D. Data · Data and Probability

Data and Probability: Unit Review

A1 D1.1 D1.2 D1.3 D1.4 D1.5 D1.6 D2.1 D2.2About 40 minutes

Learning goals

I can tell qualitative from quantitative data and primary from secondary sources.
I can organize data in frequency tables and stem-and-leaf plots, and show it in the best graph.
I can find the mean, median and mode and explain what they tell me.
I can analyse data, tell a data story and make convincing arguments.
I can use a probability line and test predictions about different populations.

Words to know

qualitative / quantitative
Data in words or categories / data in numbers from counting or measuring.

primary / secondary source
Data you collect yourself / data someone else collected.

stem-and-leaf plot
A display that organizes number data by tens (stems) and ones (leaves).

multiple-bar graph
A graph with bars side by side to compare two or more sets of data.

mean, median, mode
The fair share, the middle value, and the most common value.

probability line
A line from impossible to certain that shows how likely events are.

Let's review!

In this unit you became a real data detective. You sorted data into qualitative and quantitative, collected data from primary and secondary sources, organized it in frequency tables and stem-and-leaf plots, graphed it in multiple-bar graphs, chose the best graph, found the mean, median and mode, made an infographic, analysed data to make convincing arguments, used a probability line, and tested predictions about different populations. This review has a few questions from every lesson. Try each one, then press Show answer to check.

The data detective's journey from this unit. Answering one question often leads to a new one.

One small data set, three measures. The mode and median are both 3. The mean is 4: it balances the dots, so the 8 pulls it to the right.

Qualitative and Quantitative Data

The number of goals scored in a soccer game. Qualitative or quantitative?

Favourite Canadian animal: beaver, moose or loon. Qualitative or quantitative?

The room numbers in a school. Qualitative or quantitative?

Collecting Data: Primary and Secondary Sources

You count the cars that pass the school in 15 minutes. Primary or secondary source?

You use a population table from Statistics Canada. Primary or secondary source?

A class of 26 students has frequencies 7, 9, 5 and 4. What should you check?

Stem-and-Leaf Plots

Make a stem-and-leaf plot: 23, 31, 27, 19, 35, 23.

Which numbers does the row 4 | 2 6 8 show?

In the plot you made, what are the smallest and largest values?

Multiple-Bar Graphs

What does the legend on a multiple-bar graph tell you?

A scale counts by 2s. A bar stops halfway between 6 and 8. What value does it show?

A multiple-bar graph shows that 10 kids and 7 grown-ups chose summer. How many more kids than grown-ups chose summer?

Choosing the Best Graph

Best display to compare the favourite fruits of Grade 2 and Grade 4?

Best display for the reading minutes of 30 students (from 5 to 65 minutes)?

A scale reads 0, 10, 20, 40, 50. What's wrong?

Mean, Median and Mode

Find the median: 9, 4, 7, 2, 8.

Find the mean: 6, 9, 12, 13.

Find the mode: 5, 3, 5, 8, 3, 5.

Find the median: 20, 14, 16, 30.

Telling a Data Story with an Infographic

Name three parts of a good infographic.

9 of 20 students chose skating, more than any other activity. Is the headline "Most students chose skating" supported?

Why are key numbers shown in big print?

Data Detectives: Analysing Data and Making Decisions

What are the three parts of a convincing argument?

Class A's median number of push-ups was 30. Class B's was 22. What can you conclude?

Write a "read beyond the data" question about a graph of snack sales.

Likelihood and the Probability Line

A spinner has 4 equal parts: 1 yellow and 3 green. How likely is landing on yellow?

Where does flipping heads on a coin go on the probability line?

Roll a die numbered 1 to 6. Order from least to most likely: A: roll an odd number. B: roll a 7. C: roll a 1.

Will Another Group Have the Same Mean, Median and Mode?

Predict: Will Grade 4 students and their parents have the same mean shoe length? Give a reason.

Group P: 3, 5, 5, 7. Group Q: 2, 4, 6, 8. Compare the mean, median and mode.

Your prediction didn't come true. What should you do?

Just for fun

Why are data detectives never bored?

There is always something to count on!

How to use this review

Do one or two sections at a time. Say your answer out loud before you check it, and explain why. Mark any question you got wrong, then go back to the lesson with the same title for more practice. Try the quiz at the end when you feel ready.

Check your understanding

Quiz

Which data is qualitative?

A survey you give to your class is a...

In a stem-and-leaf plot, 3 | 6 means...

When is a multiple-bar graph the best choice?

Which scale is correct?

What is the median of 3, 9, 4, 8?

An infographic headline should be...

Which is the best evidence in an argument?

Roll a die numbered 1 to 6. Rolling a number less than 3 is...

10.

You predict that Grade 1 students' mean height will be different from Grade 4 students'. What do you predict?

For parents and teachers

What this review covers: the whole Grade 4 Data unit: qualitative and quantitative data (D1.1), primary and secondary sources, frequency tables and stem-and-leaf plots (D1.2), multiple-bar graphs and choosing graphs (D1.3), infographics (D1.4), mean, median and mode (D1.5), analysing data and making arguments (D1.6), the probability line (D2.1), and predictions about different populations (D2.2), with social-emotional learning and math process skills (A1) throughout.

Which lesson to revisit:

Calling label numbers (jersey or room numbers) quantitative: go back to Qualitative and Quantitative Data.
Mixing up primary and secondary sources, or totals that don't match: go back to Collecting Data: Primary and Secondary Sources.
Leaves out of order, missing repeated values or a missing key: go back to Stem-and-Leaf Plots.
Ignoring the legend or misreading the scale: go back to Multiple-Bar Graphs.
Choosing a graph that doesn't fit the data, or uneven scales: go back to Choosing the Best Graph.
Not ordering data before finding the median, or dividing by the wrong number: go back to Mean, Median and Mode.
Headlines the data doesn't support, or crowded posters: go back to Telling a Data Story with an Infographic.
Arguments with no numbers, or "everyone" and "always" conclusions: go back to Data Detectives.
Treating likely as certain, or ignoring spinner part sizes: go back to Likelihood and the Probability Line.
Predictions with no reason, or expecting identical results: go back to Will Another Group Have the Same Mean, Median and Mode?

Quiz guide: question 1 is lesson 1, question 2 is lesson 2, and so on through question 10, which is lesson 10.

How to help: redo one example from the lesson with real data from your home, then try a similar question. Praise explanations that use because and a number from the data.