Grade by Grade
D. Data · Two-Variable Data, Scatter Plots and Probability

Two-Variable Data, Scatter Plots 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 one-variable from two-variable data, collect two-variable data, and make and choose graphs including scatter plots.
  • I can describe relationships (strong, weak, positive, negative, none), deal with outliers and make predictions.
  • I can spot misleading graphs and claims and tell a data story with an infographic.
  • I can use Venn and tree diagrams to find probabilities of multiple independent and dependent events and compare them with experiments.

Words to know

two-variable data
Two characteristics of each person or thing, recorded as a pair.
scatter plot
A graph with one point for each ordered pair.
outlier
A point far from the pattern of the others.
trend line
A straight line through the middle of the points, used for predictions.
hidden variable
A third variable that affects both variables and makes them look related.
mutually exclusive
Events that can't happen at the same time.
dependent events
Events where one result changes the probability of the next.

Let's review!

In this unit you learned to tell one-variable from two-variable data, collected continuous two-variable data in a table of values, made scatter plots and chose the best graph for a data set, described relationships as strong or weak, positive, negative or none, handled outliers, used trend lines to predict, separated relationships from causes, caught misleading graphs and claims, and told a data story with an infographic. In probability, you used Venn diagrams for and, or and not, and tree diagrams for multiple independent and multiple dependent events, comparing theory with experiments.

This review has a few questions from every lesson. Try each one, then press Show answer to check. If a part feels tricky, go back to that lesson for more practice.

How many variables?ONE variablecategories or numbers?TWO variablesis one of them time?Categoriesbar graph orcircle graphNumbershistogram orstem-and-leafYes: timebroken-linegraphNo: both numbersscatter plot(relationship)onetwo
A quick way to choose a graph: count the variables, then ask what kind of data they are. Two numerical variables with no time? Scatter plot.

One-Variable and Two-Variable Data

1

One-variable or two-variable? Each student's hours of sleep and their reaction time.

2

Name the independent and dependent variables: "Does the amount of salt on a sidewalk affect how fast the ice melts?"

3

Turn "How tall are Grade 8 students?" into a two-variable question.

Collecting Continuous Two-Variable Data

1

Discrete or continuous? The time it takes an ice cube to melt.

2

Three trials: 14.2 s, 14.6 s, 14.4 s. Find the mean.

3

Which variable goes in the first column of a table of values?

Making Scatter Plots

1

Where do you plot (40, 12.6)?

2

Values go from 612 to 688. Suggest a scale.

3

Why aren't the points on a scatter plot joined?

Choosing and Justifying the Best Graph

1

Best graph for the relationship between hours of practice and typing speed?

2

Best graph for how a town's population changed from 1990 to 2025?

3

In a circle graph of 40 students, a category has 8 students. What angle?

Describing Relationships: Positive, Negative or None, Strong or Weak

1

Points fall from left to right and stay close to a line. Describe the relationship.

2

Describe the likely relationship between minutes a car idles and fuel left in the tank.

3

Points form a round blob. Describe the relationship.

Outliers in Two-Variable Data

1

Data: (1, 5), (2, 10), (3, 15), (4, 2), (5, 25). Which point is the outlier?

2

What should you do first when you find an outlier?

3

Describe the data above with and without the outlier.

Analysing Scatter Plots: Predictions, Causes and Conclusions

1

Use Jonah's trend line (bounce ≈ 0.587 × drop) to predict the bounce from a 120 cm drop.

2

More hot chocolate is sold on days when more people wear mittens. Name the hidden variable.

3

Why is a prediction far outside the data's range risky?

Misleading Graphs and Misleading Claims

1

A bar graph's axis starts at 40. Bars show 42 and 46. How many times as tall does the second bar look? True ratio?

2

What is cherry-picking?

3

"Kids who play chess get better math marks, so chess causes better marks." What's wrong?

Telling a Data Story: Infographics with Tables and Scatter Plots

1

Write a better headline than "Pendulum Data".

2

Find the mean of the pendulum times 9.1, 12.6, 15.6, 17.8 and 20.2 s.

3

Name two things besides a scatter plot that a two-variable infographic should include.

Venn diagramAonlyA andBBonlyneitheror = everything inside the circlesP(A or B) = P(A) + P(B) − P(A and B)Tree diagramRBRRRBBRBB5/84/7RR = 5/8 × 4/7 = 20/56Multiply ALONG a path (and then).ADD separate paths (or).
Your two probability tools. Venn diagram: "and" is the overlap, "or" is everything inside the circles (subtract the overlap once). Tree diagram (the bag of 5 red and 3 blue marbles, no replacement): multiply along a path, add separate paths.

Probability with Venn Diagrams: And, Or, Not

1

30 students: 18 hockey, 12 soccer, 7 both. Find P(hockey or soccer).

2

One die: P(even or 5)?

3

One card from a standard deck: P(queen or club)?

Multiple Independent Events: Tree Diagrams, Theory and Experiments

1

How many outcomes for 2 coins and a die?

2

Three coins: P(exactly 2 heads)?

3

Four questions with 4 choices each are guessed. P(all correct)?

Multiple Dependent Events: Without Replacement

1

Bag: 5 red, 3 blue. Two picks without replacement. P(both red)?

2

4 red and 2 black cards, 3 drawn without replacement. P(all red)?

3

Six names in a hat, three jobs, no replacement. P(one particular order of three named students)?

Just for fun

Final probability check: P(you finish this review knowing more than when you started) is very, very close to 1.

How to use this review

  • Work through one section at a time and write your steps, not just the answers.
  • Put a check mark beside each question you got right on your own. Put a star beside any you needed help with.
  • If you starred two or more questions in a section, go back to that lesson and redo its "More practice" questions.
  • Finish with the quiz. For every quiz mistake, read the explanation and find the lesson it came from.
  • Mistakes are useful: they show exactly what to practise next.
Check your understanding

Quiz

1.

Which question needs two-variable data?

2.

On a scatter plot, the independent variable usually goes on...

3.

Which graph best shows the relationship between two numerical variables?

4.

Points rise from left to right but are widely spread. The relationship is...

5.

Data: (1, 4), (2, 8), (3, 12), (4, 30), (5, 20). The outlier is...

6.

Shoe size and reading level are positively related in children aged 5 to 13. The best explanation is...

7.

A bar graph's axis starts at 46 with no zigzag. The likely effect is...

8.

In a group of 40, 25 have a dog, 15 a cat and 6 both. P(dog or cat) = ?

9.

Three coins are flipped. P(at least one head) = ?

10.

A bag has 5 red and 3 blue marbles. Two are drawn without replacement. P(both blue) = ?

For parents and teachers

Use mistakes to choose what to revisit. Each review section matches one lesson.

  • Calls two groups of one measurement "two-variable", or mixes up independent and dependent: revisit One-Variable and Two-Variable Data.
  • Mixes units, chooses values too close together, or forgets units in headings: revisit Collecting Continuous Two-Variable Data.
  • Switches coordinates, uses uneven scales, or leaves out the zigzag: revisit Making Scatter Plots.
  • Uses a circle graph for relationships, or a scatter plot for categories: revisit Choosing and Justifying the Best Graph.
  • Confuses direction (positive/negative) with strength (strong/weak): revisit Describing Relationships.
  • Deletes outliers without a reason, or keeps impossible values: revisit Outliers in Two-Variable Data.
  • Treats every relationship as a cause, or predicts far outside the data: revisit Analysing Scatter Plots.
  • Misses truncated axes, small samples or cherry-picking: revisit Misleading Graphs and Misleading Claims.
  • Writes topic headlines or forgets labels, sources and limits: revisit Telling a Data Story: Infographics.
  • Double-counts the overlap or forgets the "neither" region: revisit Probability with Venn Diagrams.
  • Adds instead of multiplying outcomes, or expects experiments to match exactly: revisit Multiple Independent Events.
  • Forgets to reduce the totals after each draw, or forgets both orders (RB and BR): revisit Multiple Dependent Events.

A few mistakes are normal. Praise clear reasoning, careful checking (probabilities add to 1, every graph has labels and a source) and honest handling of data, not only right answers.