Minds On
Making predictions
Brainstorm
Have you made a correct prediction?
Think about different times that you have made a prediction. Have you ever predicted an outcome that turned out to be correct?
What strategies did you use?
Throughout this learning activity, you can record your thoughts digitally, orally, or in print.
Predicting survey results
A group of grade four students were surveyed about their favourite sports. The results showed that their favourite sport was soccer.
Using the tool of your choice, answer the following questions:
- Do you think the results would be the same if grade one students were surveyed?
- Do you think the results would be the same if grade eight students were surveyed?
Action
Reviewing mean, median, and mode
Mean, median, and mode are all measures of central tendency.
Measures of central tendency determine and identify the middle (or average) for a set of data.
Press each measure of central tendency below to access a description and examples.
The mean is the average of all numbers in a data set. We determine the mean in quantitative data (data involving numbers).
You determine the mean by adding up all the numbers in a data set and then dividing that total by the amount of numbers in the data set.
For example, the mean of 10, 20, and 60 is the sum of the data (10 + 20 + 60 = 90) divided by amount of numbers (90 ÷ 3 = 30). Therefore, the mean is 30. We also call this an average.
Let’s explore another example:
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How to determine the mean of the following data set: 22, 28, 26, 35, 44. |
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|---|---|---|
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Step 1 |
Add the numbers together |
22 + 28 +26 + 35 + 44 = 155 |
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Step 2 |
Divide the total by the amount of numbers in the data set |
155 ÷ 5 = 31 |
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Step 3 |
Therefore, the mean is… |
31 |
The median is the number that appears in the middle of a data set when its data is ordered from smallest to greatest. We determine the median in quantitative data (data involving numbers).
You identify the median by ordering the numbers in a data set from smallest to greatest and then determining the number that appears in the middle.
For example, the median of 21, 9, 7, 39, and 14 is the number that appears in the middle when you order the data from smallest to greatest (7, 9, 14, 21, 39). Therefore, the median is 14.
Let’s explore another example:
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How to identify the median of the following data set: 12, 24, 13, 15, 22. |
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|---|---|---|
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Step 1 |
Organize the data set in order from smallest to largest |
12, 13, 15, 22, 24 |
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Step 2 |
Count the amount of numbers in the data set. If there is an odd number of data values, you can find the exact middle. |
There are five numbers, so you can find the exact middle. |
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Step 3 |
Therefore, the median is… |
15 |
Sometimes data sets have an even number of data values, which means that two numbers will appear in the middle. When this happens, in order to identify the median, you must calculate the mean of the two middle numbers.
Let’s explore an example with a data set that has an even number of data values:
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How to identify the median of the following data set: 12, 24, 13, 15, 22, 17 |
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|---|---|---|
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Step 1 |
Organize the data set in order from smallest to largest |
12, 13, 15, 17, 22, 24 |
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Step 2 |
Count the amount of numbers in the data set. If there is an odd number of data values, you can find the exact middle. If there is an even number of data values, you must calculate the mean of the two middle numbers |
There are six numbers, so you must calculate the mean of the two middle numbers. |
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Step 3 |
Identify the two middle numbers |
15 and 17 |
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Step 4 |
Determine the mean of the two middle numbers by calculating their sum and dividing by two (the total amount of numbers in the set of middle numbers) |
15 + 17 = 32 32 ÷ 2 = 16 |
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Step 5 |
Therefore, the median is… |
16 |
The mode is the number or category that appears the most amount of times in a set of data. It is important to note that unlike mean and median, we identify the mode in qualitative data (data involving categories without numbers) or quantitative data (data involving numbers).
You identify the mode by counting the frequency of the different numbers in a data set.
For example, the mode of 3, 5, 6, 5, 6, 5, 4, and 5 is the number that appears the most. The numbers three and four each appear one time each, the number five appears four times, and the number six appears two times. Therefore, the mode is 5.
Let’s explore another example:
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How to determine the mode of the following data set: 7, 4, 8, 2, 8, 5, 4, 9, 1, 8 |
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|---|---|---|
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Step 1 |
Organize the data set in order from smallest to largest |
1, 2, 4, 4, 5, 7, 8, 8, 8, 9 |
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Step 2 |
Count the frequency of the numbers in the data set. |
The numbers 1, 2, 5, 7, and 9 each appear one time. The number 4 appears two times. The number 8 appears three times. |
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Step 3 |
Therefore, the mode is… |
8 |
Sometimes data sets have more than one number that appears the most amount of times, which means that the mode will be more than one number.
Let’s explore an example with a data set that has a mode that is more than one number:
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How to determine the mode of the following data set: 10 ,7, 7, 2, 5, 1, 5, 7, 2, 10, 2, 3 |
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|---|---|---|
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Step 1 |
Organize the data set in order from smallest to largest |
1, 2, 2, 2, 3, 5, 5, 7, 7, 7, 10, 10 |
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Step 2 |
Count the frequency of the numbers in the data set. If more than one number appears the most amount of times, then the mode is more than one number. |
The numbers 1 and 3 each appear one time. The numbers 5 and 10 each appear two times. The numbers 2 and 7 each appear three times. |
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Step 3 |
Therefore, the mode is… |
2 and 7 |
Making predictions about rolling dice
Let’s practice making some predictions.
Review the following table representing the results of rolling two dice ten times:
| Rolling Two Dice Ten Times Results | |||
|---|---|---|---|
| Roll | Number on die one | Number on die two | Sum |
| 1 | 2 | 2 | 4 |
| 2 | 1 | 3 | 4 |
| 3 | 4 | 6 | 10 |
| 4 | 5 | 2 | 7 |
| 5 | 1 | 3 | 4 |
| 6 | 6 | 3 | 9 |
| 7 | 5 | 1 | 6 |
| 8 | 3 | 4 | 7 |
| 9 | 1 | 1 | 2 |
| 10 | 2 | 6 | 8 |
Using the tool of your choice, answer the following questions and explain your thinking for each:
- Calculate the mean, median, and mode of the "sum" column.
- How likely is it that your mean will be the same if you were to roll another 10 times?
- How likely is it that your median will be the same if you rolled another 10 times?
- How likely is it that your mode will be the same if you rolled another 10 times?
Press ‘Answers’ to reveal the solutions.
The mean, median and mode of the Sums column are:
Mean - 6.1
Median - 6.5
Mode - 4
When you are finished, review the following table representing the results of rolling two dice ten more times:
| Rolling Two Dice Ten More Times Results | |||
|---|---|---|---|
| Roll | Number on die one | Number on die two | Sum |
| 11 | 3 | 2 | 5 |
| 12 | 3 | 6 | 9 |
| 13 | 5 | 6 | 11 |
| 14 | 3 | 1 | 4 |
| 15 | 2 | 4 | 6 |
| 16 | 5 | 1 | 6 |
| 17 | 3 | 3 | 6 |
| 18 | 2 | 3 | 5 |
| 19 | 1 | 2 | 3 |
| 20 | 5 | 6 | 11 |
- Calculate the mean, median, and mode of the "sum" column. Now consider the data from both tables. Record your thinking using a method of your choice.
- Explain how the results compared to your predictions. Why do think this is?
Press ‘Answers’ to reveal the solutions.
The mean, median and mode of the sums of the second set of 10 rolls are:
Mean - 6.6
Median - 6
Mode - 6
Making predictions about temperature
The top daily temperature in Toronto was recorded during the first week of April and September.
Do you predict that the mean, median, and mode for the two sets of temperatures will be the same? Why or why not?
Use the tool of your choice to record your response.
Testing your prediction
Press ‘Top Daily Temperature Tables’ to reveal the tables representing the top daily temperatures in Toronto during the first week of April and September:
| Top daily temperature in Toronto | |||
|---|---|---|---|
| First seven days of April | Temperature (degrees Celsius) | First seven days of September | Temperature (degrees Celsius) |
| 1 | 10 | 1 | 28 |
| 2 | 14 | 2 | 28 |
| 3 | 11 | 3 | 29 |
| 4 | 11 | 4 | 23 |
| 5 | 10 | 5 | 21 |
| 6 | 14 | 6 | 22 |
| 7 | 14 | 7 | 25 |
Using the tool of your choice, answer the following questions:
- What is the mean, median, and mode for each month’s data set?
- Were the predictions that you made earlier correct?
- Did you find that the mean, median, and mode were the same, similar or different? Why do you think this is?
Consolidation
Reflecting on predictions
Using the tool of your choice, reflect on making and testing predictions by recording responses to the following questions:
- When might you predict that the mean, median, and mode of two data sets would be different?
- What can make the mean, median, and mode of two data sets similar?
- What can make the mean, median, and mode of two data sets different?
I feel…
Now, record your ideas using a voice recorder, speech-to-text, or writing tool.
Press ‘Discover More’ to extend your skills.
Discover MoreSurvey data from different groups
Review the following table representing the amount of time students in grade four spent reading each night:
| Grade 4 Independent Reading Data | |
|---|---|
| Mean | 20 minutes |
| Median | 24 minutes |
| Mode | 20 minutes |
Now answer the following questions using the tool of your choice:
- Do you think that the data would be the same if grade four students from a school in another city were surveyed? Why or why not?
- Do you think that the data would be the same if grade eight students were surveyed? Why or why not?
- Do you think that the data would be the same if adults were surveyed? Why or why not?