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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 tell discrete data from continuous data and organize data in equal intervals.
  • I can make, read and choose graphs, including histograms and broken-line graphs.
  • I can find the mean, median, mode and range and use them to compare data sets.
  • I can make an infographic, spot misleading graphs and build convincing arguments.
  • I can write probabilities as fractions, decimals and percents, and compare theoretical and experimental probabilities of two independent events.

Words to know

continuous data
Measured data; any value in a range is possible.
discrete data
Counted data; only certain separate values are possible.
histogram
A graph of data in equal intervals, with bars that touch.
broken-line graph
Points joined by line segments to show change over time.
range
Greatest value minus least value: a measure of spread.
independent events
Events where one result doesn't change the chances of the other.
experimental probability
Times an event happened ÷ number of trials.

Let's review!

In this unit you became a Grade 6 data scientist. You sorted discrete and continuous data, grouped data in intervals, made histograms and broken-line graphs, chose the best graph, found the range and the mean, median and mode and used them to compare data sets, built an infographic, caught misleading graphs, made convincing arguments, wrote probabilities as fractions, decimals and percents, and explored two independent events. This review has a few questions from every lesson. Try each one, then press Show answer to check.

What do you want to show?ComparecategoriesBar graphSpread of lotsof numbersHistogramChange overtimeBroken-line graphEvery value ofa small setStem-and-leaf plot
A quick graph chooser: start with the job you want the graph to do.
Liam's skating minutes: 20, 30, 35, 45, 45, 45, 601520253035404550556065range = 60 − 20 = 40mean 40median 45mode 45 (tallest stack)
All four measures on one dot plot: the range is the width, the mode is the tallest stack, the median is the middle dot and the mean is the balance point.

Discrete and Continuous Data

1

Is the number of cars in a parking lot discrete or continuous?

2

Is the time it takes to eat lunch discrete or continuous?

3

Write one question about pets that collects continuous data.

4

Why is shoe size usually treated as discrete?

Collecting Data and Organizing It in Intervals

1

What is wrong with the intervals 0–5, 5–10, 10–15?

2

Group these into 20–29, 30–39, 40–49: 23, 41, 35, 28, 39, 44, 30.

3

A jump of exactly 150 cm: which interval, "140 to less than 150" or "150 to less than 160"?

Histograms

1

Why do the bars of a histogram touch?

2

Long-jump histogram (1, 5, 7, 5, 2 in the intervals from 120 to 170 cm): how many jumped less than 140 cm?

3

Can a histogram tell you the exact largest value? Explain.

Broken-Line Graphs

1

A plant was 8 cm on Monday and 12 cm on Wednesday. Estimate its height on Tuesday.

2

What does a steep line segment going down show?

3

Snow graph (5, 12, 20, 18, 30, 35, 28, 15 cm): between which weeks did the depth increase most?

Choosing and Justifying the Best Graph

1

Which graph for the masses of 80 puppies at a vet clinic?

2

Which graph for the temperature of an oven as it heats up, every minute?

3

Which graph to compare favourite seasons of Grade 6 and Grade 7 students?

4

The tallest bar is 43. Suggest a scale.

Range and the Measures of Central Tendency

1

Find the mean, median, mode and range: 6, 9, 4, 9, 12.

2

Find the median of 2.5, 4.0, 1.5, 3.0.

3

Data: 10, 11, 12, 50. Which measure is affected most by the 50: mean or median?

Comparing Two or More Data Sets

1

Team A's scores: mean 15, range 4. Team B's: mean 15, range 20. Compare them.

2

Why compare means instead of totals when groups are different sizes?

3

Group A (4 people) mean 10. Group B (6 people) mean 15. What is the mean of all 10 people?

Creating an Infographic

1

Name three things every infographic needs.

2

Improve the headline "Screen Time".

3

Data: 3, 4, 4, 5, 30. Which key number best describes a typical value?

Misleading Graphs, Challenging Ideas and Convincing Arguments

1

A graph's scale starts at 80. Bars show 82 and 88. What is the real difference?

2

What is a preconceived notion?

3

Name the parts of a convincing argument.

4

A histogram uses intervals 0–10, 10–20 and 20–50, drawn the same width. Why is it misleading?

Probability as Fractions, Decimals and Percents

1

A bag has 9 green and 11 yellow tiles. Find P(green) as a fraction, decimal and percent.

2

P(snow) = 0.6. Is snow likely or unlikely? What is P(no snow) as a percent?

3

P(win) = 15%. About how many wins in 200 games?

Two Independent Events: Theoretical Probability

1

Flip a coin and spin a spinner with 5 equal sections. How many outcomes?

2

Two coins: P(two tails)?

3

Two dice: P(sum of 11)?

Experiments with Two Independent Events

1

Two coins, 60 trials. Expected number of HH?

2

In 60 trials you got HH 18 times. Experimental probability as a percent?

3

How can you make experimental probability more trustworthy?

Just for fun

Mean, Median and Mode walk into a café. Mean orders the average. Median grabs the seat in the middle. Mode orders whatever everyone else is having.

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, dice and a calculator to check your work.
  • Check your work: intervals have no gaps or overlaps; histogram bars touch; the mean and median are between the smallest and largest values; probabilities are between 0% and 100% and all outcomes add to 100%.
  • Put a star next to any question you got wrong, and go back to that lesson's practice.
Check your understanding

Quiz

1.

Which data is continuous?

2.

Which intervals are correct for discrete data?

3.

Which graph shows how lots of numerical data is spread out in intervals?

4.

Which graph best shows a puppy's mass each week for 10 weeks?

5.

What is the range of 14, 8, 21, 17?

6.

Set A: mean 20, range 3. Set B: mean 20, range 18. Which is true?

7.

A graph's vertical scale starts at 95 with no broken-axis symbol. You should:

8.

P(green) = 3/5. Which is the same?

9.

You flip a coin and roll a die. What is P(tails and 3)?

10.

Two coins are flipped 100 times. HH comes up 27 times. What is the best conclusion?

For parents and teachers

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

  • Calls measured data discrete, or thinks anything with decimals is continuous: revisit Discrete and Continuous Data.
  • Writes overlapping or unequal intervals, or leaves out empty intervals: revisit Collecting Data and Organizing It in Intervals.
  • Leaves gaps between histogram bars, or misreads which interval a bar covers: revisit Histograms.
  • Reads a point's value when asked for a change, or uses a broken-line graph for categories: revisit Broken-Line Graphs.
  • Picks a graph without a reason, or forgets titles, labels, scales and sources: revisit Choosing and Justifying the Best Graph.
  • Forgets to order data for the median, or writes the range as "8 to 21": revisit Range and the Measures of Central Tendency.
  • Compares totals for groups of different sizes, or ignores spread: revisit Comparing Two or More Data Sets.
  • Headline names the topic but not the finding, or displays don't fit the data: revisit Creating an Infographic.
  • Judges by bar height or line steepness without reading the scale, or argues without numbers: revisit Misleading Graphs, Challenging Ideas and Convincing Arguments.
  • Writes 0.4 as 4%, or forgets that all probabilities add to 100%: revisit Probability as Fractions, Decimals and Percents.
  • Misses outcomes (treats HT and TH as one), or adds instead of multiplying to count outcomes: revisit Two Independent Events: Theoretical Probability.
  • Expects experiments to match theory exactly, or calls a coin unfair after a few trials: revisit Experiments with Two Independent Events.

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