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 explain sampling techniques and organize data in relative-frequency tables.
I can read, choose and make graphs, including stacked-bar graphs, and spot misleading graphs.
I can find the mean, median and mode of whole-number and decimal data and make an infographic.
I can analyse data to challenge ideas and make convincing arguments.
I can write probabilities as fractions and compare theoretical and experimental probability.

Words to know

sample
The part of the population you collect data from.

relative frequency
Frequency ÷ total: the share of the whole in one category.

stacked-bar graph
A bar graph where each bar is split into parts stacked together.

median
The middle value of ordered data.

misleading graph
A graph that gives the wrong idea about the data.

probability
A number from 0 (impossible) to 1 (certain) that tells how likely an event is.

experimental probability
Times an event happened ÷ number of trials.

Let's review!

In this unit you became a Grade 5 data scientist. You chose fair samples, organized data in relative-frequency tables, read and made stacked-bar graphs, chose the best graph, found the mean, median and mode of decimal data, made an infographic, caught misleading graphs, challenged ideas with data, wrote probabilities as fractions, and compared theoretical and experimental probability. This review has a few questions from every lesson. Try each one, then press Show answer to check.

The data cycle you used in this unit. Good data detectives go around it again when their answers lead to a new question.

Populations, Samples and Sampling Techniques

A school has 480 students. The principal asks 48 of them. What is the population, and what is the sample?

You choose a random start, then every 8th name on a list. Which technique is this?

A club has 30 Grade 4s and 50 Grade 5s. Make a stratified sample of 8 that matches the club.

Why is asking only students in the hockey club about their favourite sport a biased sample?

Collecting Data and Relative-Frequency Tables

9 of 20 students chose skating. What is the relative frequency as a fraction and a decimal?

Room A: 14 of 20 walk. Room B: 18 of 30 walk. Which room has the greater share of walkers?

In a fair sample of 20, 6 chose snowshoeing. About how many of 400 students would?

Stacked-Bar Graphs

A stacked bar has parts from 0 to 9, 9 to 16 and 16 to 25. How big is each part, and what is the total?

Library graph: how many fiction books were borrowed on Tuesday?

In a stacked-bar graph of relative frequencies, why are all the bars the same length?

Choosing and Making the Best Graph

Which display would you use for the scores of 35 students on a 50-point quiz?

A stacked-bar graph has totals 32, 45 and 38. Choose a scale.

Finish the justification: "I chose a stacked-bar graph because..."

Mean, Median and Mode with Decimal Numbers

Find the mean, median and mode: 1.8, 2.4, 1.8, 3.0, 2.0

Find the median: 4.5, 6.0, 5.0, 7.5

Find the mean of 11, 14, 12, 16.

Data: 5, 6, 5, 7, 42. Which describes a typical value better, the mean or the median? Why?

Creating an Infographic

Name four parts of a good infographic.

What does a headline do?

Why do the infographic's stacked bars show relative frequencies for Room 14 (25 students) and Room 15 (20 students)?

Spotting Misleading Graphs and Claims

A graph's scale starts at 90. Bars show 92 and 98. How many times as tall does the second bar look? What's the real difference?

"Our class is the most generous: we brought 24 cans and Room 3 brought 20!" Our class has 30 students and Room 3 has 20. Is the claim fair?

List two ways a graph can mislead.

Analysing Data, Challenging Ideas and Making Convincing Arguments

Recess graph: what fraction of Grade 3 students chose outside?

Name the three parts of a convincing argument.

Some people believe "Kids don't like vegetables." A random sample of 40 students shows 26 chose a vegetable snack over chips. Does the data support or challenge the notion?

Spinner B has 6 equal sections. Each colour's probability is its number of sections out of 6: P(blue) = 1/6, P(yellow) = 2/6, P(green) = 3/6, and P(red) = 0 because there is no red.

Probability as a Fraction on the Probability Line

A bag has 3 red, 4 blue and 1 green marble. What is P(blue)?

A die is rolled. What is P(a number greater than 2)?

Spinner A (P(blue) = 3/8) is spun 24 times. Predict how many blues.

Order from least to most likely: 1/2, 1/10, 9/10, 0.

Theoretical and Experimental Probability

A coin landed on tails 13 times in 20 flips. What is the experimental P(tails)? The theoretical?

Why might the class's combined 200 flips give a result closer to 0.5 than one student's 20 flips?

A die was rolled 30 times and 1 came up 6 times. Compare with theory.

Just for fun

A data scientist asked 10 people, "Do you like answering surveys?" 7 said yes, 2 said no, and 1 ran away. That's a relative frequency of 0.1 for running away!

How to use this review

Do the review over two or three short sittings. Each section matches one lesson.
Use tools: grid paper, a ruler, coins, a die or a paper-clip spinner.
For fractions and decimals, try to make a denominator of 10 or 100.
Check your work: relative frequencies add to 1, a mean is between the smallest and largest values, and probabilities are between 0 and 1.
Put a star next to any question you got wrong, and go back to that lesson's practice.

Check your understanding

Quiz

Names are drawn from a hat so that everyone has the same chance. Which technique is this?

12 of 25 students chose sledding. What is the relative frequency?

A stacked bar has parts from 0 to 14 and from 14 to 23. How big is the top part?

Which display is best for comparing the shares of two classes of different sizes?

What is the mean of 2.5, 3.0, 4.5, 2.0?

What is the median of 3.2, 4.0, 3.6, 4.4?

A bar graph's scale starts at 40. What should you think?

Which is the evidence in an argument?

A spinner has 10 equal sections, 3 of them blue. What is P(blue)?

10.

A coin is flipped 10 times and lands on heads 7 times. What is the experimental P(heads)?

For parents and teachers

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

Mixes up population and sample, or can't spot a biased sample or name a technique: revisit Populations, Samples and Sampling Techniques.
Writes the count instead of count ÷ total, or compares counts for groups of different sizes: revisit Collecting Data and Relative-Frequency Tables.
Reads the top of a middle segment as its value (forgets to subtract): revisit Stacked-Bar Graphs.
Picks a scale from the biggest part instead of the biggest total, or gives no reason for a graph choice: revisit Choosing and Making the Best Graph.
Forgets to order data for the median, misplaces decimal points, or can't write a remainder as a decimal: revisit Mean, Median and Mode with Decimal Numbers.
Infographic has no headline or source, or too many words: revisit Creating an Infographic.
Judges bars by height without reading the scale, or trusts small or biased samples: revisit Spotting Misleading Graphs and Claims.
Says "everyone" when data shows "most", or gives a claim without evidence: revisit Analysing Data, Challenging Ideas and Making Convincing Arguments.
Writes probabilities as "3 to 5" or forgets that outcomes must be equally likely: revisit Probability as a Fraction on the Probability Line.
Expects experiments to match theory exactly, or decides a coin is unfair after a few flips: revisit Theoretical and Experimental Probability.

A few mistakes are normal. Praise careful reasoning and good questions, not only right answers.