Minds On
Completing the obstacle course
A group of athletes participated in a challenging obstacle course. The data below shows the anonymous results from the course.
The percentages indicate how much of the course the athlete completed.
Here are the completion results:
75%, 64%, 56.5%, 61.5%, 86%, 90.5%, 72.5%, 80%, 66%, 94%, 61%, 100%, 100%
Student Success
Think-Pair-Share
Based on these results, how did the athletes do?
Imagine that more than two athletes completed the obstacle course (100%). How could you use these scores to prove that the course was easy or difficult?
Throughout this learning activity, you can record your thoughts digitally, orally, or in print.
Note to teachers: See your teacher guide for collaboration tools, ideas and suggestions.
Action
What are the mean, median, and mode?
Mean, median, and mode are all measures of central tendency.
A measure of central tendency is a measure that represents the approximate center of a set of data. Mode, median, and mean are all measures of central tendency.
Let’s review how we determine the mean, and the median, and identify the mode.
Press the following tabs labelled mean, median and mode to review the definitions of these terms.
The mean of a set of numbers is calculated by adding up all the numbers and then dividing that result by the number of numbers in the set.
For example, the mean of 10, 20, and 60 is (10 + 20 + 60) ÷ 3 = 30. It is also called average.
The median is the middle value of an ordered list.
- For example, 14 is the median for the set of numbers 7, 9, 14, 21, 39.
- If there is an even number of data values, then the median is the mean, or average, of the two middle values. For example, the median of this set of number 7, 9, 14, 21 is 11.5 because 9 + 14 ÷ 2 = 11.5.
The mode is the category with the greatest frequency or the number that appears the most in a set of data.
- For example, in a set of data with the values 3, 5, 6, 5, 6, 5, 4, 5, the mode is 5.
- It is important to note that mode also emerges in qualitative data. For example, if students conduct a survey on ice cream flavours and vanilla is the most popular, then vanilla is the mode of this data. A mode may or may not prove meaningful for quantitative data.
Task 1: Leveling the bars
Explore the following data. Use this data to determine the mean, median, and mode. You can use the bars to help you.
Press ‘Hint’ to reveal the answer.
Mean:
12 + 7 + 8 + 3 + 5 + 1 = 36
36 ÷ 6 = 6
The mean is 6.
The median is 6. The two middle numbers are:
1, 3, 5, 7, 8, 12. 5 + 7 = 12
12 ÷ 2 = 6
The mode is board game.
Task 2: Determining the median
Let’s explore this video and review the stem-and-leaf plots.
Examine the following set of data:
22, 27, 32, 32.5, 47.5, 21, 20, 56, 54, 55, 55, 55, 23.5, 33.5, 42.5, 42.5, 45
Use this data to create a stem-and-leaf plot. Then, determine the median. You can create your graph digitally, on paper, or using concrete materials, or create an audio recording to discuss the data.
Reflect
Once you have created your stem-and-leaf plot, describe how you used it to find the median in the data set.
How could you use the stem-and-leaf plot to find the mean and the mode? Record your response using a method of your choice.
Press ‘Hint’ to reveal the answer.
| Stems | Leaves |
|---|---|
| 2 | 0, 1, 2, 3.5, 7 |
| 3 | 2, 2.5, 3.5 |
| 4 | 2.5, 2.5, 5, 7.5 |
| 5 | 4, 5, 5, 5, 6 |
There are 17 numbers in the data set so the median will be the middle one- the 9th! The 9th number is 42.5.
The mean would be the sum of all the numbers which is 664. There are 17 numbers in the set, so the mean would be 664 ÷ 17 = 39.1.
The mode is 55.
The stem and leaf plot didn’t make it easier to find the mean because I still had to add all the numbers up and I could just do that from the list. It did make finding the median easier because the leaves are all in order so finding the middle one was pretty easy. It also made the mode easier to locate.
Task 3: Determining the mode
Find the mode of these survey results. Select the correct answer.
Task 4: Comparing modes
Identify the mode for the data in each graph.
Does the mode in Graph A and Graph B accurately represent the data and results of the survey results in each city? Do they tell an accurate story? Why or why not?
Stretch your thinking
Create two sets of data with the same mode. The mode for one set is an appropriate representation of the data. For the other set, the mode is not an appropriate representation of the data.
You can record your thinking using a method of your choice.
Consolidation
Task 1: What is the data set?
Use the following clues to determine the data set. The mode (the most frequent number) for 5 numbers is 20. The sum of the 5 numbers is 105.
- What are the 5 numbers?
- What is the median (the middle number)?
- What is the mean (the “average” number)?
Complete The Data Set in your notebook or use the following fillable activity document.
Press the ‘Activity’ button to access The Data Set.
Reflection questions
- In your opinion, which measure of central tendency, mean, median, or mode is the most appropriate measure for representing the data?
- When might you use mean, median, or mode to prove something using data?
Record your ideas using a method of your choice.
Task 2 (Optional): Using mean and median
Complete the Finding Mean, Median and Mode in your notebook or use the following fillable activity document for additional practice.
Press the ‘Activity’ button to access the Finding Mean, Median and Mode.
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.