D. Data · Data and Probability

Data Detectives: Analysing Data and Making Decisions

D1.5 A1About 45 minutes

Learning goals

I can ask and answer questions about data in tables and graphs.
I can compare graphs of the same data that have different scales.
I can draw a conclusion from data.
I can use data to make a convincing argument and an informed decision.

Words to know

analyse
To look closely at data to find out what it tells us.

conclusion
Something you decide is true because of what the data shows.

convincing argument
A reason that makes others agree with you, because it uses facts and numbers from the data.

informed decision
A choice you make after looking at the data.

scale
The numbers along the side of a bar graph that tell how much each bar stands for.

Remember from Grade 2

In Grade 2 you asked questions about data, like "Which is most?" and "How many more?", and used data to make decisions. In Grade 3 you'll analyse data in frequency tables and in graphs with different scales, and use the mean and mode too.

Three kinds of questions

Data detectives ask three kinds of questions:

Read the data: find one number. How many chose veggie pizza?
Compare the data: use two or more numbers. How many more chose pepperoni than cheese? What is the total?
Go beyond the data: think about what it means. How much of each pizza should we order next time? Why?

Same data, different look

Two students made bar graphs of the same data: Grade 3 pizza lunch choices. Cheese 10, Pepperoni 20, Veggie 15. But their graphs look very different!

Graph A: the scale counts by 5s and stops at 20. Source: Grade 3 pizza lunch order forms.

Graph B: the same data, but the scale counts by 10s and goes up to 50. Source: Grade 3 pizza lunch order forms.

Worked example

Example 1: Compare the two graphs

In Graph A the bars look tall and very different. In Graph B they look short and closer together. Did different numbers of children choose each pizza?

Read Graph A: cheese 10, pepperoni 20, veggie 15.
Read Graph B: cheese 10, pepperoni 20, veggie 15 (halfway between 10 and 20).
The numbers are exactly the same.
Graph A's scale stops at 20, so the bars fill the space. Graph B's scale goes up to 50, so the bars look short.

No. The data is the same. The graphs look different because they have different scales. Always read the scale before you decide what a graph shows.

From data to a decision

The class is choosing one snack for the winter party. Here are the votes.

Snack	Frequency
Popcorn	9
Fruit	7
Veggies and dip	6
Pretzels	4
Total	26

Frequency table: Snack Votes for the Winter Party. Source: vote in Room 9.

Worked example

Example 2: Make a convincing argument

Which snack should the class choose? Make a convincing argument.

Read: popcorn has the most votes, 9.
Compare: popcorn has 2 more votes than fruit (9 − 7 = 2), and 5 more than pretzels (9 − 4 = 5).
Conclusion: popcorn is the most popular snack, the mode.
Decision: choose popcorn. Use numbers in your reason.

"We should choose popcorn because it got 9 votes, more than any other snack. That's 2 more than fruit."

Worked example

Example 3: A better decision?

Nadia says, "Only 9 of the 26 people chose popcorn. Most people did not choose it!" What could the class do?

26 − 9 = 17 people chose something else. That is true.
Popcorn and fruit together: 9 + 7 = 16 votes.
If the class serves two snacks, popcorn and fruit, then 16 of 26 people get their first choice.

Serving popcorn and fruit pleases more people: 16 votes instead of 9. Nadia used the data to make a convincing argument too. Good decisions look at all the data.

Careful conclusions

Say what the data shows, not what you wish it showed.
"Nobody likes pretzels" is not true: 4 people chose them!
Our data is about one class. Another class might choose differently.
Use numbers in your argument: "because 9 people chose it".

Bar graph: Sami's Reading Minutes for one week. The scale counts by 10s. Source: Sami's reading log.

Worked example

Example 4: Use the mean to analyse

Sami read for 20, 30, 10, 40 and 25 minutes. What was the mean? On which days did Sami read more than the mean?

Add: 20 + 30 + 10 + 40 + 25 = 125 minutes.
Share by 5 days: 25 + 25 + 25 + 25 + 25 = 125. The mean is 25 minutes.
More than 25: Tuesday (30) and Thursday (40).

The mean is 25 minutes a day. Sami read more than the mean on Tuesday and Thursday.

Working together

When you share a conclusion, listen to other ideas too, like Nadia's. Ask: "What did the data show you?" Changing your mind because of good evidence is what smart data detectives do.

Just for fun

Why did the data detective carry a magnifying glass to every graph?

To check the scale before believing the bars!

Hands-on activity

Family decision with data

You need: paper and a pencil.

Choose a real family decision, like what to have for a weekend breakfast or what game to play on family night.
Give everyone 3 or 4 choices and collect votes in a frequency table.
Make a bar graph with a good scale.
Ask a read, a compare and a go beyond question about your graph.
Make a decision and give a convincing argument that uses numbers.

Math talk: "Is there a choice that would make more people happy?"

Your turn

Use the snack table. How many people voted in all?

How many more people chose popcorn than pretzels?

In Graph A and Graph B, how many children chose pepperoni?

Which graph makes the difference between cheese and pepperoni look bigger? Why?

Write one conclusion about the pizza data.

Use Sami's Reading Minutes. On which day did Sami read the least? How many minutes?

More practice: warm-up

Snack table: how many people chose fruit?

Snack table: which snack got the fewest votes?

Reading graph: how many minutes did Sami read on Thursday?

Reading graph: what does the scale count by?

Reading graph: how many minutes on Friday?

More practice: on your own

How many children ordered pizza in all?

How many minutes did Sami read in all that week?

How many more minutes did Sami read on Thursday than on Monday?

Leo says, "Nobody wants veggies and dip." Is he right? Use the data.

The school will order pizza for the next lunch. Based on the data, which pizza should they order the most of? Give a convincing argument.

Challenge

Sami's teacher wants students to read for at least 25 minutes a day. On how many days did Sami meet that goal? What advice would you give?

Abby made Graph B of the pizza data and said, "The pizzas were all about the same." Explain what she missed.

Next year the class will have only enough money for one snack again. Using the snack data, write a convincing argument for choosing fruit instead of popcorn.

Check your understanding

Quiz

Graph A and Graph B show the same pizza data with different scales. Why do the bars look different?

Snack votes: popcorn 9, fruit 7, veggies and dip 6, pretzels 4. Which is a convincing argument for popcorn?

Which is a compare question?

Sami read 20, 30, 10, 40 and 25 minutes. What is the mean?

A bar graph's scale counts by 10s. A bar ends halfway between 20 and 30. What number does it show?

Which conclusion matches the snack data?

For parents and teachers

What your child is learning: to analyse data in frequency tables and in graphs with different scales, to ask and answer questions, to draw conclusions, and to make convincing arguments and informed decisions (Ontario expectation D1.5). Listening to other people's arguments and changing your mind because of evidence connect to the social-emotional and process skills in Strand A.

Common difficulties:

Judging a graph by bar heights without reading the scale.
Over-stating conclusions ("nobody likes...", "everyone wants..."). Ask, "Does the data really say that?"
Arguments without evidence. Prompt: "Which number from the data shows that?"
Confusing "the most votes" with "most people" (more than half).

At home: when you see a graph in a newspaper, flyer or news report, ask your child to read the scale first, then tell you one thing the graph shows. Make small family choices with a quick vote and a frequency table.