D. Data · Data and Probability

Will Another Group Have the Same Mode?

D2.2 D1.4 A1About 35 minutes

Learning goals

I can explain what a population is.
I can predict whether a different group will have the same mode as my group.
I can explain my prediction using likelihood words.
I can test my prediction by collecting data from the other group.

Words to know

population
The whole group you collect data from, like "Class 2B" or "the grown-ups who work at our school".

mode
The answer that appears most often in a set of data.

prediction
A smart guess about what will happen, using what you know.

test
To collect data to check if a prediction is right.

Let's get started!

Class 2B found that their favourite season is winter. Then they wondered:

"Would the other Grade 2 class say winter too? What about the grown-ups who work at our school?"

Let's make predictions and then test them!

What is a population?

A population is the whole group you collect data from.

All the children in Class 2B is a population.
All the children in Class 2C is another population.
All the grown-ups who work at the school is another population.

Different populations can give different data. People of different ages, or who live in different places, may like different things.

Class 2B's data. The tallest bar is winter, so the mode is winter.

Remember

The mode is the answer that appears most often. In Class 2B, winter has 9 votes, the most. So the mode is winter.

Worked example

Predicting for a similar population

Class 2B's mode is winter. Predict: will Class 2C (the other Grade 2 class at the same school) also have winter as its mode?

Think about how the two populations are alike. Both classes are in Grade 2. They are the same age. They live in the same town, with the same snow and the same outdoor rink.
Because the groups are so alike, they might like the same things.
But it is not certain. The classes have different children, so the data could be different.

Prediction: It is likely that Class 2C's mode will also be winter, because the children are the same age and live in the same place. It is possible it will be different.

Worked example

Testing the prediction

Class 2B asked Class 2C. Here is the data: winter 8, spring 4, summer 6, fall 5. Was the prediction correct?

Find Class 2C's mode: the biggest number is 8, for winter.
Compare: Class 2B's mode is winter. Class 2C's mode is winter.
The modes are the same. The numbers are a little different (9 and 8), but the mode is the same.

The prediction was correct. Both classes have winter as the mode.

Worked example

Predicting for a different population

Now predict: will the grown-ups who work at the school also have winter as their mode?

Think about how the populations are different. The grown-ups are much older than the children.
Grown-ups might not go tobogganing as much. Some might not like shovelling snow! They might like other seasons better.
So it is less likely that the mode will be the same.

Prediction: It is possible that the grown-ups' mode will be winter, but it is less likely than for Class 2C, because grown-ups are a very different group.

The school staff's data. The tallest bar is fall.

Testing: The grown-ups' data shows winter 3, spring 4, summer 5, fall 8. Their mode is fall, not winter! Our prediction that the mode would probably be different was correct.

The two populations had different modes. Children in Class 2B liked winter most. The grown-ups liked fall most.

Predictions can surprise us

A prediction is a smart guess, not a promise. If your test shows something different from what you predicted, that's great! You learned something new. Ask, "Why might this group be different?"

Just for fun

Prediction: if you asked a group of dogs about their favourite food, the mode would be… whatever you are eating right now! 🐶

Population	Mode	Same as Class 2B?
Class 2B	winter	(our group)
Class 2C	winter	yes
School staff	fall	no

Comparing the modes of three populations.

Thinking about populations

When you predict, ask yourself:

How are the groups alike? Same age? Same place? Same activities? If they are very alike, the mode is more likely to be the same.
How are the groups different? Different ages? Different places, weather or traditions? Then the mode is less likely to be the same.

For example, if you asked children who live in a town near lots of lakes, "What is your favourite summer activity?", swimming or canoeing might be the mode. Children in a big city might choose something else, like going to the park.

Hands-on activity

Predict and test at home

Ask your family members (or neighbours, or friends by phone) a question with 3 or 4 choices, like "What is your favourite snack: popcorn, fruit, cheese or crackers?"
Tally the answers and find the mode.
Choose a different population, like your cousins, your grandparents' friends, or kids on your team.
Predict: Will their mode be the same? Use the words likely, possible, or less likely, and say why.
Test: Ask the second group and find their mode.
Was your prediction right? What did you learn?

Your turn

What is a population?

Class 2C's data: winter 8, spring 4, summer 6, fall 5. What is the mode?

Why did we predict Class 2C would likely have the same mode as Class 2B?

The school staff's mode was fall. Is it the same as Class 2B's mode?

Mia's class's favourite fruit mode is apple. Will a Kindergarten class at the same school have the same mode? Make a prediction with a reason.

Is it certain that two populations will have the same mode?

How do you test a prediction about another population?

More practice: warm-up

Is all the children in your class a population?

What is the mode? hockey 7, soccer 4, swimming 2

Two groups have modes pizza and pizza. Are the modes the same?

Two groups have modes winter and summer. Are the modes the same?

What is a prediction?

More practice: on your own

Grade 2 class A: favourite pet mode is dog. Grade 2 class B (same school): dog 9, cat 6, fish 3. Was a prediction of same mode correct?

Which group is more likely to have the same favourite playground game as your class: another Grade 2 class at your school, or a group of grandparents?

A class tests a prediction and finds a different mode. Did they do something wrong?

Grade 2 data: favourite season mode is winter. Group of grown-ups: winter 4, spring 4, summer 6, fall 3. What is the grown-ups' mode? Is it the same?

Name two populations that you think would probably have different modes for "What is your favourite TV show?" Explain.

Challenge

Class 2B's mode is winter (9 votes), but 14 of the 23 children chose another season. Does that mean Class 2B does not like winter? Explain.

A class in Iqaluit, Nunavut, and a class in Toronto are asked, "What is your favourite winter activity: skating, sledding, building snow forts, or playing indoors?" Do you think the modes will be the same? Explain with a likelihood word.

Class A: soccer 8, hockey 5. Class B: soccer 7, hockey 8. The two classes have different modes. What is the mode when you put both classes together?

Check your understanding

Quiz

What is a population?

Class 2B's mode is winter. Which group is most likely to have the same mode?

How do you test a prediction about another group's mode?

Staff data: winter 3, spring 4, summer 5, fall 8. What is the mode?

Your prediction was that another class would have the same mode, but it was different. What does this mean?

Which is a good prediction?

For parents and teachers

What your child is learning: to make and test predictions about whether the mode of data from one population (group) will be the same as the mode from a different population (Ontario expectation D2.2), using likelihood words like likely, possible and less likely. It also practises finding the mode (D1.4). Predicting, testing and reflecting are mathematical processes in Strand A.

Key idea: the more alike two groups are (age, place, experiences), the more likely their modes match, but it is never certain. A prediction that turns out differently is not a mistake; it is new information.

Common difficulties:

Saying the other group will definitely have the same mode. Encourage likely or possible.
Predicting without a reason. Ask, "Why do you think so? How are the groups alike or different?"
Forgetting to actually test. The fun is in collecting the second set of data!

At home: ask a question to the people in your home, then to grandparents, cousins or neighbours (a phone or video call works). Predict first, then compare the modes.