press ‘TVO Mathify’ to connect with an Ontario Certified Teacher math tutor of your choice. You will need a TVO Mathify login to access this resource.

TVO Mathify (Opens in new window)