D. Data · Data Literacy and Probability

Data Literacy 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 use percentages to describe and organize data, and make and read circle graphs.
I can choose and justify graphs, build infographics and spot misleading graphs.
I can explain how adding or removing data changes the mean, median, mode and shape of the data.
I can tell independent from dependent events and find and compare their theoretical and experimental probabilities.

Words to know

distribution
How the data is shared out among the categories or values.

circle graph
A graph showing parts of one whole as sectors; 1% = 3.6°.

outlier
A value far from the rest of the data.

skewed
Lopsided, with a long tail on one side.

independent events
The first result does not change the probability of the second.

dependent events
The first result changes the probability of the second.

Let's review!

In this unit you used percentages to describe distributions, planned data collection with fair samples, read and drew circle graphs, chose and justified graphs, saw how adding or removing data changes the mean, median, mode and shape, created infographics, caught misleading graphs, and explored independent and dependent events with theory and 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.

Percent and central angle side by side: 100% is the whole circle, 360°. Multiply a percentage by 3.6 to get its angle, and divide an angle by 3.6 to get its percentage.

Three shapes to know. In a symmetric distribution the mean and median match; a long tail pulls the mean toward it, past the median.

Why We Use Percentages to Describe Data

27 of 90 students play a musical instrument. What percentage is that?

Class A: 14 of 20 like snow days best. Class B: 18 of 30 do. Which class has the greater share?

A fair sample shows 15% of students in a town have a library card. The town has 4 000 students. Estimate how many have a card.

Collecting Data and Organizing It with Percentages

Is "the time it takes to run 100 m" qualitative, discrete or continuous?

Rewrite this biased question: "Isn't hockey the best sport?"

20 people: tea 7, coffee 9, hot chocolate 4. Find the percentages.

Census or sample: the favourite snack of all 3 000 students in a school board?

Reading Circle Graphs

A sector is 15%. What is its central angle?

A sector has a central angle of 144°. What percentage is it?

A circle graph of 250 students shows 20% chose basketball. How many is that?

Making Circle Graphs

In a survey of 36 people, how many degrees does each person get?

Survey of 36: dogs 18, cats 12, fish 6. Find the central angles.

Sleep 10 hours in a 24-hour day. What is the central angle?

Choosing and Justifying the Best Graph

Best graph for the outdoor temperature every hour on a winter day?

A "choose all that apply" survey gives 70%, 55% and 40%. Can you use a circle graph?

Best graph for the percent of a class that chose each of 4 field-trip options (one vote each)?

How Adding or Removing Data Changes the Mean, Median and Mode

Data: 6, 8, 8, 10, 13. Find the mean, median and mode.

Add 27 to the data above. Find the new mean, median and mode.

The mean of 4 tests is 70. What mark on the 5th test makes the mean 74?

Shape and Distribution: How Changes in Data Change the Picture

Data: 3, 4, 4, 5, 5, 5, 6, 6, 7. Describe the shape.

A value of 25 is added. How does the shape change?

The mean is 40 and the median is 52. Which way is the data skewed?

Creating an Infographic with Tables and Circle Graphs

Name four parts of a good infographic.

Survey of 40: soup 18, salad 12, sandwich 10. Give the percentages and a headline.

Why should an infographic avoid long paragraphs?

Analysing Circle Graphs and Misleading Graphs

School E (200 students): 30% bike. School F (900 students): 15% bike. Which has more bikers?

A circle graph shows 50%, 35% and 25%. What's wrong?

Someone says "Most of our class reads every day," but the data says 40%. Respond respectfully with evidence.

Independent and Dependent Events

Rolling a die, then flipping a coin: independent or dependent?

A bag has 4 green and 2 blue marbles. You pick a blue one and keep it out. P(blue) next?

Same bag (4 green, 2 blue). You pick a blue one and put it back. P(blue) next?

Theoretical Probability of Two Independent or Two Dependent Events

Cards 1, 2, 3, 4, 5, 6. Two drawn without replacement. How many outcomes?

Same cards, without replacement. P(both greater than 4)?

Same cards, with replacement. P(both greater than 4)?

A bag has 3 green and 2 blue. Two drawn without replacement. P(both green) using a tree diagram?

Experiments: Comparing Experimental and Theoretical Probability

In 60 trials, an event happened 21 times. Experimental probability?

P(event) = 1/3. About how many times in 90 trials?

Why might a 12-trial experiment be far from the theoretical probability?

Just for fun

Why are data scientists great friends?

They always know what's mean, but they never are!

How to use this review

Do the review in two or three short sittings. Each section matches one lesson.
Use a calculator for divisions, but write each step so you can check it.
For circle graphs, remember 1% = 3.6° and check that angles add to 360°.
For probability, first ask: "Is the first item put back?"
Put a star beside any question you got wrong and go back to that lesson's practice.

Check your understanding

Quiz

18 of 72 people chose skating. What percentage is that?

Which sample is fair for finding the favourite sport of students in a school?

A sector is 35%. What is its central angle?

A circle graph of 400 people shows 15% chose cycling. How many people is that?

Which data should not go in a circle graph?

Data: 5, 7, 9. You add 19. What happens?

A dot plot has a long tail to the left. How do the mean and median usually compare?

Which pair of events is dependent?

A bag has 2 red and 3 yellow tiles. Two are drawn without replacement. What is P(both red)?

10.

The theoretical P(event) is 1/4. Which result is the strongest support for it?

For parents and teachers

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

Compares counts when groups are different sizes, or divides total ÷ count: revisit Why We Use Percentages to Describe Data.
Mixes up discrete and continuous, writes leading questions, or trusts a friends-only sample: revisit Collecting Data and Organizing It with Percentages.
Thinks the angle is the number of people, or forgets the total is needed for counts: revisit Reading Circle Graphs.
Gets angles that don't add to 360°, or measures every angle from the start line: revisit Making Circle Graphs.
Uses a circle graph for change over time or for overlapping ("choose all") data: revisit Choosing and Justifying the Best Graph.
Uses the old number of values for the new mean, or averages means instead of using totals: revisit How Adding or Removing Data Changes the Mean, Median and Mode.
Names skew by the side with most data instead of the tail, or deletes outliers without a reason: revisit Shape and Distribution: How Changes in Data Change the Picture.
Writes topic headlines ("Sports") or circle graphs that don't add to 100%: revisit Creating an Infographic with Tables and Circle Graphs.
Thinks a bigger sector always means more people, or says "most" for less than half: revisit Analysing Circle Graphs and Misleading Graphs.
Forgets to reduce the total after an item is kept out, or believes tails is "due": revisit Independent and Dependent Events.
Uses 5 × 5 instead of 5 × 4 for draws without replacement, or forgets both orders: revisit Theoretical Probability of Two Independent or Two Dependent Events.
Expects experiments to match theory exactly, or trusts a tiny number of trials: revisit Experiments: Comparing Experimental and Theoretical Probability.

A few mistakes are normal. Praise clear reasoning, careful checking (percentages to 100%, angles to 360°, probabilities to 1) and honest data, not only right answers.